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:

a. Use the data in the table to estimate the true mean difference between the test scores for the new method and the standard method. Use a 95% confidence interval.

• 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 sizes, Means, Differnece of Means, followed by 95% confidence interval for the population mean difference.

b. Find a 99% confidence interval by following the steps given below:

• 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.
• Step 7: Click on the "Options" button on the upper right hand side of the window.
• Step 8: Change only Alpha from 5.0 to 1.0.
• Step 9: Click on the "OK" button.

The output will include: Sample sizes, Means, Differnece of Means, followed by 99% confidence interval for the population mean difference.

c. By using your answers to a and b, what can you say about the effectiveness of the new method?