## Homework

22 May

#### Question 2 (Essay Worth 1 points)

In a study of heart surgery, one issue was the effect of drugs called beta-blockers on the pulse rate of patients during surgery. The available subjects were divided at random into two groups of 30 patients each. One group received a beta-blocker; the other, a placebo. The pulse rate of each patient at a critical point during the operation was recorded. The treatment group had mean 65.2 and standard deviation 7.8. For the control group, the mean was 70.3 and the standard deviation was 8.3.

(a) Do beta-blockers reduce the pulse rate at the 5% level? At the 1% level? Carry out a complete test.

(b) Give a 99% confidence interval for the difference in mean pulse rates.

#### Question 3 (Essay Worth 1 points)

In a study of cereal leaf beetle damage on oats, researchers measured the number of beetle larvae per stem in small plots of oats after randomly applying one of two treatments: no pesticide or Malathion at the rate of 0.25 pound per acre.

Is there significant evidence at the 1% level that the mean number of larvae per stem is reduced by Malathion? Carry out a complete test.

Question 4 (Essay Worth 1 points)

A bank compares two proposals to increase the amount that its credit card customers charge on their cards. (The bank earns a percentage of the amount charged, paid by the stores that accept the card.) Proposal A offers to eliminate the annual fee for customers who charge \$2400 or more during the year. Proposal B offers a small percent of the total amount charged as a cash rebate at the end of the year. The bank offers each proposal to an SRS of 150 of its existing credit card customers. At the end of the year, the total amount charged by each customer is recorded. Here are the summary statistics:

 Group n x s A 150 \$1987 \$392 B 150 \$2056 \$413

1. a) Do the data show a significant difference between the mean amounts charged by customers offered the two plans? Carry out a complete test.
2. b) The distributions of amounts charged are skewed to the right, but outliers are prevented by the limits that the bank imposes on credit balances. Do you think that skewness threatens the validity of the test? Explain your answer.