Question

a simple random sample of 28 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 0.16mg.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 0.20 mg, which is the standard deviation for unfiltered King size cigarettes

Answer 1

H₀: = 0.20

H₁: 0.20

The test statistic = (n - 1)s²/

                                 = 27 * (0.16)^2/(0.2)^2

                                 = 17.28

At alpha = 0.05, the critical values are = 14.5734

                                                              = 43.1945

Since the test statistic value lies between the critical values(14.5734 < 17.28 < 43.1945), so we should not reject the null hypothesis.

At 0.05 significance level there is not sufficient evidence to support the claim that the tar content of filtered 100-mm cigarettes has a standard deviation different from 0.20 mg,