Question

(1 point) The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) u and standard deviation o= 0.1. The brand advertises that the mean nicotine content of their cigarettes is 1.5 mg. Now, suppose a reporter wants to test whether the mean nicotine content is actually higher than advertised. He takes measurements from a SRS of 20 cigarettes of this brand. The sample yields an average of 1.55 mg of nicotine. Conduct a test using a significance level of a = 0.05. (a) The test statistic (b) The critical value, z* = (c) The final conclusion is A. There is not sufficient evidence to show that the ad is misleading. B. The nicotine content is probably higher than advertised.

Answer 1

Solution :

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$    / $\sqrt$ n

= (1.55 - 1.5) / 0.1 / $\sqrt$ 20

= 2.24

Test statistic = 2.24

Critical value = 1.645

B. The nicotine content is probably higher than advertised.