Question

A simple random sample of 29 filtered 100-mm cigarettes is obtained from a normally distributed population, and the tar content of each cigarette is measured. The sample has a standard deviation of 0.220.22mg. Use a 0.05 significance level to test the claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.35 mg, which is the standard deviation for unfiltered king-size cigarettes. Complete parts (a) through (d) below.

a) find the test statistic.

b) find the p-value of the test statistic

Answer 1

given data are:-

sample size (n) = 29

sample sd (s) = 0.22

hypothesized sd () = 0.35

level of significance () = 0.05

hypothesis:-

a).test statistic be:-

degrees of freedom = (n-1) = (29-1) = 28

b).p value = 0.0035

[ using minitab for df = 28, chi square = 11.063, both tailed test]

you can also use p value calculator .

decision:-

p value = 0.0035 < 0.05

so, we reject the null hypothesis.

we conclude that,

there is sufficient evidence at 0.05 significance level to claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.35 mg