1. State the effect on the probability of a Type I and of a Type II error of:
(a) the difference between population means
(b) the variance
(c) the sample size
(d) the significance level
2. Suppose a new drug is discovered that improves digit span (the number of digits that can be remembered). The population mean digit span of people not taking the drug is 6.5, the population mean digit span of taking the drug is 7.8, and the standard deviation in both populations is 1.5. An experiment is conducted to establish the effectiveness of the drug. Twenty subjects are chosen at random and are divided randomly into two groups of 10. One group is given the new drug and the other group is given a placebo. A two-tailed t-test is conducted to test the null hypothesis that the drug has no effect. What is the probability that the test will be significant at the .05 level? What is the probability it will be significant at the .01 level?
3. A standardized achievement test has been known for years to have a population mean of 450. A researcher suspects that the mean has now dropped to 400. Assume the researcher is correct and that the
variance of the test is 10,000. What sample size would be required so that a two-tailed test at the .05 level would have a .80 probability of showing that the population mean is not 450? What sample size would be necessary for power of .80 if a one-tailed test (using the .05 level) were used?
4. For the experiment described in Problem 3, what would the power (using the .05 level) have been for a sample size of 25 if thee xperimenter had known that the population variance was 10,000 and therefore conducted a z test instead of a t test?
5. Two population means differ by 1.5 standard deviations. If nine subjects are sampled from each population, what is the chance that the means will be significantly different at the .01 level?
6. What is the most difficult step in estimating power?
7. Why do published experiments tend to contain overestimates of effect sizes?
8. An experiment is conducted in which 15 subjects are each tested in each of two conditions. The population mean of each condition, the sample size, and the variance of each condition are known. The scores are normally distributed. There is one piece of information missing without which power cannot be calculated. What is it?