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. What are the null and alternative​ hypotheses?

Answer 1

The null hypothesis is
`H_0: \sigma = 0.3`

The alternative hypothesis is
`H_1: \sigma \\eq 0.3`

Explanation:

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

At the null hypothesis, we test if the standard deviation is of 0.3, that is:

`H_0: \sigma = 0.3`

At the alternative hypothesis, we test if the standard deviation is different of 0.3, that is:

`H_1: \sigma \\eq 0.3`