The mean tar content of a simple random sample of 25 unfiltered​ king-size cigarettes is 21.4 ​mg, with a standard deviation of 4 mg. The mean tar content of a simple random sample of 25 filtered​...


The mean tar content of a simple random sample of 25 unfiltered​ king-size cigarettes is 21.4 ​mg, with a standard deviation of 4 mg. The mean tar content of a simple random sample of 25 filtered​ 100-mm cigarettes is 13.1 mg with a standard deviation of 3.8 mg. The accompanying table shows the data. Assume that the two samples are independent simple random samples selected from normally distributed​ populations, and do not assume that the population standard deviations are equal. Let population 1 be unfiltered​ king-size cigarettes. Complete parts​ (a) through​ (c) below.


a. Use a 0.10 significance level to test the claim that unfiltered​ king-size cigarettes have a mean tar content greater than that of filtered​ 100-mm cigarettes. What does the result suggest about the effectiveness of cigarette​ filters?


Identify the null and alternative hypotheses.

The test statistic is?

The​ P-value is?



b. Construct an 80​% confidence interval estimate of the difference between the mean tar content of unfiltered​ king-size cigarettes and the mean tar content of filtered​ 100-mm cigarettes. Does the result suggest that​ 100-mm filtered cigarettes have less tar than unfiltered​ king-size cigarettes?


The 80​% confidence interval estimate is ?<>



Jun 05, 2022
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