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.

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cigarettes has a mean nicotine content of more than 16 mg?
c)What is a mean nicotine content for lowest 3% of all
cigarettes?
d) What is the probability randomly chosen cigarette has a nicotine
content greater than...

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