Question

# The nicotine content in cigarettes of a certain brand is normally distributed with mean (in milligrams)...

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.

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.

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