Question

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 3.84 mg. Use a 0.05 significance level to test the claim that the mean tar content of fitered 100 mm cigarettes is less than 21.1 mg, which is th mean for unfiltered king size cigarettes. What do the results suggest, if anything, about the effectiveness of the filters? O A Fail to reject Ho. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. OB. Reject Ho. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. OC. Fail to reject Ho. 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 Ho. There is insufficient evidence to support the claim that the meantar content of filtered 100 mm cigarettes is less than 21.1 mg. What do the results suggest, if anything, about the effectiveness of the filters?

Answer 1

solution in filtered 100mm content let the mean tar cigarettes be w we have to hest Hol = 21.1 at HiiM L 21.1 significancex 0.05 Level The given informations n=25 the sauple size x 18.6 The sample mean is deviation is s= 3.84 and the sauple standad t- hest. a left-tailed to perform tence we have is thest statistic SO the appropriate t-un (x - 21.1) 1 s t = vas (18.6 - 21.1) -3.255 3-84 dt = 24, test =-3.255 so P-value = 0.00168 [ose pually frovet calcator es then the significar a level co.os). the hest is So we reject Ho i.c u it lees hinal)