# A cigarette manufacturer wants to test the claim that the variance of the nicotine content of its cigs

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 to_{}and_{} 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.

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