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 alphaα=0.05 level of significance for the given sample data.

​(b) Construct a 99​% confidence interval about μ1−μ2

	population1	population2
n	21	19
x bar	48.5	42.3
s	7.1	11.9

(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​: 1μ =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 rejectThere is not is not sufficient evidence at the alphaα=0.05 level of significance to conclude that μ1>μ2.

B. Reject Upper H0. There is not is not sufficient evidence at the alphaα=0.05 level of significance to conclude that μ1> μ2.

C. Do not reject Upper H0. There is sufficient evidence at the alphaα =0.05 level of significance to conclude that μ1>μ2.

D.Reject Upper H0. There is sufficient evidence at the alphaα=0.05level of significance to conclude that

μ1> μ2.

​(b) The 99​% confidence interval about μ1− μ2 is the range from a lower bound of nothing to an upper bound of

nothing.

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

Answer 1

Solution:

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

Answer:

E.

  

Find the test statistic for this hypothesis test.

Answer: The test statistic is given below:

  

  

Therefore, the test statistic is

Determine the P-value for this hypothesis test.

Answer: The P-value is given below:

State the conclusion for this hypothesis test.

Answer: D. Reject Upper . There is sufficient evidence at the alpha α=0.05 level of significance to conclude that μ1> μ2.

(b) Construct a 99 % confidence interval about μ1−μ2

Answer: We can use TI 84 to find the 99% confidence for the given data. The steps are as follows:

Step 1: Press STAT Key and then scroll right to TESTS

Step 2: Scroll down to 2-SampTInt... and scroll right to Stats and type:

C-Level : 0.99

Pooled: No

Calculate.

Therefore, the 99% confidence interval about μ1− μ2 is the range from a lower bound of -2.457 to an upper bound of 14.857.