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DataMultiple
RegressionR^20.39479551630.37638520610.0383451414000000
000000000012345678910111213141516171819Y1X1X2X3X4X
5X6X7X8X9X101231200000000000000Sl.No.SalaryOnesAgeEx
perGenderAgeExperGenderAgeExper0000000000000014171113
00130013000000000000000022773912611261126100000000000
00036797714230423042300000000000000432950138613861386
00000000000000572899143414341434000000000000006300961
32413241324000000000000007425131322132213220000000000
00008486301385138513850000000000000095145013770377037
70000000000000010463191365136513650000000000000011744
25147404740474000000000000001262426141104110411000000
00000000132949513031303130300000000000000145829714313
14313143130000000000000015404701441304413044130000000
00000001677395150715071507000000000000001741410137150
37150371500000000000000184730013001300130000000000000
00019260741232023202320000000000000020264511243124312
43000000000000002125367121012101210000000000000002225
82012211221122100000000000000233200813750375037500000
00000000024279961282028202820000000000000025459991421
90421904219000000000000002648924133013301330000000000
00000274698613751375137500000000000000287955015000500
05000000000000000029724641450145014500000000000000030
39932133121331213312000000000000003155869141914191419
00000000000000325204513981398139800000000000000332620
81230023002300000000000000034303441334133413340000000
00000003558054142110421104211000000000000003668133151
14051140511400000000000000373152913551355135500000000
00000038355651397139713970000000000000039359861408040
80408000000000000004024539121012101210000000000000004
12562312100210021000000000000000424495614118141181411
80000000000000043312981344134413440000000000000044281
41128212821282000000000000004529926131303130313000000
00000000466013614610146101461000000000000000472652712
54125412540000000000000048561401411014110141100000000
00000004943992134303430343000000000000005028429129212
92129200000000000000515480015420054200542000000000000
00052374741411004110041100000000000000053296311313131
31313000000000000005455784140914091409000000000000005
53149713551355135500000000000000565442914081408140800
00000000000057317951365136513650000000000000058945411
55905590559000000000000005936716121012101210000000000
00000606236114711147111471100000000000000616975015215
05215052150000000000000062443141391703917039170000000
00000006349405142141421414214000000000000006476986148
60486048600000000000000653199513651365136500000000000
00066313011355035503550000000000000067398501421114211
14211000000000000006859644144150441504415000000000000
00694907313970397039700000000000000703712812861286128
60000000000000071667081491314913149130000000000000072
38666129712971297000000000000007344690135413541354000
00000000000744795513200320032000000000000000753100213
44134413440000000000000076422041311031103110000000000
00007780456154100541005410000000000000007849042136713
67136700000000000000797715414550455045500000000000000
80250191210021002100000000000000081647411400040004000
00000000000008246047140014001400000000000000008352175
14918149181491800000000000000843062113340334033400000
00000000085493571407140714070000000000000086275141265
02650265000000000000008727987127112711271000000000000
00882573812201220122000000000000000896475614812148121
48120000000000000090410771361413614136140000000000000
09137118141914191419000000000000009251759138813881388
00000000000000939743115710057100571000000000000000948
55941538153815380000000000000095854571526052605260000
00000000009632589137603760376000000000000009728643130
30303030300000000000000985198714516145161451600000000
00000099338031396139613960000000000000010043186138160
38160381600000000000000101100000000000000000001021000
00000000000000001031000000000000000000010410000000000
00000000010510000000000000000000106100000000000000000
00107100000000000000000001081000000000000000000010910
00000000000000000011010000000000000000000111100000000
00000000000112100000000000000000001131000000000000000
00001141000000000000000000011510000000000000000000116
10000000000000000000117100000000000000000001181000000
00000000000001191000000000000000000012010000000000000
00000012110000000000000000000122100000000000000000001
23100000000000000000001241000000000000000000012510000
00000000000000012610000000000000000000127100000000000
00000000128100000000000000000001291000000000000000000
01301000000000000000000013110000000000000000000132100
00000000000000000133100000000000000000001341000000000
00000000001351000000000000000000013610000000000000000
00013710000000000000000000138100000000000000000001391
00000000000000000001401000000000000000000014110000000
00000000000014210000000000000000000143100000000000000
00000144100000000000000000001451000000000000000000014
61000000000000000000014710000000000000000000148100000
00000000000000149100000000000000000001501000000000000
00000001511000000000000000000015210000000000000000000
15310000000000000000000154100000000000000000001551000
00000000000000001561000000000000000000015710000000000
00000000015810000000000000000000159100000000000000000
00160100000000000000000001611000000000000000000016210
00000000000000000016310000000000000000000164100000000
00000000000165100000000000000000001661000000000000000
00001671000000000000000000016810000000000000000000169
10000000000000000000170100000000000000000001711000000
00000000000001721000000000000000000017310000000000000
00000017410000000000000000000175100000000000000000001
76100000000000000000001771000000000000000000017810000
00000000000000017910000000000000000000180100000000000
00000000181100000000000000000001821000000000000000000
01831000000000000000000018410000000000000000000185100
00000000000000000186100000000000000000001871000000000
00000000001881000000000000000000018910000000000000000
00019010000000000000000000191100000000000000000001921
00000000000000000001931000000000000000000019410000000
00000000000019510000000000000000000196100000000000000
00000197100000000000000000001981000000000000000000019
91000000000000000000020010000000000000000000©2007
DrJimMirabella.com
&A
Page &P
Do not erase the 1's in this column.
Enter the dependent variable in this column. Up to 200 values
can be entered.
Use these labels for sorting the columns as desired. For
example. If you wish to interchange columns 1 and 2,
interchange the name X1 and X2 at the top and use the sort
command to sort the columns X1 and X2.
Use this row for entering names of columns.
ResultsMultiple Regression
Results012345678910InterceptAgeExperGender0000000b-
23898.24666252812098.1541589458-1092.5236625734-
1364.25202963640000000s(b)4227.3490625278120.0793404764
199.77535497181700.2509926480000000t-
5.653246587617.4730653135-5.4687609627-
0.80238272790000000p-
value0.00000.00000.00000.42430.00000.00000.00000.00000.00
000.00000.0000VIF1.65231.60361.03990.00000.00000.00000.0
0000.00000.00000.0000ANOVA
TableSourceSSdfMSFFCriticalp-
valueRegn.24590867059.476238196955686.49205122.85590664
192.69939260360.0000s8168.2359235294Error6405127497.833
829666720078.1024356Total30995994557.3199313090854.1142
42R20.7934Adjusted R20.7868986678Prediction IntervalGiven
XAgeExperGender0000000130011-a(1-a) P.I. for Y for given
X1-a(1-a) P.I. for E[Y | X]95%37682.1260762083+ or -
16459.95614415695%37682.1260762083+ or -
2835.8781647066©2007 DrJimMirabella.com
Do not delete this cell.
Enter the given values for all the independent varaibles in this
row.
CorrelationCorrelation
matrixCorrelation12345678910CoefficientsAgeExperGender000
00001Age1.00002Exper0.61271.00003Gender-0.1919-
0.08671.0000400.00000.00000.00001.0000500.00000.00000.000
00.00001.0000600.00000.00000.00000.00000.00001.0000700.00
000.00000.00000.00000.00000.00001.0000800.00000.00000.000
00.00000.00000.00000.00001.0000900.00000.00000.00000.0000
0.00000.00000.00000.00001.00001000.00000.00000.00000.0000
0.00000.00000.00000.00000.00001.0000YSalary0.85250.3205-
0.21010.00000.00000.00000.00000.00000.00000.0000P-
values12345678910AgeExperGender00000001Age2Exper0.0000
*3Gender0.05580.3909400.000000.000000.00000500.000000.00
0000.000000.00000600.000000.000000.000000.000000.0000070
0.000000.000000.000000.000000.000000.00000800.000000.000
000.000000.000000.000000.000000.00000900.000000.000000.0
00000.000000.000000.000000.000000.000001000.000000.00000
0.000000.000000.000000.000000.000000.000000.00000YSalary
0.0000*0.0012*0.0359*0.000000.000000.000000.000000.00000
0.000000.00000* = significant at .05 levelT-
scores12345678910AgeExperGender00000001Age2Exper7.6746
3Gender-1.9356-
0.86197.6746400.00000.00000.0000500.00000.00000.00000.000
0600.00000.00000.00000.00000.0000700.00000.00000.00000.00
000.00000.0000800.00000.00000.00000.00000.00000.00000.000
0900.00000.00000.00000.00000.00000.00000.00000.00001000.0
0000.00000.00000.00000.00000.00000.00000.00000.0000Y2620
816.14403.3491-
2.12690.00000.00000.00000.00000.00000.00000.0000P-
values12345678910AgeExperGender00000001Age2Exper0.0000
3Gender0.05580.3909400.00000.00000.0000500.00000.00000.0
0000.0000600.00000.00000.00000.00000.0000700.00000.00000.
00000.00000.00000.0000800.00000.00000.00000.00000.00000.0
0000.0000900.00000.00000.00000.00000.00000.00000.00000.00
001000.00000.00000.00000.00000.00000.00000.00000.00000.00
00Y561400.00000.00120.03590.00000.00000.00000.00000.0000
0.00000.0000P-
values12345678910AgeExperGender00000001Age2Exper0.0000
*3Gender0.05580.3909400.00000.00000.0000500.00000.00000.
00000.0000600.00000.00000.00000.00000.0000700.00000.0000
0.00000.00000.00000.0000800.00000.00000.00000.00000.00000
.00000.0000900.00000.00000.00000.00000.00000.00000.00000.
00001000.00000.00000.00000.00000.00000.00000.00000.00000.
0000Y494050.0000*0.0012*0.0359*0.00000.00000.00000.0000
0.00000.00000.0000©2007 DrJimMirabella.com
1. (TCO 1) How has the relationship between government and
managed care evolved over the years? What factors have driven
this changing relationship? (Points : 20)
Question 2.2. (TCO 1) Describe the preferred provider
organization (PPO) model of managed care. Why do you feel
that this is the dominant form of managed care today? (Points :
20)
Question 3.3. (TCO 2) Why do managed care organizations have
a board of directors? What is the function of the board of
directors? (Points : 20)
Question 4.4. (TCO 2) What is the role of the Peer Review
Committee in a managed care organization? And why is this
function so crucial? (Points : 20)
Question 5.5. (TCO 3) Describe the calculation of capitated
payments. How are these rates determined in managed care
organizations? (Points : 20)
Question 6.6. (TCO 3) Describe the use of evidence-based
clinical criteria in managed care. Why is this process so
important in managed care today? (Points : 20)
Question 7.7. (TCO 4) What is meant by transitional case
management (TCM) under managed care? Provide some specific
examples of TCM functions. (Points : 20)
Question 8.8. (TCO 4) Discuss tools for changing physician
behavior. Provide specific examples and perspectives on what
will work best for changing behavior. (Points : 20)
Question 9.9. (TCO 7) What is the purpose of hold-harmless and
balance-billing clauses in managed care contracts? (Points : 20)
Question 10.10. (TCO 7) What is the purpose of the declarations
in managed care contracts? (Points : 20)
DataCopyVariable(X-
XBar)^227.424.4027.225.5024.123022.720.2022.120.1018.317.5
017.516.1017.513.3016.814.7016.513.60
CorrelationCorrelation & RegressionDataX-DataY-
DataObservationAdsSalesREGRESSION STATISTICSObs
12048Observations10Obs 21538Correlation coefficient
(r)0.978Obs 31233Coefficient of determination (r-
squared)96%Obs 43265Standard error of the estimate3.469Obs
51740Obs 6818REGRESSION EQUATIONObs
71025Slope2.017Obs 81635Intercept5.134Obs 92050Sales =
5.134 + 2.017 (Ads)Obs 10512Obs 11PREDICTING WITH THE
REGRESSION EQUATIONObs 12X value20Obs 13Confidence
Level95%Obs 14Predicted Y value45.477Obs 15Confidence
Interval45.477+2.978Obs 16Prediction
Interval45.477+8.535Obs 17Obs 18HYPOTHESIS TEST FOR
CORRELATIONObs 19Null hypothesis: Slope = 0 (no
correlation)Obs 20Level of Significance0.05Obs 21t-Statistic
(computed)13.3189Obs 22p-value0.0000Obs 23DecisionReject
the null hypothesisObs 24ConclusionConclude that correlation
exists.Obs 25Obs 26ANOVASSdfMSFF critObs
27Regression2134.154412134.1544177.39245.3177Obs
28Error96.2456812.0307Obs 29Total2230.40009Obs 30Obs
31Obs 32CORRELATION GUIDELINESObs 33Step 1: input
the data (note which is the dependent variable)Obs 34Step 2:
assess the scatter diagram for linearity (if not linear, STOP)Obs
35Step 3: hypothesis test for correlation (if correlation does not
exist, STOP)Obs 36Step 4: evaluate regression statistics (if
correlation is weak, reconsider its value)Obs 37Obs 38Obs
39Obs 40©2007 DrJimMirabella.comObs 41Obs 42Obs 43Obs
44Obs 45Obs 46Obs 47Obs 48Obs 49Obs 50Obs 51Obs 52Obs
53Obs 54Obs 55Obs 56Obs 57Obs 58Obs 59Obs 60Obs 61Obs
62Obs 63Obs 64Obs 65Obs 66Obs 67Obs 68Obs 69Obs 70Obs
71Obs 72Obs 73Obs 74Obs 75Obs 76Obs 77Obs 78Obs 79Obs
80Obs 81Obs 82Obs 83Obs 84Obs 85Obs 86Obs 87Obs 88Obs
89Obs 90Obs 91Obs 92Obs 93Obs 94Obs 95Obs 96Obs 97Obs
98Obs 99Obs 100Obs 101Obs 102Obs 103Obs 104Obs 105Obs
106Obs 107Obs 108Obs 109Obs 110Obs 111Obs 112Obs
113Obs 114Obs 115Obs 116Obs 117Obs 118Obs 119Obs
120Obs 121Obs 122Obs 123Obs 124Obs 125Obs 126Obs
127Obs 128Obs 129Obs 130Obs 131Obs 132Obs 133Obs
134Obs 135Obs 136Obs 137Obs 138Obs 139Obs 140Obs
141Obs 142Obs 143Obs 144Obs 145Obs 146Obs 147Obs
148Obs 149Obs 150Obs 151Obs 152Obs 153Obs 154Obs
155Obs 156Obs 157Obs 158Obs 159Obs 160Obs 161Obs
162Obs 163Obs 164Obs 165Obs 166Obs 167Obs 168Obs
169Obs 170Obs 171Obs 172Obs 173Obs 174Obs 175Obs
176Obs 177Obs 178Obs 179Obs 180Obs 181Obs 182Obs
183Obs 184Obs 185Obs 186Obs 187Obs 188Obs 189Obs
190Obs 191Obs 192Obs 193Obs 194Obs 195Obs 196Obs
197Obs 198Obs 199Obs 200
&A
This is the measure of the degree of relationship between the X
and Y variables. 1 is perfect, .70 to 1.00 is strong, .30 to .69 is
moderate, less than .30 is weak, 0 means no correlation. The
same rules apply to positive or negative correlations.
Also referred to as ALPHA. This is your tolerance for error; it
is the probability of incorrectly rejecting the null hypothesis.
The X-data is the independent variable.
Enter up to 125 paired observations.
Enter the x-value that you want to use to predict the y-value.
You should never input an X-value that is beyond the range of
the data (i.e., it should be between the smallest and largest X-
Data observation).
This is the predicted value using the x-value above and the
regression equation.
This estimates the mean value of Y given X.
This estimates the range of values of Y for a given X and should
be larger than the confidence interval.
This explains the percent of the variability in Y that can be
explained by the regression equation.
This explains the degree of relationship between the dependent
and independent variables.
Enter the confidence level to be used in the confidence and
prediction intervals.
The X-data is the independent variable from which a prediction
is made.
The Y-data is the dependent variable that is being predicted by
the regression equation.
Also referred to as ALPHA. This is your tolerance for error; it
is the probability of incorrectly rejecting the null hypothesis.
A one unit change in X results in a change in Y equal to the
value of the slope.
A p-value is the probability of making a type 1 error if you
reject the null hypothesis. In other words, it is the probability
you would be making a mistake to reject the null.
A measure of dispersion of the data around the regression line.
Similar to standard deviation, for a given prediction you would
expect with 95% confidence that the prediction would be with 2
standard errors of the regression line.
ScatterDiagramSales = 5.134 + 2.017 (Ads)SalesAdsr = 0.978r-
squared = 0.957
ScatterDiagram201512321781016205
Sales
48
38
33
65
40
18
25
35
50
12
ChiSquare GOF EqualChi-Square Goodness of Fit Test
(Assuming Equal Expected)ItemsObservedExpectedChi
SquareRoll a 11320.002.45Roll a 23320.008.45Roll a
31420.001.80Roll a 4720.008.45DataRoll a 53620.0012.80Level
of Significance0.01Roll a 61720.000.45Degrees of Freedom5-
0- 0- 0- 0- 0- 0Results- 0- 0Critical Value15.0863- 0- 0Chi-
Square Test Statistic34.40- 0- 0p-Value0.0000- 0- 0Reject the
null hypothesis- 0- 0- 0- 0This tests the null hypothesis that the
distribution is equal across all categories.- 0- 0It also tests if
there is a difference in the frequencies of the categories /
items.- 0- 0Rejecting the null implies a difference in the
categories / items.- 0- 0- 0- 0- 0- 0- 0- 0- 0- 0- 0- 0- 0- 0- 0-
0©2007 DrJimMirabella.com
A p-value is the probability of making a type 1 error if you
reject the null hypothesis. In other words, it is the probability
you would be making a mistake to reject the null.
This is computed from the sample size minus one.
Also referred to as ALPHA. This is your tolerance for error; it
is the probability of incorrectly rejecting the null hypothesis.
ChiSquare GOF UnequalChi-Square Goodness of Fit Test
(Assuming Unequal Expected)ItemsObserved%
ExpectedExpectedChi
SquareSunday16540.00%160.000.16Monday7920.00%80.000.01
Tuesday5014.00%56.000.64Wednesday4410.00%40.000.40Data
Thursday328.00%32.00- 0Level of
Significance0.05Friday206.00%24.000.67Degrees of
Freedom6Saturday102.00%8.000.50- 0- 0- 0- 0Results- 0-
0Critical Value12.5916- 0- 0Chi-Square Test Statistic2.38- 0-
0p-Value0.8818- 0- 0Do not reject the null hypothesis- 0- 0- 0-
0This tests the null hypothesis that the distribution is as
expected.- 0- 0In other words, it tests if the results fit the
expected distribution.- 0- 0Rejecting the null implies that the
results do not fit the distribution.- 0- 0- 0- 0- 0- 0- 0- 0- 0- 0- 0-
0- 0- 0- 0- 00©2007 DrJimMirabella.com
A p-value is the probability of making a type 1 error if you
reject the null hypothesis. In other words, it is the probability
you would be making a mistake to reject the null.
This is computed from the sample size minus one.
Also referred to as ALPHA. This is your tolerance for error; it
is the probability of incorrectly rejecting the null hypothesis.
ChiSquare TableChi-Square Test of IndependenceObserved
FrequenciesColumn variableCalculationsRow
variableC1C2C3C4C5Totalfo-feR1273533251203.005.00-3.00-
5.000.00R21315272580-3.00-5.003.005.000.00Use the
YELLOW cells to set up the Chi Square
table.R300.000.000.000.000.00The table can handle up to 5
rows and 5 columns of values.R400.000.000.000.000.00If fewer
rows or columns are needed, leave the excess
blank.R500.000.000.000.000.00The BLUE table computes the
expected frequencies needed to compute the chi
squareTotal405060500200statistic. The only values that
ultimately matter to you is in the RESULTS table.Expected
FrequenciesColumn variableRow
variableC1C2C3C4C5Total(fo-
fe)^2/feR124.0030.0036.0030.000.001200.380.830.250.830.00R
216.0020.0024.0020.000.00800.561.250.381.250.00R30.000.000
.000.000.0000.000.000.000.000.00R40.000.000.000.000.0000.0
00.000.000.000.00R50.000.000.000.000.0000.000.000.000.000.
00Total405060500200DataLevel of Significance0.05Number of
Rows2Number of Columns4Degrees of Freedom3ResultsCritical
Value7.8147277639Chi-Square Test Statistic5.7291666667p-
Value0.1256Do not reject the null hypothesisThis tests the null
hypothesis that the row variable and column variable are
independent.Rejecting the null implies that the two variables are
related (one is dependent on the other).©2007
DrJimMirabella.com
A p-value is the probability of making a type 1 error if you
reject the null hypothesis. In other words, it is the probability
you would be making a mistake to reject the null.
Also referred to as ALPHA. This is your tolerance for error; it
is the probability of incorrectly rejecting the null hypothesis.
ContentsHYPOTHESIS TESTING NOTES2-Tailed TestTests if
a mean or proportion is different from a theoretical value.Ho: m
= 100Word problem might state that the mean is "equal to"
100.H1: m <> 100Word problem might state that the mean is
"different from" or "not equal to" 100.Upper-Tail TestTests if a
mean or proportion is greater than a theoretical value.Ho: m <
100Word problem might state that the mean is "no more than"
or "at most" 100H1: m > 100Word problem might state that the
mean is "greater than" 100.Lower-Tail TestTests if a mean or
proportion is less than a theoretical value.Ho: m > 100Word
problem might state that the mean is "at least" 100H1: m <
100Word problem might state that the mean is "less than" 100.If
the null is rejected, there is sufficient evidence to conclude the
alternate hypothesis is true.If the null is not rejected, there is
insufficient evidence to conclude the alternate hypothesis is
true.©2007 DrJimMirabella.com
Hyp Mean - One SampleOne Sample Hypothesis Test for the
MeanNull Hypothesis m =500Level of
Significance0.05Sample Size30Sample Mean535Standard
Deviation100Test Statistic (Computed)1.92Direction of
TestLower Crit ValueUpper Crit Valuep-ValueDecisionTwo-
Tailed Test-1.96001.96000.0552Do not reject the null
hypothesisH1: m <> 500Upper-Tail Testn/a1.64490.0276Reject
the null hypothesisH1: m > 500Lower-Tail Test-
1.6449n/a0.9724Do not reject the null hypothesisH1: m < 500If
you REJECT the null hypothesis, conclude that H1 is true.If you
DO NOT REJECT the null hypothesis, there is insufficient
evidence to conclude that H1 is true.NEVER conclude that the
null hypothesis is true (i.e., we CANNOT ACCEPT the
null).©2007 DrJimMirabella.com
&A
If the sample size is less than 30, the statistic is the t-score. If
the sample size is greater than 30, the statistic is the z-score.
This is the hypothesized value that is being tested.
This is the mean of the sample that is being compared to the
hypothesized value.
A p-value is the probability of making a type 1 error if you
reject the null hypothesis. In other words, it is the probability
you would be making a mistake to reject the null.
If the p-value is less than the significance level, than the risk of
error is within your tolerance, so you reject the null hypothesis.
If the p-value is greater, you do not reject the null because the
risk is too great. Another way to look at the decision is that if
the test statistic > upper critical value or < lower critical value,
the null hypothesis is rejected.
Depending on the alternate hypothesis, you select the
appropriate test and make the subsequent decision.
Also referred to as ALPHA. This is your tolerance for error; it
is the probability of incorrectly rejecting the null hypothesis.
Hyp Mean - One Sample (data)Observation #DataOne Sample
Hypothesis Test for the MeanObservation 11Observation 22Null
Hypothesis m =20Observation 34Level of
Significance0.05Observation 45Sample Size25Observation
56Sample Mean15.96Observation 67Standard
Deviation10.46Observation 79Observation 89Test Statistic
(Computed)-1.93Observation 910Observation 1010Observation
1112Direction of TestLower Crit ValueUpper Crit Valuep-
ValueDecisionObservation 1212Observation 1314Two-Tailed
Test-2.06392.06390.0653Do not reject the null
hypothesisObservation 1415H1: m <> 20Observation
1516Observation 1618Upper-Tail Testn/a1.71090.9673Do not
reject the null hypothesisObservation 1720H1: m >
20Observation 1822Observation 1923Lower-Tail Test-
1.7109n/a0.0327Reject the null hypothesisObservation 2025H1:
m < 20Observation 2126Observation 2228If you REJECT the
null hypothesis, conclude that H1 is true.Observation 2332If
you DO NOT REJECT the null hypothesis, there is insufficient
evidence to conclude that H1 is true.Observation 2433NEVER
conclude that the null hypothesis is true (i.e., we CANNOT
ACCEPT the null).Observation 2540Observation 26Observation
27Observation 28Observation 29©2007
DrJimMirabella.comObservation 30Observation 31Observation
32Observation 33Observation 34Observation 35Observation
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193Observation 194Observation 195Observation
196Observation 197Observation 198Observation
199Observation 200
&A
If the sample size is less than 30, the statistic is the t-score. If
the sample size is greater than 30, the statistic is the z-score.
This is the hypothesized value that is being tested.
This is the mean of the sample that is being compared to the
hypothesized value.
A p-value is the probability of making a type 1 error if you
reject the null hypothesis. In other words, it is the probability
you would be making a mistake to reject the null.
If the p-value is less than the significance level, than the risk of
error is within your tolerance, so you reject the null hypothesis.
If the p-value is greater, you do not reject the null because the
risk is too great. Another way to look at the decision is that if
the test statistic > upper critical value or < lower critical value,
the null hypothesis is rejected.
Depending on the alternate hypothesis, you select the
appropriate test and make the subsequent decision.
Also referred to as ALPHA. This is your tolerance for error; it
is the probability of incorrectly rejecting the null hypothesis.
Hyp Test Prop - One SampleOne Sample Hypothesis Test for
the ProportionNull Hypothesis P =0.5Level of
Significance0.05Number of Successes59Sample Size100Sample
Proportion0.59(computed from Successes / Sample Size)Z Test
Statistic (Computed)1.80Direction of TestLower Crit
ValueUpper Crit Valuep-ValueDecisionTwo-Tailed Test-
1.96001.96000.0719Do not reject the null hypothesisH1: P <>
0.5Upper-Tail Testn/a1.64490.0359Reject the null
hypothesisH1: P > 0.5Lower-Tail Test-1.6449n/a0.9641Do not
reject the null hypothesisH1: P < 0.5If you REJECT the null
hypothesis, conclude that H1 is true.If you DO NOT REJECT
the null hypothesis, there is insufficient evidence to conclude
that H1 is true.NEVER conclude that the null hypothesis is true
(i.e., we CANNOT ACCEPT the null).©2007
DrJimMirabella.com
&A
Depending on the alternate hypothesis, you select the
appropriate test and make the subsequent decision.
A p-value is the probability of making a type 1 error if you
reject the null hypothesis. In other words, it is the probability
you would be making a mistake to reject the null.
This is the hypothesized value that is being tested.
Also referred to as ALPHA. This is your tolerance for error; it
is the probability of incorrectly rejecting the null hypothesis.
This is the number of observations in the sample that meet the
specified condition.
If the p-value is less than the significance level, than the risk of
error is within your tolerance, so you reject the null hypothesis.
If the p-value is greater, you do not reject the null because the
risk is too great. Another way to look at the decision is that if
the test statistic > upper critical value or < lower critical value,
the null hypothesis is rejected.
SampleSizeSample Size Determination for ProportionEstimate
of True Proportion* =0.50Sampling Error =0.05Confidence
Level =95.00%Sample Size Needed =385Z Value-
1.9599639845Calculated Sample Size384.1458820694Finite
Population Size =500Sample Size Needed =218Calculated
Sample Size217.4872180626*Use .50 for the "estimate of true
proportion" when unknown.Sample Size Determination for
MeanPopulation Standard Deviation =100Sampling Error
=25Confidence Level =95.00%Sample Size Needed =62Z Value-
1.9599639845Calculated Sample Size61.4633411311Finite
Population Size =500Sample Size Needed =55Sample Size with
FPC54.8326149281©2007 DrJimMirabella.com
Use .50 for the "estimate of true proportion" when unknown.
Use this if the population size is known. It will not impact the
results unless it is relatively small.
Use this if the population size is known. It will not impact the
results unless it is relatively small.
This is the minimal sample needed to assure the resulting
confidence interval will be no larger than the sampling error.
This is the minimal sample needed to assure the resulting
confidence interval will be no larger than the sampling error.
Input the maximum size of the confidence interval; in other
words, you want to be X% confident that the true population
proportion deviates from the sample proportion by no more than
this.
Input the maximum size of the confidence interval; in other
words, you want to be X% confident that the true mean deviates
from the sample mean by no more than this.
Input the level of confidence that you want to assure the
population mean deviates by no more than the sampling error.
Input the level of confidence that you want to assure the
population proportion deviates by no more than the sampling
error.
Confidence-MeanConfidence Interval Estimate for the
MeanStandard Deviation =8Sample Mean =40Sample Size
=25Confidence IntervalEstimate + Sampling ErrorConfidence
Level =95.00%--->36.698<= m <=43.302=40 +/-
3.302Standard Error of the Mean1.6Degrees of Freedom24t
Value2.0638985473Interval Half Width (t)3.3022376757Z
Value-1.9599639845Interval Half Width (z)3.1359423753Finite
Population Size =200--->36.903<= m <=43.097=40 +/-
3.097FPC Factor0.9377616888Interval Half Width
(t)3.0967119795Interval Half Width (z)2.9407666177(X-
mu)/sigma(X-mu)/sigmaf(X)f(X)-
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3.0235.1735.170.000000.00261-
3.0135.1835.180.000000.00269©2007 DrJimMirabella.com-
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41.620.149720.000001.0241.6341.630.148210.000001.0341.654
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30.000001.2041.9241.920.121370.000001.2141.9441.940.11991
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442.1442.140.101600.000001.3542.1642.160.100240.000001.36
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142.9042.90.048460.000001.8242.9142.910.047590.000001.834
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Confidence-Mean
Confidence-Mean (raw data)Observation #DataObservation
11Confidence Interval Estimate for the MeanStandard Error of
the Mean2.0916341299Observation 22Degrees of
Freedom24Observation 34Standard Deviation =10.46t
Value2.0638985473Observation 45Sample Mean =15.96Interval
Half Width (t)4.3169206422Observation 56Sample Size
=25Confidence IntervalEstimate + Sampling ErrorZ Value-
1.9599639845Observation 67Confidence Level =95.00%---
>11.643<= m <=20.277=15.96 +/- 4.317Interval Half Width
(z)4.0995275634Observation 79Observation 89FPC
Factor0.9377616888Observation 910Finite Population Size
=200--->11.912<= m <=20.008=15.96 +/- 4.048Interval Half
Width (t)4.0482427917Observation 1010Interval Half Width
(z)3.844379891Observation 1112Observation 1212Observation
1314Observation 1415Observation 1516Observation
1618Observation 1720Observation 1822Observation
1923Observation 2025Observation 2126Observation 2228(X-
mu)/sigma(X-mu)/sigmaf(X)f(X)Observation 2332-
3.209.279.270.000000.00114Observation 2433-
3.199.299.290.000000.00118Observation 2540-
3.189.319.310.000000.00121Observation 26-
3.179.339.330.000000.00125Observation 27-
3.169.359.350.000000.00129Observation 28-
3.159.379.370.000000.00134Observation 29-
3.149.399.390.000000.00138Observation 30-
3.139.419.410.000000.00142Observation 31-
3.129.439.430.000000.00147Observation 32-
3.119.469.460.000000.00151Observation 33-
3.109.489.480.000000.00156Observation 34©2007
DrJimMirabella.com-3.099.509.50.000000.00161Observation
35-3.089.529.520.000000.00166Observation 36-
3.079.549.540.000000.00171Observation 37-
3.069.569.560.000000.00177Observation 38-
3.059.589.580.000000.00182Observation 39-
3.049.609.60.000000.00188Observation 40-
3.039.629.620.000000.00194Observation 41-
3.029.649.640.000000.00200Observation 42-
3.019.669.660.000000.00206Observation 43-
3.009.699.690.000000.00212Observation 44-
2.999.719.710.000000.00218Observation 45-
2.989.739.730.000000.00225Observation 46-
2.979.759.750.000000.00232Observation 47-
2.969.779.770.000000.00239Observation 48-
2.959.799.790.000000.00246Observation 49-
2.949.819.810.000000.00253Observation 50-
2.939.839.830.000000.00261Observation 51-
2.929.859.850.000000.00268Observation 52-
2.919.879.870.000000.00276Observation 53-
2.909.899.890.000000.00285Observation 54-
2.899.929.920.000000.00293Observation 55-
2.889.949.940.000000.00302Observation 56-
2.879.969.960.000000.00310Observation 57-
2.869.989.980.000000.00319Observation 58-
2.8510.00100.000000.00329Observation 59-
2.8410.0210.020.000000.00338Observation 60-
2.8310.0410.040.000000.00348Observation 61-
2.8210.0610.060.000000.00358Observation 62-
2.8110.0810.080.000000.00368Observation 63-
2.8010.1010.10.000000.00378Observation 64-
2.7910.1210.120.000000.00389Observation 65-
2.7810.1510.150.000000.00400Observation 66-
2.7710.1710.170.000000.00411Observation 67-
2.7610.1910.190.000000.00423Observation 68-
2.7510.2110.210.000000.00435Observation 69-
2.7410.2310.230.000000.00447Observation 70-
2.7310.2510.250.000000.00459Observation 71-
2.7210.2710.270.000000.00472Observation 72-
2.7110.2910.290.000000.00485Observation 73-
2.7010.3110.310.000000.00498Observation 74-
2.6910.3310.330.000000.00512Observation 75-
2.6810.3510.350.000000.00526Observation 76-
2.6710.3810.380.000000.00540Observation 77-
2.6610.4010.40.000000.00555Observation 78-
2.6510.4210.420.000000.00570Observation 79-
2.6410.4410.440.000000.00585Observation 80-
2.6310.4610.460.000000.00600Observation 81-
2.6210.4810.480.000000.00616Observation 82-
2.6110.5010.50.000000.00633Observation 83-
2.6010.5210.520.000000.00649Observation 84-
2.5910.5410.540.000000.00666Observation 85-
2.5810.5610.560.000000.00684Observation 86-
2.5710.5810.580.000000.00702Observation 87-
2.5610.6110.610.000000.00720Observation 88-
2.5510.6310.630.000000.00739Observation 89-
2.5410.6510.650.000000.00758Observation 90-
2.5310.6710.670.000000.00777Observation 91-
2.5210.6910.690.000000.00797Observation 92-
2.5110.7110.710.000000.00817Observation 93-
2.5010.7310.730.000000.00838Observation 94-
2.4910.7510.750.000000.00859Observation 95-
2.4810.7710.770.000000.00881Observation 96-
2.4710.7910.790.000000.00903Observation 97-
2.4610.8110.810.000000.00925Observation 98-
2.4510.8410.840.000000.00948Observation 99-
2.4410.8610.860.000000.00972Observation 100-
2.4310.8810.880.000000.00996Observation 101-
2.4210.9010.90.000000.01020Observation 102-
2.4110.9210.920.000000.01045Observation 103-
2.4010.9410.940.000000.01071Observation 104-
2.3910.9610.960.000000.01097Observation 105-
2.3810.9810.980.000000.01123Observation 106-
2.3711.00110.000000.01150Observation 107-
2.3611.0211.020.000000.01178Observation 108-
2.3511.0411.040.000000.01206Observation 109-
2.3411.0711.070.000000.01234Observation 110-
2.3311.0911.090.000000.01263Observation 111-
2.3211.1111.110.000000.01293Observation 112-
2.3111.1311.130.000000.01323Observation 113-
2.3011.1511.150.000000.01354Observation 114-
2.2911.1711.170.000000.01386Observation 115-
2.2811.1911.190.000000.01418Observation 116-
2.2711.2111.210.000000.01450Observation 117-
2.2611.2311.230.000000.01484Observation 118-
2.2511.2511.250.000000.01517Observation 119-
2.2411.2711.270.000000.01552Observation 120-
2.2311.3011.30.000000.01587Observation 121-
2.2211.3211.320.000000.01623Observation 122-
2.2111.3411.340.000000.01659Observation 123-
2.2011.3611.360.000000.01696Observation 124-
2.1911.3811.380.000000.01734Observation 125-
2.1811.4011.40.000000.01772Observation 126-
2.1711.4211.420.000000.01811Observation 127-
2.1611.4411.440.000000.01851Observation 128-
2.1511.4611.460.000000.01891Observation 129-
2.1411.4811.480.000000.01932Observation 130-
2.1311.5011.50.000000.01974Observation 131-
2.1211.5311.530.000000.02016Observation 132-
2.1111.5511.550.000000.02059Observation 133-
2.1011.5711.570.000000.02103Observation 134-
2.0911.5911.590.000000.02147Observation 135-
2.0811.6111.610.000000.02193Observation 136-
2.0711.6311.630.000000.02239Observation 137-
2.0611.6511.650.022850.00000Observation 138-
2.0511.6711.670.023330.00000Observation 139-
2.0411.6911.690.023810.00000Observation 140-
2.0311.7111.710.024300.00000Observation 141-
2.0211.7311.730.024800.00000Observation 142-
2.0111.7611.760.025300.00000Observation 143-
2.0011.7811.780.025810.00000Observation 144-
1.9911.8011.80.026330.00000Observation 145-
1.9811.8211.820.026860.00000Observation 146-
1.9711.8411.840.027400.00000Observation 147-
1.9611.8611.860.027940.00000Observation 148-
1.9511.8811.880.028490.00000Observation 149-
1.9411.9011.90.029050.00000Observation 150-
1.9311.9211.920.029620.00000Observation 151-
1.9211.9411.940.030190.00000Observation 152-
1.9111.9611.960.030780.00000Observation 153-
1.9011.9911.990.031370.00000Observation 154-
1.8912.0112.010.031970.00000Observation 155-
1.8812.0312.030.032580.00000Observation 156-
1.8712.0512.050.033200.00000Observation 157-
1.8612.0712.070.033820.00000Observation 158-
1.8512.0912.090.034450.00000Observation 159-
1.8412.1112.110.035100.00000Observation 160-
1.8312.1312.130.035750.00000Observation 161-
1.8212.1512.150.036400.00000Observation 162-
1.8112.1712.170.037070.00000Observation 163-
1.8012.2012.20.037750.00000Observation 164-
1.7912.2212.220.038430.00000Observation 165-
1.7812.2412.240.039120.00000Observation 166-
1.7712.2612.260.039820.00000Observation 167-
1.7612.2812.280.040530.00000Observation 168-
1.7512.3012.30.041250.00000Observation 169-
1.7412.3212.320.041970.00000Observation 170-
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1.7112.3812.380.044200.00000Observation 173-
1.7012.4012.40.044960.00000Observation 174-
1.6912.4312.430.045730.00000Observation 175-
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1.6312.5512.550.050520.00000Observation 181-
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1.5712.6812.680.055610.00000Observation 187-
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1.5512.7212.720.057380.00000Observation 189-
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1.4812.8612.860.063790.00000Observation 196-
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3.2022.6522.650.000000.00114
Use this if the population size is known. It will not impact the
results unless it is relatively small.
Input the level of confidence in which you want to be assured of
capturing the population mean in the interval.
We are X% confident that the population mean is between the
two numbers shown. The red region of the graph illustrates this
interval.
Confidence-Mean (raw data)
Confidence-ProportionConfidence Interval Estimate for the
ProportionSample Size =200Number of Successes
=110Confidence IntervalEstimate + Sampling ErrorConfidence
Level =95.00%--->0.481<= P <=0.619=0.55 +/- 0.069Sample
Proportion0.55Z Value-1.9599639845Standard Error of the
Proportion0.0351781182Interval Half Width0.069Finite
Population Size =500--->0.497<= P <=0.603=0.55 +/-
0.053FPC Factor0.7753724297Interval Half
Width0.0534602579(X-mu)/sigma(X-mu)/sigmaf(X)f(X)-
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2.970.450.4460.000000.13779©2007 DrJimMirabella.com-
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1.900.480.4831.865250.00000-1.890.480.4841.900930.00000-
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1.660.490.4922.859340.00000-1.650.490.4922.907060.00000-
1.640.490.4922.955280.00000-1.630.490.4933.003990.00000-
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1.320.500.5044.745480.00000-1.310.500.5044.808290.00000-
1.300.500.5044.871450.00000-1.290.510.5054.934950.00000-
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1.260.510.5065.127370.00000-1.250.510.5065.192120.00000-
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1.000.520.5156.878440.00000-0.990.520.5156.947230.00000-
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550.55211.326470.000000.060.550.55211.320240.000000.070.5
50.55211.312890.000000.080.550.55311.304410.000000.090.55
0.55311.294800.000000.100.550.55411.284080.000000.110.550
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55511.245210.000000.140.560.55511.230040.000000.150.560.5
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611.177940.000000.180.560.55611.158400.000000.190.560.557
11.137780.000000.200.560.55711.116080.000000.210.560.5571
1.093310.000000.220.560.55811.069490.000000.230.560.55811
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991720.000000.260.560.55910.963730.000000.270.560.55910.9
34710.000000.280.560.5610.904680.000000.290.560.5610.8736
50.000000.300.560.56110.841620.000000.310.560.56110.80860
0.000000.320.560.56110.774610.000000.330.560.56210.739650
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00000.380.560.56310.550700.000000.390.560.56410.510160.00
0000.400.560.56410.468730.000000.410.560.56410.426420.000
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00.440.570.56510.294320.000000.450.570.56610.248610.00000
0.460.570.56610.202090.000000.470.570.56710.154760.000000
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500.570.56810.008080.000000.510.570.5689.957660.000000.52
0.570.5689.906510.000000.530.570.5699.854640.000000.540.5
70.5699.802060.000000.550.570.5699.748780.000000.560.570.
579.694830.000000.570.570.579.640210.000000.580.570.579.5
84930.000000.590.570.5719.529030.000000.600.570.5719.4725
00.000000.610.570.5719.415360.000000.620.570.5729.357630.
000000.630.570.5729.299330.000000.640.570.5739.240470.000
000.650.570.5739.181060.000000.660.570.5739.121120.000000
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0.570.5748.938270.000000.700.580.5758.876370.000000.710.5
80.5758.814010.000000.720.580.5758.751210.000000.730.580.
5768.688000.000000.740.580.5768.624380.000000.750.580.576
8.560360.000000.760.580.5778.495970.000000.770.580.5778.4
31230.000000.780.580.5778.366140.000000.790.580.5788.3007
20.000000.800.580.5788.234990.000000.810.580.5788.168970.
000000.820.580.5798.102660.000000.830.580.5798.036090.000
000.840.580.587.969270.000000.850.580.587.902210.000000.8
60.580.587.834930.000000.870.580.5817.767450.000000.880.5
80.5817.699790.000000.890.580.5817.631940.000000.900.580.
5827.563940.000000.910.580.5827.495800.000000.920.580.582
7.427520.000000.930.580.5837.359140.000000.940.580.5837.2
90650.000000.950.580.5837.222080.000000.960.580.5847.1534
30.000000.970.580.5847.084740.000000.980.580.5847.015990.
000000.990.590.5856.947230.000001.000.590.5856.878440.000
001.010.590.5866.809660.000001.020.590.5866.740890.000001
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0.590.5876.534800.000001.060.590.5876.466230.000001.070.5
90.5886.397730.000001.080.590.5886.329320.000001.090.590.
5886.261020.000001.100.590.5896.192830.000001.110.590.589
6.124780.000001.120.590.5896.056870.000001.130.590.595.98
9110.000001.140.590.595.921520.000001.150.590.595.854100.
000001.160.590.5915.786880.000001.170.590.5915.719850.000
001.180.590.5925.653030.000001.190.590.5925.586440.000001
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0.590.5935.388100.000001.230.590.5935.322500.000001.240.5
90.5945.257170.000001.250.590.5945.192120.000001.260.590.
5945.127370.000001.270.600.5955.062920.000001.280.600.595
4.998770.000001.290.600.5954.934950.000001.300.600.5964.8
71450.000001.310.600.5964.808290.000001.320.600.5964.7454
80.000001.330.600.5974.683020.000001.340.600.5974.620910.
000001.350.600.5974.559180.000001.360.600.5984.497820.000
001.370.600.5984.436840.000001.380.600.5994.376250.000001
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0.600.64.196880.000001.420.600.64.137920.000001.430.600.64
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3560.000001.460.600.6013.906310.000001.470.600.6023.84950
0.000001.480.600.6023.793130.000001.490.600.6023.737220.0
00001.500.600.6033.681770.000001.510.600.6033.626770.0000
01.520.600.6033.572240.000001.530.600.6043.518180.000001.
540.600.6043.464580.000001.550.610.6053.411470.000001.560
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0.6063.255000.000001.590.610.6063.203820.000001.600.610.6
063.153120.000001.610.610.6073.102920.000001.620.610.6073
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5280.000001.650.610.6082.907060.000001.660.610.6082.85934
0.000001.670.610.6092.812130.000001.680.610.6092.765420.0
00001.690.610.6092.719210.000001.700.610.612.673510.00000
1.710.610.612.628310.000001.720.610.6112.583620.000001.73
0.610.6112.539440.000001.740.610.6112.495760.000001.750.6
10.6122.452580.000001.760.610.6122.409920.000001.770.610.
6122.367760.000001.780.610.6132.326100.000001.790.610.613
2.284950.000001.800.610.6132.244300.000001.810.610.6142.2
04150.000001.820.610.6142.164510.000001.830.610.6142.1253
60.000001.840.620.6152.086720.000001.850.620.6152.048570.
000001.860.620.6152.010920.000001.870.620.6161.973760.000
001.880.620.6161.937100.000001.890.620.6161.900930.000001
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0.620.6181.795340.000001.930.620.6181.761110.000001.940.6
20.6181.727360.000001.950.620.6190.000001.694081.960.620.
6190.000001.661291.970.620.6190.000001.628961.980.620.620
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01.534792.010.620.6210.000001.504322.020.620.6210.000001.
474312.030.620.6210.000001.444762.040.620.6220.000001.415
662.050.620.6220.000001.387002.060.620.6220.000001.358792
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0.620.6240.000001.276782.100.620.6240.000001.250312.110.6
20.6240.000001.224272.120.630.6250.000001.198652.130.630.
6250.000001.173442.140.630.6250.000001.148662.150.630.626
0.000001.124282.160.630.6260.000001.100312.170.630.6260.0
00001.076742.180.630.6270.000001.053582.190.630.6270.0000
01.030812.200.630.6270.000001.008432.210.630.6280.000000.
986442.220.630.6280.000000.964832.230.630.6280.000000.943
602.240.630.6290.000000.922742.250.630.6290.000000.902262
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30.630.000000.842982.290.630.6310.000000.823942.300.630.6
310.000000.805252.310.630.6310.000000.786902.320.630.6320
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0000.733882.350.630.6330.000000.716872.360.630.6330.00000
0.700192.370.630.6330.000000.683822.380.630.6340.000000.6
67772.390.630.6340.000000.652032.400.630.6340.000000.6366
02.410.640.6350.000000.621482.420.640.6350.000000.606652.
430.640.6350.000000.592112.440.640.6360.000000.577872.450
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0.6370.000000.536842.480.640.6370.000000.523722.490.640.6
380.000000.510862.500.640.6380.000000.498272.510.640.6380
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0000.462062.540.640.6390.000000.450502.550.640.640.000000
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62.580.640.6410.000000.406652.590.640.6410.000000.396272.
600.640.6410.000000.386122.610.640.6420.000000.376192.620
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0.6430.000000.347702.650.640.6430.000000.338632.660.640.6
440.000000.329752.670.640.6440.000000.321082.680.640.6440
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0000.296232.710.650.6450.000000.288332.720.650.6460.00000
0.280602.730.650.6460.000000.273062.740.650.6460.000000.2
65692.750.650.6470.000000.258502.760.650.6470.000000.2514
82.770.650.6470.000000.244622.780.650.6480.000000.237922.
790.650.6480.000000.231392.800.650.6480.000000.225012.810
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0.650.000000.206792.840.650.650.000000.201012.850.650.650.
000000.195372.860.650.6510.000000.189872.870.650.6510.000
000.184512.880.650.6510.000000.179282.890.650.6520.000000
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4372.920.650.6530.000000.159642.930.650.6530.000000.15504
2.940.650.6530.000000.150562.950.650.6540.000000.146192.9
60.650.6540.000000.141932.970.650.6540.000000.137792.980.
660.6550.000000.133752.990.660.6550.000000.129813.000.660
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60.000000.118623.030.660.6570.000000.115093.040.660.6570.
000000.111653.050.660.6570.000000.108303.060.660.6580.000
000.105043.070.660.6580.000000.101873.080.660.6580.000000
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2873.110.660.6590.000000.090033.120.660.660.000000.087263
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60.6610.000000.079433.160.660.6610.000000.076963.170.660.
6620.000000.074573.180.660.6620.000000.072243.190.660.662
0.000000.069973.200.660.6630.000000.06777
Use this if the population size is known. It will not impact the
results unless it is relatively small.
Input the level of confidence in which you want to be assured of
capturing the population mean in the interval.
We are X% confident that the population mean is between the
two numbers shown. The red region of the graph illustrates this
interval.
Confidence-Proportion
Use this if the population size is known. It will not impact the
results unless it is relatively small.
We are X% confident that the population proportion is between
the two numbers shown. The red region of the graph illustrates
this interval.
Input the level of confidence in which you want to be assured of
capturing the population proportion in the interval.
This is the number of observations in the sample that meet a
specified condition. Just because it is called a "success" doesn't
imply the condition is a good one.
NormalNormal ProbabilityMean =500Standard Deviation
=100Compute probability:X <300==>2.28%Compute
probability:X >700==>2.28%Compute probability:Range250<=
X <=450==>30.23%(i.e., between 2 values)Find actual
score:Percentage ABOVE =5.00%==>664.49(i.e. % greater
than)Find actual score:Percentage BELOW
=95.00%==>664.49(i.e. % less than)Approximately 68% of all
observations within 1 standard deviation of the
meanApproximately 95% of all observations within 2 standard
deviations of the meanApproximately 99.7% of all observations
within 3 standard deviations of the mean
Input the value of the mean.
Input the value of the standard deviation.
Input the value for which you want to compute the probability
of being less than.
Input the value for which you want to compute the probability
of being greater than.
Input the lower value of the range for which you want to
compute the probability.
Input the upper value of the range for which you want to
compute the probability.
Input the percent below which your desired value lies.
Input the percent above which your desired value lies.
Normal-CLTNormal Probability for Means (Central Limit
Theorem)Mean =500Standard Deviation =100Sample Size
=4Compute probability:X-bar <450==>15.87%Compute
probability:X-bar >600==>2.28%Compute
probability:Range350<= X-bar <=450==>15.73%(i.e., between
2 values)Find actual mean:Percentage ABOVE
=5.00%==>582.24(i.e. % greater than)Find actual
mean:Percentage BELOW =95.00%==>582.24(i.e. % less
than)Approximately 68% of all observations within 1 standard
deviation of the meanApproximately 95% of all observations
within 2 standard deviations of the meanApproximately 99.7%
of all observations within 3 standard deviations of the mean
Input the value for which you want to compute the probability
of being less than.
Input the value for which you want to compute the probability
of being greater than.
Input the lower value of the range for which you want to
compute the probability.
Input the percent below which your desired value lies.
Input the upper value of the range for which you want to
compute the probability.
Input the value of the mean.
Input the value of the standard deviation.
Input the percent below which your desired value lies.
Graph(Left)Normal Probability (Graphing below a value)(X-
mu)/sigma(X-mu)/sigmaf(X)f(X)-3.20-3.20.000020.00000Mean
=500-3.19-3.190.000020.00000Standard Deviation =100-3.18-
3.180.000030.00000-3.17-3.170.000030.00000Compute
probability:X <300==>2.28%-3.16-3.160.000030.00000-3.15-
3.150.000030.00000Probability (Z) <-2.00-3.14-
3.140.000030.00000-3.13-3.130.000030.00000-3.12-
3.120.000030.00000-3.11-3.110.000030.00000-3.10-
3.10.000030.00000-3.09-3.090.000030.00000-3.08-
3.080.000030.00000-3.07-3.070.000040.00000-3.06-
3.060.000040.00000-3.05-3.050.000040.00000-3.04-
3.040.000040.00000-3.03-3.030.000040.00000-3.02-
3.020.000040.00000-3.01-3.010.000040.00000-3.00-
30.000040.00000-2.99-2.990.000050.00000-2.98-
2.980.000050.00000-2.97-2.970.000050.00000-2.96-
2.960.000050.00000-2.95-2.950.000050.00000-2.94-
2.940.000050.00000-2.93-2.930.000050.00000-2.92-
2.920.000060.00000-2.91-2.910.000060.00000-2.90-
2.90.000060.00000-2.89-2.890.000060.00000-2.88-
2.880.000060.00000-2.87-2.870.000060.00000-2.86-
2.860.000070.00000-2.85-2.850.000070.00000-2.84-
2.840.000070.00000-2.83-2.830.000070.00000-2.82-
2.820.000070.00000-2.81-2.810.000080.00000-2.80-
2.80.000080.00000-2.79-2.790.000080.00000-2.78-
2.780.000080.00000-2.77-2.770.000090.00000-2.76-
2.760.000090.00000-2.75-2.750.000090.00000-2.74-
2.740.000090.00000-2.73-2.730.000100.00000-2.72-
2.720.000100.00000-2.71-2.710.000100.00000-2.70-
2.70.000100.00000-2.69-2.690.000110.00000-2.68-
2.680.000110.00000-2.67-2.670.000110.00000-2.66-
2.660.000120.00000-2.65-2.650.000120.00000-2.64-
2.640.000120.00000-2.63-2.630.000130.00000-2.62-
2.620.000130.00000-2.61-2.610.000130.00000-2.60-
2.60.000140.00000-2.59-2.590.000140.00000-2.58-
2.580.000140.00000-2.57-2.570.000150.00000-2.56-
2.560.000150.00000-2.55-2.550.000150.00000-2.54-
2.540.000160.00000-2.53-2.530.000160.00000-2.52-
2.520.000170.00000-2.51-2.510.000170.00000-2.50-
2.50.000180.00000-2.49-2.490.000180.00000-2.48-
2.480.000180.00000-2.47-2.470.000190.00000-2.46-
2.460.000190.00000-2.45-2.450.000200.00000-2.44-
2.440.000200.00000-2.43-2.430.000210.00000-2.42-
2.420.000210.00000-2.41-2.410.000220.00000-2.40-
2.40.000220.00000-2.39-2.390.000230.00000-2.38-
2.380.000230.00000-2.37-2.370.000240.00000-2.36-
2.360.000250.00000-2.35-2.350.000250.00000-2.34-
2.340.000260.00000-2.33-2.330.000260.00000-2.32-
2.320.000270.00000-2.31-2.310.000280.00000-2.30-
2.30.000280.00000-2.29-2.290.000290.00000-2.28-
2.280.000300.00000-2.27-2.270.000300.00000-2.26-
2.260.000310.00000-2.25-2.250.000320.00000-2.24-
2.240.000320.00000-2.23-2.230.000330.00000-2.22-
2.220.000340.00000-2.21-2.210.000350.00000-2.20-
2.20.000350.00000-2.19-2.190.000360.00000-2.18-
2.180.000370.00000-2.17-2.170.000380.00000-2.16-
2.160.000390.00000-2.15-2.150.000400.00000-2.14-
2.140.000400.00000-2.13-2.130.000410.00000-2.12-
2.120.000420.00000-2.11-2.110.000430.00000-2.10-
2.10.000440.00000-2.09-2.090.000450.00000-2.08-
2.080.000460.00000-2.07-2.070.000470.00000-2.06-
2.060.000480.00000-2.05-2.050.000490.00000-2.04-
2.040.000500.00000-2.03-2.030.000510.00000-2.02-
2.020.000520.00000-2.01-2.010.000530.00000-2.00-
20.000540.00000-1.99-1.990.000000.00055-1.98-
1.980.000000.00056-1.97-1.970.000000.00057-1.96-
1.960.000000.00058-1.95-1.950.000000.00060-1.94-
1.940.000000.00061-1.93-1.930.000000.00062-1.92-
1.920.000000.00063-1.91-1.910.000000.00064-1.90-
1.90.000000.00066-1.89-1.890.000000.00067-1.88-
1.880.000000.00068-1.87-1.870.000000.00069-1.86-
1.860.000000.00071-1.85-1.850.000000.00072-1.84-
1.840.000000.00073-1.83-1.830.000000.00075-1.82-
1.820.000000.00076-1.81-1.810.000000.00078-1.80-
1.80.000000.00079-1.79-1.790.000000.00080-1.78-
1.780.000000.00082-1.77-1.770.000000.00083-1.76-
1.760.000000.00085-1.75-1.750.000000.00086-1.74-
1.740.000000.00088-1.73-1.730.000000.00089-1.72-
1.720.000000.00091-1.71-1.710.000000.00092-1.70-
1.70.000000.00094-1.69-1.690.000000.00096-1.68-
1.680.000000.00097-1.67-1.670.000000.00099-1.66-
1.660.000000.00101-1.65-1.650.000000.00102-1.64-
1.640.000000.00104-1.63-1.630.000000.00106-1.62-
1.620.000000.00107-1.61-1.610.000000.00109-1.60-
1.60.000000.00111-1.59-1.590.000000.00113-1.58-
1.580.000000.00115-1.57-1.570.000000.00116-1.56-
1.560.000000.00118-1.55-1.550.000000.00120-1.54-
1.540.000000.00122-1.53-1.530.000000.00124-1.52-
1.520.000000.00126-1.51-1.510.000000.00128-1.50-
1.50.000000.00130-1.49-1.490.000000.00131-1.48-
1.480.000000.00133-1.47-1.470.000000.00135-1.46-
1.460.000000.00137-1.45-1.450.000000.00139-1.44-
1.440.000000.00141-1.43-1.430.000000.00144-1.42-
1.420.000000.00146-1.41-1.410.000000.00148-1.40-
1.40.000000.00150-1.39-1.390.000000.00152-1.38-
1.380.000000.00154-1.37-1.370.000000.00156-1.36-
1.360.000000.00158-1.35-1.350.000000.00160-1.34-
1.340.000000.00163-1.33-1.330.000000.00165-1.32-
1.320.000000.00167-1.31-1.310.000000.00169-1.30-
1.30.000000.00171-1.29-1.290.000000.00174-1.28-
1.280.000000.00176-1.27-1.270.000000.00178-1.26-
1.260.000000.00180-1.25-1.250.000000.00183-1.24-
1.240.000000.00185-1.23-1.230.000000.00187-1.22-
1.220.000000.00190-1.21-1.210.000000.00192-1.20-
1.20.000000.00194-1.19-1.190.000000.00197-1.18-
1.180.000000.00199-1.17-1.170.000000.00201-1.16-
1.160.000000.00204-1.15-1.150.000000.00206-1.14-
1.140.000000.00208-1.13-1.130.000000.00211-1.12-
1.120.000000.00213-1.11-1.110.000000.00215-1.10-
1.10.000000.00218-1.09-1.090.000000.00220-1.08-
1.080.000000.00223-1.07-1.070.000000.00225-1.06-
1.060.000000.00227-1.05-1.050.000000.00230-1.04-
1.040.000000.00232-1.03-1.030.000000.00235-1.02-
1.020.000000.00237-1.01-1.010.000000.00240-1.00-
10.000000.00242-0.99-0.990.000000.00244-0.98-
0.980.000000.00247-0.97-0.970.000000.00249-0.96-
0.960.000000.00252-0.95-0.950.000000.00254-0.94-
0.940.000000.00256-0.93-0.930.000000.00259-0.92-
0.920.000000.00261-0.91-0.910.000000.00264-0.90-
0.90.000000.00266-0.89-0.890.000000.00268-0.88-
0.880.000000.00271-0.87-0.870.000000.00273-0.86-
0.860.000000.00276-0.85-0.850.000000.00278-0.84-
0.840.000000.00280-0.83-0.830.000000.00283-0.82-
0.820.000000.00285-0.81-0.810.000000.00287-0.80-
0.80.000000.00290-0.79-0.790.000000.00292-0.78-
0.780.000000.00294-0.77-0.770.000000.00297-0.76-
0.760.000000.00299-0.75-0.750.000000.00301-0.74-
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx
DataMultiple RegressionR^20.39479551630.37638520610.03834514140000.docx

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