INFERENCE ON DIFFERENCE BETWEEN POPULATION MEANS

TEST OF HYPOTHESIS FOR THE DIFFERENCE BETWEEN POPULATION MEANS (INDEPENDENT SAMPLES)

Population Standard Deviations Unknown-Small Samples

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 only the sample means and standard deviations for the two independent samples together with the sample sizes you can use the Statlets window at the end of this page.

ACTIVITY

Suppose that you wish to compare a new method of teaching reading to "slow learners" to the current standard method. You decide to base this comparison on the results of a reading test given at the end of a learning period of 6 months. Of a random sample of 22 slow learners, 10 are taught by the new method and 12 are taught by the standard method. The summary statistics for these two independent samples are given below:

	Number of Obs.	Mean	Standard Deviation
New Method	10	76.4	5.83476
Standard Method	12	72.3	6.34369

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 "New Method" in the "Sample 1 Label" box and "Standard Method" in the "Sample 2 Label" box.
Step 3: Type "10" in the "Sample 1 size" box and "12" in the "Sample 2 size" box.
Step 4: Type "76.4" in the "Sample 1 mean" box and "72.3" in the "Sample 2 mean" box.
Step 5: Type "5.83476" in the "Sample 1 standard deviation" box and "6.34369" in the "Sample 2 standard deviation" box.
Step 6: Select the "t test" from menu options.

The output will include: Sample size, Mean difference (New Method - Standard Method), 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 "New Method" in the "Sample 1 Label" box and "Standard Method" in the "Sample 2 Label" box.
Step 3: Type "10" in the "Sample 1 size" box and "12" in the "Sample 2 size" box.
Step 4: Type "76.4" in the "Sample 1 mean" box and "72.3" in the "Sample 2 mean" box.
Step 5: Type "5.83476" in the "Sample 1 standard deviation" box and "6.34369" in the "Sample 2 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 (New Method - Standard Method), 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.