1. Two large corporations, A and B, hire many new college graduates as accountants at entry-level positions. In 2009 the starting salary for an entry-level accountant position was $36,000 a year at both corporations. At each corporation, data were collected from 30 employees who were hired in 2009 as entry-level accountants and were till employed at the corporation five years later. The yearly salaries of the 60 employees in 2014 are summarized in the boxplots below.
(a) Write a few sentences comparing the distributions of the yearly salaries at the two corporations.
(b) Suppose both corporations offered you a job for $36,000 a year as an entry-level accountant.
(i) Based on the boxplots, give one reason why you might choose to accept the job at corporation A.
(ii) Based on the boxplots, give one reason why you might choose to accept the job at corporation B.
2. To increase business, the owner of a restaurant is running a promotion in which a customer’s bill can be randomly selected to receive a discount. When a customer’s bill is printed, a program in the cash register randomly determines whether the customer will receive a discount on the bill. The program was written to generate a discount with a probability of 0.2, that is, giving 20 percent of the bills a discount in the long run.However, the owner is concerned that the program has a mistake that results in the program not generating the intended long-run proportion of 0.2.
The owner selected a random sample of bills and found that only 15 percent of them received discounts. A confidence interval for p, the proportion of bills that will receive a discount in the long run, is 0.15±0.06.All conditions for inference were met.
(a) Consider the confidence interval 0.15±0.06.
(i) Does the confidence interval provide convincing statistical evidence that the program is not working as intended? Justify your answer.
(ii) Does the confidence interval provide convincing statistical evidence that the program generates the discount with a probability of 0.2 ? Justify your answer.
A second random sample of bills was taken that was four times the size of the original sample. In the second sample 15 percent of the bills received the discount.
(b) Determine the value of the margin of error based on the second sample of bills that would be used to compute an interval for p with the same confidence level as that of the original interval.
(c) Based on the margin of error in part (b) that was obtained from the second sample, what do you conclude about whether the program is working as intended? Justify your answer.
3. A shopping mall has three automated teller machines (ATMs). Because the machines receive heavy use, they sometimes stop working and need to be repaired. Let the random variable X represent the number of ATMs that are working when the mall opens on a randomly selected day. The table shows the probability distribution of X.
(a) What is the probability that at least one ATM is working when the mall opens?
(b) What is the expected value of the number of ATMs that are working when the mall opens?
(c) What is the probability that all three ATMs are working when the mall opens, given that at least one ATM is working?
(d) Given that at least one ATM is working when the mall opens, would the expected value of the number of ATMs that are working be less than, equal to, or greater than the expected value from part (b) ? Explain.
SECTION II, Part B部分