Question

The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams) μ and standard deviation σ=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 10 cigarettes of this brand. The sample yields an average of 1.55 mg of nicotine. Conduct a test using a significance level of α=0.05.

(a) The test statistic

(b) The critical value, z* =

(c) The final conclusion is

A. The nicotine content is probably higher than advertised.
B. There is not sufficient evidence to show that the ad is misleading.

Answer 1

Given that, population standard deviation σ = 0.1

sample size ( n ) = 10

sample mean = 1.55 mg

significance level of α = 0.05

The null and the alternative hypotheses are,

a) Test statistic is,

Test statistic = 1.58

b) The critical value at  significance level of α = 0.05 is,

Z^* = 1.645

c) Since, test statistic = 1.58 < 1.645

we fail to reject the null hypothesis.

The final conclusion is, there is not sufficient evidence to show that the ad is misleading.