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## 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 0.10 significance level for both parts.   Treatment Placebo

 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 0.10 significance level for both parts. Treatment Placebo μ μ1 μ2 n 25 35 x overbar x 2.35 2.62 s 0.88 0.59

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

What are the null and alternative​ hypotheses?

A.

Upper H 0

H0​:

mu 1

μ1

equals

=

mu 2

μ2

Upper H 1

H1​:

mu 1

μ1

greater than

>

mu 2

μ2

B.

Upper H 0

H0​:

mu 1

μ1

less than

<

mu 2

μ2

Upper H 1

H1​:

mu 1

μ1

greater than or equals

mu 2

μ2

C.

Upper H 0

H0​:

mu 1

μ1

not equals

mu 2

μ2

Upper H 1

H1​:

mu 1

μ1

less than

<

mu 2

μ2

D.

Upper H 0

H0​:

mu 1

μ1

equals

=

mu 2

μ2

Upper H 1

H1​:

mu 1

μ1

not equals

mu 2

The test​ statistic, t, is ___

The​ P-value is ____

State the conclusion for the test.

A. Reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

B.Reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

C.Fail to reject the null hypothesis. There is sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

D.Fail to reject the null hypothesis. There is not sufficient evidence to warrant rejection of the claim that men and women have the same mean BMI.

b. Construct a confidence interval suitable for testing the claim that males and females have the same mean BMI.

___< μ1 – μ2<___

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

Does the confidence interval support the conclusion of the​ test?

_____ because the confidence interval contains____

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