a Test the claim that the two samples are from populations w

a. Test the claim that the two samples are from populations with the same mean.

What are the null and alternative? hypotheses?

b. The test statistic is _______.

c. The P-value is _______.

d. State the conclusion of the test. (Reject, Fail to reject...sufficient or insufficient evidence)

e. Construct a confidence interval suitable for testing the claim that the two samples are from populations with the same mean.

Solution

Null hypothesis : it is claim that the two samples are from populations with the same mean i.e., Ho:₁=₂ against the alternative hypothesis : it is not claim that the two samples are from populations with the same mean  i.e., H₁:₁not = to ₂ . The statistic is t=((X₁^bar-X₂^bar)/S)*(((n1n2)/(n1+n2)) ,where S=((((n1-1)S₁²)+((n2-1)S₂²))/(n1+n2-2))=.8259, t_cal=-1.3568, |t_cal|=1.3568,  |t_cal|<t_tab=1.3568<1.684 ,so we accept null hypothesis i.e.it is claim that the two samples are from populations with the same mean i.e., Ho:₁=₂ . The confidence limits are ((X₁^bar-X₂^bar)+or-(1.684)*(S(((1/n1)+(1/n2))))=(-.6499,.0699).