Question

Refer to the accompanying data table, which shows the amounts of nicotine (mg per cigarette) in king-size cigarettes, 100-mm menthol cigarettes, and 100-mm nonmenthol cigarettes. The king-size cigarettes are nonfiltered, while the 100-mm menthol cigarettes and the 100-mm nonmenthol cigarettes are filtered. Use a 0.05 significance level to test the claim that the three categories of cigarettes yield the same mean amount of nicotine. Given that only the king-size cigarettes are not filtered, do the filters appear to make a difference? EEE Click the icon to view the data table of the nicotine amounts. Determine the null and alternative hypotheses Ho Hi: Find the F test statistic (Round to four decimal places as needed.) F= Find the P-value using the F test statistic. (Round to four decimal places as needed.) P-value What is the conclusion for this hypothesis test? O A. Fail to reject Ho. There is insufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine. O B. Reject Ho. There is insufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine. O C. Reject Ho. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine. O D. Fail to reject Ho. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine. Do the filters appear to make a difference? O A. The results are inconclusive because the king-size cigarettes are a different size than the filtered cigarettes. O B. No, the filters do not appear to make a difference because there is insufficient evidence to warrant rejection of the claim. O c. No, the filters do not appear to make a difference because there is sufficient evidence to warrant rejection of the claim O D. Given that the king-size cigarettes have the largest mean, it appears that the filters do make a difference (although this conclusion is not justified by the results from analysis of variance)

Answer 1

Ho The three categories of cigarettes yield the same mean amount of nicotine. H The three categories of cigarettes yield different mean amount of nicotine. EXCEL (Data Analysis) output:

Anova: Single Factor SUMMARY Groups King-Size 100-mm Menthol 100-mm Nonmenthol Count Sum Average Variance 10 11.9 1.19 0.029889 1.06 0.033778 10 10.6 0.93 0.077889 10 9.3 ANOVA Source of Variation Between Groups Within Groups Total df SS MS F P-value F crit 0.338 2. 0.169 3.581633 0.041721 3.354131 1.274 27 0.047185 1.612 29 The value of F test statistic is F= 3.5816 Pvalue 0.0417 C. Reject H. There is sufficient evidence to warrant rejection of the claim that the three categories of cigarettes yield the same mean amount of nicotine.

Post hoc analysis p-values for pairwise t-tests King -Size 1.19 100-mm Nonmenthol 100-mm Menthol 0.93 1.06 100-mm Nonmenthol 0.93 .1920 0125 100-mm Menthol 1.06 .1920 King -Size 1.19 D. Given that the king-size cigarettes have the largest mean, it appears that the filters do make a difference