## Inferences about Two Populations Two Sample T-Interval

The following results were gathered independently from two different colleges in Florida. The number of hours spent studying for the Statistics Final Exam. are shown below:

Give the point estimate of the difference between the two means, and develop a 98% confidence interval for the difference between the two means.

For this problem we will use a two sample T-interval since n1 < 30, n2 < 30. Again we will start from the "TESTS" menu. Press

Arrow right to "TESTS" and choose "0: 2-SampTInt..." (see screen below)
Press ( see lower left screen)

Once again we will highlight "Stats" and press (see screen above)

There is one new line on this menu. It is " Pooled : No Yes " Pooled or non-pooled is based on equal or not equal population variances. There is a test for this assumption:

This test can be performed on the TI-83PLUSPlus. First go to the tests menu by pressing and choose option "D: 2-SampFTest...". You will have the same choices as with any of the tests. We will highlight Stats for this problem since we are entering the statistics ourselves. Match your screen to this problemÕs statistics and ALWAYS highlight and press at the test line. Arrow down to calculate and press As you can see from your screen the p-value is .5694 . We would reject Ho only if p < . At 98% CI the a = .02. Therefore this p-value is not less than so we can not reject Ho. Therefore we should assume equal variances which means we will choose "pooled", so highlight "Yes" for the 2-SampleTInv, and press

Arrow down to "Calculate" and press (this screen will appear)

As you can see from the screen the Interval estimate of the difference is ( -.412 , 5.212 ). We can also calculate the point estimate of the difference from this screen. It is 22.5 Š 20.1 which is 2.5