Here are some statistics questions (36) that I thought up for you Bill. I tried to include a good mix of hard and easy- randomly arranged, of course.
1. For a mound-shaped distribution, what is a decent way to estimate the standard deviation from the range?
2. If you were to do a test to see if Passing and Failing an examination were independent of Before and After applying a drug, what is the name of a test you would use?
3. If you wanted to see if a digital blood pressure cuff's results can be used in place of a traditional blood pressure cuff's results (ie. are "the same"), what statistic/test would you use?
4. Is it possible to have a two-sided alternative hypothesis for a test using the chi-square distribution?
5. Is it possible for degrees of freedom to be a non-integer?
6. P(x) = e^(a+bx)/[1+e^(a+bx)] is a linear model, true or false.
7. If two individual 2x2 tables in a chi-square test for independence showed non-significance, but the combined 2x2 table (ie, literally table 1 + table 2) showed significance, how would you interpret that?
8. Why is testing if the population correlation is 0 equivalent to testing if the population slope coefficient is 0?
9. If we only observe the outcomes from coin flipping (Heads = 1, Tails = 0): 1000100010101, what is the most sensible estimate of the probability of Heads? What general mathematical technique would you use here?
10. If I am studying bugs in a statistics class, what statistics am I studying?
11. What was the name of the person who gave an example of the correlation coefficients be the same for multiple sets of data, but their plots looking completely different?
12. If X's are distributed normally, what do you do to them to get to a log-normal distribution?
13. If X and Y are individually distributed as chi-squares, what do you do to them to get to a F distribution?
14. If X and Y are individually distributed normally, what do you do to them to get to Cauchy?
15. How do you transform between a similarity measure and a distance measure?
16. If X's are distributed as an Exponential, what do you do to them to get to a Double Exponential?
17. Are partial derivatives important in asymptotic normality? If so, how?
18. What are the conditions for a distribution belonging to the Regular Exponential Family?
19. How do you determine if a statistic, T(
x), is sufficient for estimating, say, the parameter, theta?
20. Why is ancillarity important in theoretical statistics?
21. Canberra and Bhattacharyya formulas are used for...?
22. What is a sensible plotting technique in a repeated measure analysis?
23. Why is the F distribution called an F distribution?
24. Let's say forty subjects are randomly assigned to four treatment groups, ten to each group. Three responses are measured on each subject. What specific distribution would you use to draw inferences about the differences between means in the different treatment groups?
25. Who worked with the quincunx?
26. Does this make sense: "The probability of the population mean being in the interval [26.4, 28.8]mg's is 95%"?
27. What statistician had a ladder?
28. What are the differences between a confidence interval, prediciton interval, and a statistical tolerance interval?
29. Is a MVUE accurate, or precise?
30. For what distributions is range/SD >= sqrt(2) ?
31. How do you interpret: "The Pearson correlation coefficient of age and gender is .96."
32. What is the average of a dataset with n elements if you repeatedly take a 1st level Winsorized mean?
33. Why do we worry about S (the sample standard deviation)? Why not just focus on S^2?
34. If X_i = K*Y_i+C, then what is the mean and the standard deviation of X?
("_i" is a subscript)
35. What is the general name for the mean of the means?
36. Show mathematically that for a standard normal random variable Z, that the variance of Z is 1.