Question

10. Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim.

A simple random sample of 25 filtered 100 mm cigarettes is​ obtained, and the tar content of each cigarette is measured. The sample has a mean of 18.6 mg and a standard deviation of 3.87 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 ​mg, which is the mean for unfiltered king size cigarettes. What do the results​ suggest, if​ anything, about the effectiveness of the​ filters?

What are the​ hypotheses?

A.H 0​: µ = 21.1 mg

H 1​: µ ≥ 21.1 mg

B.H 0​: µ < 21.1 mg

H 1​: µ ≥ 21.1 mg

C. H 0​: µ > 21.1 mg

    H 1​: µ <21.1 mg

D.H 0​: µ = 21.1 mg

H 1​: µ < 21.1 mg

Identify the test statistic.

T=____

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

Identify the​ P-value.

The​ P-value is _____

(Round to four decimal places as​ needed.)

State the final conclusion that addresses the original claim. Choose the correct answer below.

A.Fail to reject Upper H 0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

B.Fail to reject Upper H 0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

C.Reject Upper H 0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

D.Reject Upper H 0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

This is the correct answer.

What do the results​ suggest, if​ anything, about the effectiveness of the​ filters?

A.The results suggest that the filters are effective.

B.The results are inconclusive because the sample size is less than 30.

C.The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes.

D.The results do not suggest that the filters are effective.

E.The results suggest that the filters increase the tar content.

Answer 1

D.Reject Upper H 0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.

A.The results suggest that the filters are effective.