This set of problems is due at the beginning of class, Wednesday, 6 February.

Note: You do not have to show the R commands you use to solve the following problems. However, you do need to print out any graphical results, and label them appropriately. Moreover, for any hypothesis test, you must state the null hypothesis you are testing, define all parameters or random variables that you use, state the p-value for the test, and state what conclusion you may draw from the test.

Problems from Chapter 2: 2.51, 2.54, 2.85

And:

1. Suppose Talia claims to have ESP. To test her claim, researchers use a deck of five cards, each of which has a different image drawn on it. As an assistant concentrates on one of the cards (out of Talia's sight), Talia is asked to identify the card. Suppose the test is repeated 200 times.
   1. What should be the null hypothesis for this test?
   2. What would you use for a test statistic?
   3. What is the p-value of the test if she identifies 61 cards correctly?
   4. How many cards should she be required to identify correctly so that the test has a significance level as close as possible to 0.05?
   5. Plot the power function of the test using the criterion found in d.
2. In a 1958 study on the smoking habits of twins, R. A. Fisher classified 53 monozygotic (identical) twins and 18 dizygotic (fraternal) twins as having either alike or not alike smoking habits. His results were as follows:

Test the hypothesis that the rate of “alike” smoking habits is the same among monozygotic twins as it is among dizygotic twins.