11. How many degrees of freedom did STUDY A have?

12. How many degrees of freedom did STUDY B have?

13. What was the effect size of STUDY A?

14. What was the effect size of STUDY B?

15. What is the statistical power of STUDY A? (Bonus: How many additional subjects would be required to reach a minimum power of 0.80 for this study?)

16. What is the statistical power of STUDY B? (Bonus: How many additional subjects would be required to reach a minimum power of 0.80 for this study?)

17. Based of this comparison of STUDY A and STUDY B, which type of experimental design would you prefer for testing the memory effects of IGF2?

Consider the following study that is being planned:

·      μ = 95, σ = 4, predicted mean = 98, N = 30, α = .01, two-tailed test

a. Compute the effect size

b. Compute the power

c. If you wanted to plan a study with the conventional minimum power, what is the best variable to change in order to increase power?

Use the following scenario for questions 6 – 8. In 2016-17, the average SAT score of the UVA first year class was 1420 out of 1600. An advisor in the statistics department is interested in determining whether statistics majors from that class have higher SAT scores than the average. He tests H,:µ = 1420 against Hạ: µ > 1420, where u is the mean SAT score for statistics majors from the 2016-17 first year class. In a simple random sample of 30 statistics majors, he finds a sample mean SAT score of 1440 with sample standard deviation of 40.

6. What is the value of the test statistic for this significance test?

a. 0.09

b. 0.5

c. 2.73

d. 20

7. From what distribution is this test statistic?

a. N(0, 1)

b. N(1420, 7.30)

c. t distribution with 29 degrees of freedom

d. t distribution with 28 degrees of freedom

8.) The p-value for this test is 0.005. Which of the following is a proper interpretation of this p- value?

a.There is a 0.5% chance that the null hypothesis is true.

b. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample a. mean SAT score from 30 statistics majors would equal 1440.

c.If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or lower.

d. If the population mean SAT score really is 1420, there's a 0.5% chance that the sample mean SAT score from 30 statistics majors would be 1440 or higher.

Suppose you are evaluating a grant proposal. The proposer seeks $250,000 to conduct a series of experiments on patients with a rare kind of brain lesion. Let's say the proposer will measure ability to remember lists of words in the experiment. A very interesting and provocative theory, described clearly in the proposal, predicts that the brain-damaged people should actually remember slightly better than the control group, and so the investigator proposes an experiment to test this prediction. A pilot study shows that among normals, the mean number of words remembered (from a list of 20) is 12.2, and the standard deviation is 3.1. (The SD in the lesion group could be assumed to be bigger, but we'll just assume that it's the same.) The investigator explains that a pool of 24 subjects with brain lesions is already available from a local clinic for the braindamaged group. Suppose that you, as a reviewer of the proposal, want a power of .80 in proposed experiments. What effect size would be required to generate this power? (Assume a Type I error rate, i.e. alpha, of 0.05.) Suppose that the effect size is actually 0.2 (small, as predicted by the proposed theory). What sample size would be needed to achieve a power of .80? (Should you fund the proposal?)