TEST OF HYPOTHESIS FOR THE DIFFERENCE BETWEEN POPULATION PROPORTIONS

TEST OF HYPOTHESIS FOR THE DIFFERENCE BETWEEN POPULATION PROPORTIONS

Null & Alternative Hypothesis
Significance Level Of the Test	a	a	a
Test Statistics
p-value	Table IV	Table IV	Table IV
Decision

ACTIVITY

In the past decade intensive antismoking campaigns have been sponsored by both federal and private agencies. Suppose the American Cancer Society randomly sampled 1,500 adults in 1989 and then sampled 2,000 adults in 1999 to determine whether there was evidence that the percentage of smokers had decreased. The results of the two independent sample surveys are shown in the following table.

	1989	1999
Number of Observations	1,500	2,000
Number of Smokers	551	652

a. Use the data in the table to test the hypothesis that the proportion of smokers changed from 1989 to 1999. Carry out your test at a significance level of 0.05.

Step 1: Make sure that "Input" menu option is selected.
Step 2: Type "1989" in the "Sample 1 Label" box and "1999" in the "Sample 2 Label" box.
Step 3: Type "1500" in the "Sample 1 size" box and "2000" in the "Sample 2 size" box.
Step 4: Type ".367" in the "Sample 1 proportion" box and ".326" in the "Sample 2 proportion" box.
Step 5: Select the "Hypothesis test" from menu options.

The output will include: Sample sizes, Means, Proportions, Difference of proprtions, a 95% confidence interval for the difference between population proportions, and the results of the test.

Report the p-value of the test and present your conclusion.

b. Do this data indicate that the fraction of smokers decreased over this 10-year period? Use a significance level of 0.01.

Step 1: Make sure that "Input" menu option is selected.
Step 2: Type "1989" in the "Sample 1 Label" box and "1999" in the "Sample 2 Label" box.
Step 3: Type "1500" in the "Sample 1 size" box and "2000" in the "Sample 2 size" box.
Step 4: Type ".367" in the "Sample 1 proportion" box and ".326" in the "Sample 2 proportion" box.
Step 5: Select the "Hypothesis test" from menu options.Do not use the ouput yet.
Step 6: Click on the "Options" button on the upper right hand side of the window.
Step 7: Make sure that "Null hypothesis" box shows 0.0.
Step 8: Select "Greater than" option for the "Alt. hypothesis".
Step 9: Type "1.0" in the "Alpha" box.
Step 10: Click on the "OK" button.

Report the p-value of the test and present your conclusion.