Problem

A simple random sample of 26 filtered $100-\mathrm{mm}$ cigarettes is obtained from a normally distributed population, and the tar content of each cigarette is measured. The sample has a standard deviation of $0.20 \mathrm{mg}$. Use a 0.05 significance level to test the claim that the tar content of filtered $100-\mathrm{mm}$ cigarettes has a standard deviation different from $0.30 \mathrm{mg}$, which is the standard deviation for unfiltered king-size cigarettes. Complete parts (a) through (d) below. b. Find the test statistic. $\chi^{2}=\square$ (Round to three decimal places as needed.)

Solution

Step 1 :Given that the sample size (n) is 26, the sample standard deviation (s) is 0.20 mg, and the hypothesized population standard deviation (σ) is 0.30 mg.

Step 2 :The test statistic for a chi-square test for a single variance is given by the formula: \(\chi^{2} = \frac{(n - 1)s^{2}}{\sigma^{2}}\)

Step 3 :Substitute the given values into the formula: \(\chi^{2} = \frac{(26 - 1)(0.20)^{2}}{(0.30)^{2}}\)

Step 4 :Simplify the expression to find the test statistic.

Step 5 :Final Answer: The test statistic is \(\boxed{11.111}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8243/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download