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Confidence Intervals for the Difference of Two Means

Example:
A new peer tutorial program is implemented in the mathematics department of a middle school. Two groups of similar students are used to test the effectiveness of the program. One group uses the tutorial program and the other group uses a traditional study method. After 9 weeks with this arrangement both groups take the same test with the following results:

sample mean standard deviation

Traditional Group 19 73.2 9.1

Peer Tutoring Group 23 78.9 5.7

Use a 95% confidence interval to estimate the improvement in scores when the peer tutoring method is used. Find the 95% confidence interval of the population if the population standard deviations of group are same as sample.

Solution:
Now since you have two different sample, you can use 2-sample t interval. From the statistical data list, press "F4" (INTR), then press "F2" (t), and then press "F2" (2-S). Since you do not have the actual data list, select variable for the data type. Enter the confidence level, sample 1 mean, sample 1 standard deviation, sample 1 size, sample 2 mean, sample 2 standard deviation, sample 2 size. Pooling should be on when the variances are not significantly different; however, it is safe to choose the off option. Press "F1" (CALC) to calculate. You can use down button to see the complete information.

When you know the population standard deviations, you can use 2-sample Z interval. From the statistical data list, press "F4" (INTR), then press "F1" (Z), and then press "F2" (2-S). Choose variable for data type. Enter confidence level, population standard deviation of sample 1, population standard deviation of sample 2, sample 1 mean, sample 1 size, sample 2 mean, sample 2 size. Press "F1" (CALC) to calculate.

The 95% confidence interval of sample is about (0.79, 10.61). Although the interval predicts an increase in the test scores, it is so wide that it is difficult to predict the size of the increase. The 95% confidence interval of population is about (0.99, 10.41).