Question

A simple random sample of 49 filtered 100-mg cigarettes are obtained, and the tar content of each cigarette is measured. The sample has a standard deviation of 3.7mg. Use a 0.10 significance level to test the claim that the tar content of filtered 100-mg cigarettes has a standard deviation different from 3.2 mg, which is the standard deviation for unfiltered cigarettes.

Answer 1

Solution:

Solution:

Here, we have to use chi square test for population standard deviation.

Null hypothesis: H₀: the tar content of filtered 100-mg cigarettes has a standard deviation of 3.2 mg.

Alternative hypothesis: H_a: the tar content of filtered 100-mg cigarettes has a standard deviation different from 3.2 mg.

H₀: σ = 3.2 versus H_a: σ ≠ 3.2

This is a two tailed test.

We assume that the sample is come from normally distributed population.

The test statistic formula is given as below:

Chi square = (n – 1)*S^2/σ^2

We are given n = 49, S = 3.7

df = n – 1 = 49 – 1 = 48

Chi square = (49 - 1)*3.7^2/3.2^2

Chi square = 64.17188

P-value = 0.0592

(by using chi square table)

P-value < α = 0.10

So, we reject the null hypothesis

There is sufficient evidence to conclude that the tar content of filtered 100-mg cigarettes has a standard deviation different from 3.2 mg.