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Name: The mean tar content of a simple random sample of 25 unfiltered king-
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Description: 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 deviatio

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 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 ?<μ1−μ2<?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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