Conduct a test using a significance level of 𝛼=0.05.

Question

The nicotine content in cigarettes of a certain brand is normally distributed with mean (𝜇) and standard deviation 𝜎= 0.1. The brand advertises that the mean nicotine 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 15 cigarettes of this brand. The sample yields an average of 1.4 mg of nicotine. Conduct a test using a significance level of 𝛼=0.05.

(a) The test statistic:

(b) The critical value, z* =

Answer 1

z = (sample mean - population mean)/(standard deviation/sqrt(sample size))

This is a right side test so critical value is z* corresponding to 0.95 probability (1.645).

Because the sample mean is less than the population mean there is no way that it will be determined that the mean nicotine level is higher than advertised.