1 Find 95 confidence intervals for samples of size 10 30 and

1) Find 95% confidence intervals for samples of size 10, 30, and 100.

2) Find 99% confidence intervals for the same samples used in problem 1.

3) Recall that the true population mean is 29.959. Which confidence intervals do not contain the true mean?

4) Suppose the researchers wish to perform a hypothesis test to determine whether the true mean is greater than 22, sing each of the samples from problem 1

5) Choose one of your 95% confidence intervals (make sure you specify which one you choose). Interpret it.

6) Using the same sample you chose in problem 5, interpret the corresponding 99% confidence interval.

7) Choose a p-value (specify which). Interpret it. Note: Interpreting the p-value is different than using it to make a conclusion. Try to tell me what the p-value means in context of the problem.

8) Use the p-values from each of the samples to make a reject/FTR decision at both the 0.01 and the 0.05 significance levels. Interpret (at least) one of these decisions in terms of the problem.

9) Which of the hypothesis tests is the most reliable? Are any of the tests completely unreliable? How do you know?

10) Recall that we know the true population mean. Did any hypothesis test(s) result in an error? Which one(s)? Are they Type I or Type II errors?

Solution