Question

Use the given statistics to complete parts​ (a) and​ (b). Assume that the populations are normally distributed. ​(a) Test whether μ1>μ2 at the α=0.01 level of significance for the given sample data.​ (b) Construct a 99​% confidence interval about μ1−μ2.			Population 1	Population 2
		n	29	21
		x overbarx	51.1	41.5
		s	4.3	14.8

(a) Identify the null and alternative hypotheses for this test.

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

E. H0​: μ1<μ2

H1​: μ1=μ2

F. H0​: μ1=μ2

H1​: μ1>μ2

Find the test statistic for this hypothesis test.

____(Round to two decimal places as​ needed.)

Determine the​ P-value for this hypothesis test.

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

State the conclusion for this hypothesis test.

A. Do not reject H0. There is sufficient evidence at the α=0.01 level of significance to conclude that μ1>μ2.

B. Reject H0. There is not sufficient evidence at the α=0.01 level of significance to conclude that μ1>μ2.

C. Reject H0. There is sufficient evidence at the α=0.01 level of significance to conclude that μ1>μ2.

D. Do not reject H0. There is not sufficient evidence at the α=0.01 level of significance to conclude that μ1>μ2.

(b) The 99​% confidence interval about μ1−μ2 is the range from a lower bound of ____ to an upper bound of ____.

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

Answer 1

C. Reject H0. There is sufficient evidence at the α=0.01 level of significance to conclude that μ1>μ2.