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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?

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Answer:

The null hypothesis is [tex]H_0: \sigma = 0.3[/tex]

The alternative hypothesis is [tex]H_1: \sigma \neq 0.3[/tex]

Step-by-step 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:

[tex]H_0: \sigma = 0.3[/tex]

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

[tex]H_1: \sigma \neq 0.3[/tex]

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