Question

The following data is the heights (in inches) of two groups:

F=73.28, 69.63, 68.62, 69.19, 64.88, 68.74, 73.01, 71.16, 64.32, 68.11, 68.91, 65.05

S=73.03, 68.34, 69.28, 72.02, 70.50, 69.48, 71.27, 70.53, 68.59, 66.92, 73.51, 59.78

Test for the equality of means assuming equal variances.

Ho:

Ha:

Test statistic=

Critical value for the test=

p-value:

conclusion:

Answer 1

MeanF=68.74 & MeanS=69.44

Ho will be MeanF is equal to MeanS

Ho: MF=MS

Alternative Hypothesis will be opposite to Hypothesis Ho

Ha: MF=! MS

Now we have test to use is z-test (Populatioon Variance is knkown)

z= (MF-MS)/sqrt(Var(MF)+Var(MS)-2Cov(MF,MS)

Its given VarMF=VarMS These are population variances

But if we calcuate then Variances of samples are differnt VarMF=(2.93)^2 and VarMS=(3.61)^2

Hence will use t test

t=(69.44-68.74)/(8.56+13.03-2*5.87)=0.7/(21.6-11.74)=0.7/9.86)=0.08

Critical Value for thet test is 1.83 ( two tailed test we have assumed here)

for samlpe size of 10 if we keep p value to be 0.95

and calculated p value is 0.9380

Hence we cant reject the hypothesis Ho Hence MF=MS