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.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?
a. Determine the null and alternative hypotheses.
b.Find the F test statistic.
c.Find the​ P-value using the F test statistic.
d.What is the conclusion for this hypothesis​ test?
e.Do the filters appear to make a​ difference?