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?
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?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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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
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 ?<μ1−μ2<?
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