Statistics: Calculating Confidence Intervals – #504


Question: Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal.

Nicotine (mg)
Filtered Kings Nonfiltered Kings
n1 = 21 n2 = 8
x1 = 0.94 x2 = 1.65
s1 = 0.31 s2 = 0.16

Refer to the sample results listed in the margin for the measure nicotine contents of randomly selected filtered and nonfiltered king-size cigarettes. All measurements are in milligrams, and the data are from the Federal Trade Commission.

a. Use a 0.05 significance level to test the claim that king-size cigarettes with filters have a lower mean amount of nicotine than the mean of nicotine in nonfiltered king-size cigarettes.

b. Construct a 90% confidence interval estimate of the difference between the two population means.

c. Do cigarette filters appear to be effective in reducing nicotine?

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