The Oregon Health Science Universitys news website httpwwwo

The Oregon Health & Science University\'s news website (http://www.ohsu.edu/news/2003/071803smoke.html) gives information on a study that found that some commercial cigarette brands contained 10 to 20 times higher percentages of nicotine in the \"free-base\" form, that is, the form thought to be the most addictive. Consider another study designed to compare the nicotine content of two different brands of cigarettes. The nicotine content was determined for 20 cigarettes of brand A and 20 cigarettes of brand B. The sum of ranks for brand A equals 677, and the sum of ranks for brand B equals 143. Use the Mann-Whitney U statistic to test the null hypothesis that the average nicotine content is the same for the two brands versus the alternative that the average nicotine content differs. Use ? = .01.

(a) Find U.

(b) Find z. (Give your answer correct to two decimal places.)

(c) Find the P-value. (Give your answer correct to four decimal places.)

(d) State the appropriate conclusion.

Solution

The Oregon Health & Science University\'s news website (http://www.ohsu.edu/news/2003/071803smoke.html) gives information on a study that found that some commercial cigarette brands contained 10 to 20 times higher percentages of nicotine in the \"free-base\" form, that is, the form thought to be the most addictive. Consider another study designed to compare the nicotine content of two different brands of cigarettes. The nicotine content was determined for 20 cigarettes of brand A and 20 cigarettes of brand B. The sum of ranks for brand A equals 677, and the sum of ranks for brand B equals 143. Use the Mann-Whitney U statistic to test the null hypothesis that the average nicotine content is the same for the two brands versus the alternative that the average nicotine content differs. Use ? = .01.

R1=677

U= n1*n2+n1(n1+1)/2