A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributedpopulations, and do not assume that the population standard deviations are equal. Complete parts(a) and(b) below. Use a 0.10 significance level for both parts.

Treatment

Placebo

= 1 2

n= 29. 38

x= 2.35 2.69

s= 0.93 0.52

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

What are the null and alternativehypotheses?The teststatistic, t is _____ (Round to two decimal places asneeded.)

TheP-value is ________ . (Round to three decimal places asneeded.)

State the conclusion for the test.

A.

Failtoreject the null hypothesis. There isnot sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

B.

Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

C.

Reject the null hypothesis. There isnot sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

D.

Failtoreject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

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

_____<12<______

(Round to three decimal places asneeded.)