Question

. A manufacturer of cigarettes wishes to test the claim that the variance of the nicotine content of cigarettes his company makes is .638 milligrams. The variance of 25 cigarettes is .930 milligrams. Test this claim at the alpha = .05 level.

Answer 1

A manufacturer of cigarettes wishes to test the claim that the variance of the nicotine content of cigarettes his company makes is = 0.638 milligrams. Also given that variance of n = 25 cigarettes is s² = 0.930 milligrams.

To test the hypothesis based on the given claim the hypotheses are:

Based on the hypothesis it will be a two-tailed test.

Rejection region:

At given significance level and given sample size n = 25, the critical values is calculated using the excel formula for the chi-square distribution which takes the significance level and the degree of freedom, df = n-1= 25-1 = 24.

The formula used is =CHISQ.INV(0.025, 24) AND =CHISQ.INV(0.975, 24), thus the critical values are:

12.401 and 39.364.

Thus reject Ho if the test statistic is less than 12.401 or greater than 39.364.

Test Statistic:

Conclusion:

Since the test statistic is not in the rejection region hence we failed to reject the null hypothesis and conclude that there is insufficient evidence to warrant the rejection of the claim.