TEST OF HYPOTHESIS FOR THE DIFFERENCE BETWEEN POPULATION MEANS (PAIRED EXPERIMENTS)

TEST OF HYPOTHESIS FOR THE DIFFERENCE BETWEEN POPULATION MEANS (PAIRED EXPERIMENTS)

Null & Alternative Hypothesis
Significance Level Of the Test	a	a	a
Test Statistics
p-value	Table VI with d.f.=	Table VI with d.f.=	Table VI with d.f.=
Decision

If you have been given or calculated the sample mean and sample standard deviation together with the sample size for the differences between two treatments you can use the Statlets window presented below.

ACTIVITY

Eight pairs of slow learners with similar reading IQs are found, one member of each pair is randomly assigned to the standard teaching method while the other is assigned to the new method. The difference (New Method - Standard Method) in reading test scores for the eight subjects has a mean of 4.375, and a standard deviation of 1.685.

a. Use the data in the table to test the claim that these two methods produces different student learning outcome. Use a significance level of 0.05.

Step 1: Make sure that "Input" menu option is selected.
Step 2: Type "Difference" in the "Data label" box.
Step 3: Type "8" in the "Sample size" box.
Step 4: Type "4.375" in the "Sample mean" box.
Step 5: Type "1.685" in the "Sample standard deviation" box.
Step 6: Select the "t test" from menu options.

The output will include: Sample size, Mean difference, and Standard deviation of the difference, a 95% confidence interval for the population mean difference and the results of the test.

Report the p-value and interpret.

b. Do the data support the hypothesis that the population maen reading score for slow learners taught by the new method is greater than the mean reading score for those taught by the standard method? Use the significance level of 0.01.

Step 1: Make sure that "Input" menu option is selected.
Step 2: Type "Difference" in the "Data label" box.
Step 3: Type "8" in the "Sample size" box.
Step 4: Type "4.375" in the "Sample mean" box.
Step 5: Type "1.685" in the "Sample standard deviation" box.
Step 6: Select the "t test" from menu options.Do not use the ouput yet.
Step 7: Click on the "Options" button on the upper right hand side of the window.
Step 8: Make sure that "Null hypothesis" box shows 0.0.
Step 9: Select "Greater than" option for the "Alt. hypothesis".
Step 10: Type "1.0" in the "Alpha" box.
Step 11: Click on the "OK" button.

The output will include: Sample size, Mean difference, and Standard deviation of the difference, a 99% confidence interval for the population mean difference and the results of the test.

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