William H. Knapp III

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This homework was due on Wednesday, November 14 at 06:00 a.m. Turkish time. Late submissions receive half credit.

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1. When two independent samples are drawn, when is it reasonable to pool the unbiased estimates of the population variance into a single estimate.
When the populations from which the samples are drawn are assumed to have the same variance.
When the populations from which the samples are drawn are normally distributed.
When the sample sizes are both greater than 30.
When the samples are drawn from the same populations.

2. To pool the unbiased variance estimates for two equal sample sizes, one can just take the mean of the two estimates.
True.
False.

3. To pool the unbiased variance estimates for two unequal sample sizes, what should one do?
One should just take the mean of the two estimates.
One should multiply each estimate by the corresponding degrees of freedom and divide the sum of the weighted estimates by the sum of the degrees of freedom.
One should multiply each estimate by the corresponding degrees of freedom and divide the sum of the weighted estimates by the sum of the sample sizes.
One should multiply each estimate by the corresponding sample size and divide the sum of the weighted estimates by the sum of the sample sizes.

4. For the next set of questions, please use the following two samples.
Sample 1: n=15, mean=68, unbiased variance estimate (later referred to as UVE)=113.
Sample 2: n=37, mean=71, UVE=139.
If you wanted to create a 95% confidence interval for the population mean estimated by sample 1, how many degrees of freedom should you use?

5. What's the standard error of the mean for the first sample?

6. What's the standard error of the mean for the second sample?

7. What's the pooled variance estimate?

8. What's standard error of the difference between means?

9. How many degrees of freedom should we use if we want to perform a t-test on the difference between the means?

10. Use an alpha of .05. If your null hypothesis is that the 2 population means are equal, what is your upper critical t?

11. What is the t for the difference between the means you observed given the null hypothesis? To make sure we get the same answers in this and the following questions, subtract the second mean from the first in your calculation.

12. What's the p-value for your observed t given the null hypothesis?

13. What should you do?
Fail to reject the null.
Reject the null.
Not enough information to tell.

14. If you were going to create the smallest 99% confidence interval around the difference you observed, what would your upper limit be?

15. If you were going to create the smallest 99% confidence interval around the difference you observed, what would your lower limit be?

16. Use an alpha of .05. If your null hypothesis is that mean second population is greater than or equal to 10 more than the first, what is your critical t? (Hint, there's only 1 critical t for this hypothesis.)

17. What is the t for the difference between the means you observed given the null hypothesis?

18. What's the p-value for your observed t given the null hypothesis?

19. What should you do?
Fail to reject the null.
Reject the null.
Not enough information to tell.

20. If you were going to create the smallest 99% confidence interval around the difference you observed, what would your upper limit be?