Question

A simple random sample of 27 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 0.20 mg. 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 0.30 mg, which is the standard deviation for unfiltered​ king-size cigarettes. Complete parts​ (a) through​ (d) below.

A. Identify the null and alternative hypotheses for this test.

B. Identify the test statistic for this hypothesis test.

C. Identify the​ P-value for this hypothesis test.

D. Identify the conclusion for this hypothesis test.

Answer 1

A.

Claim the tar content of filtered​ 100-mm cigarettes has a standard deviation different from 0.30 mg

Hypothesized population standard deviation : = 0.30

Null hypothesis :

Alternate hypothesis :

Two tailed test

B.

s : sample standard deviation : 0.20

n : sample size = 27

C.

for two tailed test :

Degrees of freedom = n-1 =27-1 =26

For 26 degrees of freedom ;

D.

Level of significance = 0.05

As P-Value is less than Level of significance i.e (P-value:0.0132 < 0.05:Level of significance); Reject Null Hypothesis

There is sufficient evidence to conclude that the tar content of filtered​ 100-mm cigarettes has a standard deviation different from 0.30 mg