12. Hypothesis Test for Cigarette Tar. Refer to the sample data, below, and use

Question

12. Hypothesis Test for Cigarette Tar. Refer to the sample data, below, and use a 0.05 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?

The mean tar content of a simple random sample of 25 unfiltered king size cigarettes is 21.1 mg, with a standard deviation of 3.2 mg. The mean tar content of a simple random sample of 25 filtered 100 mm cigarettes is 13.2 mg with a standard deviation of 3.7 mg (based on data from Data Set 4 in Appendix B). Construct a 90% 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?

Explanation / Answer

If you have a TI-83/84, press STAT -> TESTS -> T-Test, then select STATS, MU0 is 21.1, x-bar is 18.8, Sx is 3.45, n is 25, then select the LESS THAN option, then select CALCULATE. You will see the answers to TEST statistic and P-Value. To find the critical value, look in your t-table in the df=24 row. Because it's a one-tailed test, all of alpha (.05) is contained in one tail. Hope that helps!

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