Question

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 distributed​ populations, 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

μ          μ1                    μ2

n          27                    40

x          2.38                 2.61

s           0.68                 0.99

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

What are the null and alternative​ hypotheses?

A. H0​: μ1≠μ2

H1​: μ1<μ2

B. H0​: μ1=μ2

H1​: μ1≠μ2

C. H0​: μ1<μ2

H1​: μ1≥μ2

D. H0​: μ1=μ2

H1​: μ1>μ2

The test​ statistic, t, is _____. ​(Round to two decimal places as​ needed.)

The​ P-value is _____. ​(Round to three decimal places as​ needed.)

State the conclusion for the test.

A. Fail to 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.

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 is not sufficient evidence to warrant rejection of the claim that the two samples are from populations with the same mean.

D. Fail to reject the null hypothesis. There is not 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.

_____<μ1−μ2< _____

​(Round to three decimal places as​ needed.)

Answer 1

What are the null and alternative​ hypotheses?

B. H0​: μ1=μ2

H1​: μ1≠μ2

The test​ statistic, t, is _____. ​(Round to two decimal places as​ needed.)

Test Statistic :-


t = -1.1273 - 1.13

The​ P-value is _____. ​(Round to three decimal places as​ needed.)

Uing excel to calculate exact P value = 0.264

State the conclusion for the test.

Reject null hypothesis if P value < level of significance

0.264 > 0.10, we fail to reject ull hypothesis

D. Fail to reject the null hypothesis. There is not 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.

Confidence interval :-


Lower Limit =
Lower Limit = -0.5707   - 0.571
Upper Limit =
Upper Limit = 0.1107 0.111
Confidence interval is ( -0.571 , 0.111 )

- 0.571 < μ1−μ2 < 0.111