Question

A simple random sample of 25 filtered 100-mm cigarettes of brand A is obtained, and the tar content of each cigarette is measured. The sample has a mean of 15.3 mg of tar and a standard deviation of 3.7 mg.

a) Use a 0.05 significance level to test the claim that the mean tar content of filtered 100-mm cigarettes is smaller than the mean tar content of brand B which is 22.8 mg. Use the p-value method.

b) Repeat the test using the critical value method.

c) What is the probability of a type I error in this test?

Answer 1

null hypothesis: HO:		μ	=	22.8
Alternate Hypothesis: Ha:		μ	<	22.8

since p value is less than 0.05 we reject null hypothesis and conclude that the mean tar content of filtered 100-mm cigarettes is smaller than the mean tar content of brand B

b)

for 0.05 level with left tailed test and n-1= 24 degree of freedom, critical value of t=					1.711
Decision rule :                   reject Ho if test statistic t<-1.711

since test statistic -10.135 falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that the mean tar content of filtered 100-mm cigarettes is smaller than the mean tar content of brand B

c) type I error =significance level =0.05