1. Section 3.1, Exercise 1 It is known that 20% of a certain species of insect exhibit a particular characteristic A. Eighteen insects of that species are obtained from an unusual environment and none have characteristic A. Is it reasonable to assume that insects from that environment have the same probability of 0.20 that the species in general has? Use a two-tailed test.

2. Section 3.1, Exercise 5 Twenty independent observations on a random variable X with the unknown distribution function F(x) resulted in the following numbers:

142 134 98 119 131 103 154 122 93 137 86 119 161 144 158 165 81 117 128 103

Find a 95% confidence interval for F(100).

3. Section 3.1, Exercise 6 (reworded slightly from book) A civic group reported to the town council that at least 60% of the town residents were in favor of a particular bond issue. The town council then asked a random sample of 100 residents if they were in favor of the bond issue. Forty-eight said yes. Test whether there is sufficient evidence to doubt the report and conclude the percent favoring the bond is actually lower than 60%.

4. Section 3.1, Exercise 10 (reworded slightly from book) Twenty Texas Tech law school graduates took the bar exam and 18 of them passed. If this represents a random sample of all Texas Tech law graduates, is this sufficient evidence to conclude that the probability of a Texas Tech law school graduate passing the law exam is higher than the state average, which is 70%?

5. Section 3.1, Exercise 11 (reworded slightly from book) Twenty torpedoes are released in an underwater war exercise. Fifteen of them hit their target. Find a 90% confidence interval for the probability of a torpedo hitting the target. (a) solve this problem. (b) Use the large sample approximation to solve this problem. (c) Discuss the assumptions you are making in this problem.

6. Section 2.4 Exercise 1 (reworded slightly from book) A coin is tossed 5 times. At each toss the experimenter observes whether it is a head or a tail, and a blindfolded subject being tested for extrasensory perception "states" whether it is a head or a tail. The null hypothesis is that the subject's predictions have probability of p=0.5 being correct, while the alternative hypothesis is that p>0.50. The null hypothesis is rejected if all 5 predictions are correct. (a) Find the significance level, alpha. (b) What is the power function? (c) Draw a graph of the power function. (d) Is the test unbiased?

7. Section 2.4, Exercise 2 (reworded slightly from book) Two types of shoe leather are being tested to see which is more durable. Eight pairs of shoes are made. The shoes seem to be identical except that one shoe is made from leather A and the other from leather B. These shoes are subjected to normal wear for a period of time and are then judged as to which leather seemed to be more durable for each pair. Let X equal the number of pairs of shoes where leather A is judged to be more durable. The null hypothesis is that p=0.5, where p is the probability that the shoe made out of leather A was more durable than the other shoe, while H1 is p0.5. The critical region corresponds to X=0,1,7,8. (i.e., reject H0 if X1 or X7). (a) Find the significance level, alpha. (b) What is the power function? (c) Draw a graph of the power function. (d) Is the test unbiased?

8. Section 2.4, Exercise 3 Let T1, T2,... represent a sequence of tests and suppose the power of Tn is given by n/(n+10). Is the sequence of tests consistent?

9. Section 2.4, Exercise 4 Let T1, T2,... represent a sequence of tests and suppose the power of Tn is given by n/(2n+10). Is the sequence of tests consistent?

10. Section 2.4, Exercise 6 The hypothesis H0: p=0.5 is being tested against H1: p 0.5 using two tests at the same level of significance. T2 needs a sample size of 30 when T1 has a sample size 15 in order for their power functions to be equal at the particular alternative p=1/3. (a) What is the efficiency of T2 relative to T1? (b) Is the efficiency necessarily the same at the alternative p=2/3?