1. (10 pts) Studies show that drivers who use cell phones while driving increase their risk of an accident. In a sample of 371 cases of new drivers using a cell phone while driving, 24 resulted in a crash. Find a 99% confidence interval estimate of the true population proportion of new drivers who were in a crash while using their cell phone.
2. (5 pts) A medical center wants to estimate the mean time a staff member spends with each patient. How many people should they sample if the desired MOE equals 4 minutes at the 95% confidence level? Assume a population standard deviation of 10 minutes.
3. (15 pts) An auditor is tasked with evaluating the reimbursement for office visits to physicians paid by Medicare. The audit was conducted on a sample of 80 reimbursements where the average amount paid was $281.70 with a sample standard deviation of $59.55. At the 0.05 level of significance, is there evidence that the population mean reimbursement was different than $300.00?
4. (15 pts) A major home improvement store conducted its biggest brand recognition campaign with series of new TV ads featuring well-known entertainers. A key metric of success of the TV ads is the proportion of viewers who “like the ads a lot”. A study of 200 adults who viewed the ads reported that 54 indicated they “like the ads a lot”. The percentage of typical TV ads receiving the “like the ads a lot” score is believed to be 25%. Is there is evidence that the population proportion of “like the ads a lot” for the company’s ads is greater than 25% at a 0.01 level of significance. Solve using the p-value approach only.
5. (15 pts) Are American managers less motivated than Japanese managers? A randomly selected group of 25 American managers and 12 Japanese managers were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The average score for American managers was 65.7 with a sample standard deviation of 9.3. The average score for Japanese managers was 72.8 with a sample standard deviation of 6.1. At the 0.05 level of significance, is there evidence that American managers are less motivated than Japanese managers?
6. (15pts) The US Office of Management requires governement agencies to produce annual performance reports. The data below contains performance scores for five agencies for two consecutive years. Conduct a paired differences test to determine whether the true mean evaluation score of government agencies in year 2 exceeds the score form year 1.(Alpha = 0.05).
Agency Year 2 score Year 1 score
GSA 40 34
Agriculture 35 33
Social Security 33 33
USAID 42 32
Defense 32 17
7. (10 pts) A survey was given to determine whether hours of sleep per night are independent of age. The following table shows the results. Conduct a test of independence to determine whether hours of sleep are independent of age at the 0.05 level.
USE CHI SQUARE STAT = 8.92
. What is your conclusion?
Hours of sleep 39 or younger 40 or older
fewer than 6 58 66
6 – 6.9 60 47
7 – 7.9 47 55
8 or more 35 82
8. (15 pts) Reese’s Pieces candies come in three colors: brown, orange, and yellow. The overall proportions for the colors are 30% brown, 45% orange, and 25% yellow. In a sampling study, several bags of candy were opened and the following color counts were observed. Complete a Goodness of Fit test (alpha = 0.05) to determine if there is enough evidence to conclude that the overall proportions for the colors are not as stated above. SHOW YOUR WORK!!