Question

A simple random sample of 29 filtered​ 100-mm cigarettes is obtained from a normally distributed​ population, and the tar content of each cigarette is measured. The sample has a standard deviation of 0.18 mg. Use a 0.01 significance level to test the claim that the tar content of filtered​ 100-mm cigarettes has a standard deviation different from 0.25 ​mg, which is the standard deviation for unfiltered​ king-size cigarettes. Complete parts​ (a) through​ (d) below. a. What are the null and alternative​ hypotheses? A. H0​: sigma does not equal 0.25 mg Upper H1 : sigma equals 0.25 mg B. H0​: sigma equals 0.25 mg Upper H1 : sigma less than 0.25 mg C. H0​: sigma greater than 0.25 mg Upper H1 : sigma less than or equals 0.25 mg D. H0​: sigma equals 0.25 mg Upper H1 : sigma does not equal 0.25 mg b. Find the test statistic. chi-squared equals nothing ​(Round to three decimal places as​ needed.) c. Find the​ P-value of the test statistic. The​ P-value of the test statistic is nothing. ​(Round to three decimal places as​ needed.) d. State the conclusion. ▼ Fail to reject Reject Upper H 0. There ▼ is not sufficient evidence to conclude that the tar content of filtered​ 100-mm cigarettes has a standard deviation different from 0.25 mg.

Answer 1

There is not sufficient evidence to conclude that the tar content of filtered​ 100-mm cigarettes has a standard deviation different from 0.25 mg.