A cigarette manufacturer wants to test the claim that the variance of the nicotine content of its cigs. is 0.644 milligram. Assume that it is normally distributed. A sample of 20 cigs. has a std. dev. of 1.00 milligram. At a = 0.05, is there ample evidence to reject the manufacturer’s claim?
Solution: We need to test the following null and alternative hypotheses
We will use a Chi-Squared test to check the null hypothesis. The Chi-Square statistics is defined as
The critical values for the two-tailed test are equal toand for 19 degrees of freedom, . That means that, and therefore, we don’t have enough evidence to reject the null hypothesis, which means that we reject the claim.