QNT 561 FINAL EXAM 1 – QUESTION AND ANSWERS

QNT 561 FINAL EXAM 1 – QUESTION AND ANSWERS 1. According to the central limit theorem, for samples of size 64 drawn from a population with µ = 800 and σ = 56, the mean of the sampling distribution of sample means would equal _______. a. 800 2. The empirical rule says that approximately what percentage of the values would be within 2 standard deviations of the mean in a bell shaped set of data? a. 95% 3. Ophelia O'Brien, VP of Consumer Credit of American First Banks (AFB), monitors the default rate on personal loans at the AFB member banks. One of her standards is "no more than 5% of personal loans should be in default." On each Friday, the default rate is calculated for a sample of 500 personal loans. Last Friday's sample contained 30 defaulted loans. Ophelia's null hypothesis is _______. a. P = 0.05 4. According to the central limit theorem, for samples of size 64 drawn from a population with µ = 800 and σ = 56, the standard deviation of the sampling distribution of sample means would equal _______. a. 7 5. The mean life of a particular brand of light bulb is 1200 hours and the standard deviation is 75 hours. Tests show that the life of the bulb is approximately normally distributed. It can be concluded that approximately 68% of the bulbs will last between _______. a. hours 6. A researcher wants to determine the sample size necessary to adequately conduct a study to estimate the population mean to within 5 points. The standard deviation of population values is 80 and the researcher plans to use a 90% level of confidence. The sample size should be at least _______. a. 693 7. If x is a binomial random variable with n=10 and p=0.8, the mean value of x is _____. a. 8 8. The mean life of a particular brand of light bulb is 1200 hours. If you know that at about 95% of this brand of bulbs will last between 1100 and 1300 hours, then what is the standard deviation of the light bulbs’ life? a. 50 9. Life tests performed on a sample of 13 batteries of a new model indicated: (1) an average life of 75 months, and (2) a standard deviation of 5 months. Other battery models, produced by similar processes, have normally distributed life spans. The 98% confidence interval for the population mean life of the new model is _________. a. 71.28 to 78.72 10. A large industrial firm allows a discount on any invoice that is paid within 30 days. Of all invoices, 10% receive the discount. In a company audit, 10 invoices are sampled at random. The probability that fewer than 3 of the 10 sampled invoices receive the discount is approximately_______________. a. 0.9298 11. The weight of a USB flash drive is 30 grams and is normally distributed. Periodically, quality control inspectors at Dallas Flash Drives randomly select a sample of 17 USB flash drives. If the mean weight of the USB flash drives is too heavy or too light the machinery is shut down for adjustment; otherwise, the production process continues. The last sample showed a mean and standard deviation of 31.9 and 1.8 grams, respectively. Using α = 0.10, the appropriate decision is _______. a. Reject the null hypothesis and shut down the process 12. Elwin Osbourne, CIO at GFS, Inc., is studying employee use of GFS e-mail for non-business communications. He plans to use a 95% confidence interval estimate of the proportion of e-mail messages that are non-business; he will accept a 0.05 error. Previous studies indicate that approximately 30% of employee e-mail is not business related. Elwin should sample _______ e-mail messages. a. 323 13. Completion time (from start to finish) of a building remodeling project is normally distributed with a mean of 200 work-days and a standard deviation of 10 work-days. To be 99% sure that we will not be late in completing the project, we should request a completion time of _______ work-days. a. 223 14. If x is a binomial random variable with n=10 and p=0.8, what is the probability that x is equal to 4? a. .0055 15. James Desreumaux, VP of Human Resources of American First Banks (AFB), is reviewing the employee training programs of AFB banks. His staff randomly selected personnel files for 100 tellers in the Southeast Region and determined that their mean training time was 25 hours. Assume that the population standard deviation is 5 hours. The 95% confidence interval for the population mean of training times is ________. a. 24.02 to 25.98 16. A large national company is considering negotiating cellular phone rates for its employees. The Human Resource department would like to estimate the proportion of its employee population who own an Apple iPhone. A random sample of size 250 is taken and 40% of the sample own and iPhone.. The 95% confidence interval to estimate the population proportion is _______. a. 0.34 to 0.46 17. Suppose a population has a mean of 400 and a standard deviation of 24. If a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean less than 402 is _______. a. 0.8413 18. Maureen McIlvoy, owner and CEO of a mail order business for wind surfing equipment and supplies, is reviewing the order filling operations at her warehouses. Her goal is 100% of orders shipped within 24 hours. In previous years, neither warehouse has achieved the goal, but the East Coast Warehouse has consistently out-performed the West Coast Warehouse. Her staff randomly selected 200 orders from the West Coast Warehouse (population 1) and 400 orders from the East Coast Warehouse (population 2), and reports that 190 of the West Coast Orders were shipped within 24 hours, and the East Coast Warehouse shipped 372 orders within 24 hours. Maureen's alternative hypothesis is _______. a. P1 – P2 > 0 19. A market research team compiled the following discrete probability distribution on the number of sodas the average adult drinks each day. In this distribution, x represents the number of sodas which an adult drinks. a. The mean (average) value of x is…..1.4 20. Catherine Chao, Director of Marketing Research, is evaluating consumer acceptance of a new toothpaste package. Her staff reports that 17% of a random sample of 200 households prefers the new package to all other package designs. If Catherine concludes that 17% of all households prefer the new package, she is using a. A point estimate. 21. The number of finance majors within the School of Business is an example of _______. a. A discrete random variable. 22. The normal distribution is used to test about a population mean for large samples if the population standard deviation is known. "Large" is usually defined as _______. a. At least 30 23. The following frequency distribution was constructed for the wait times in the emergency room. a. b. Skewed to the left 24. Medical Wonders is a specialized interior design company focused on healing artwork. The CEO, Kathleen Kelledy claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay. Her current client is a children’s cancer hospital. Kathleen is interested in determining the effect of three different pieces of healing artwork on children. She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting. Kathleen's null hypothesis is _____________. a. µ1 = µ2 = µ3 25. The number of bags arriving on the baggage claim conveyor belt in a 3 minute time period would best be modeled with the _________. a. Poisson distribution 26. Consider the following null and alternative hypotheses. Ho: µ ≤ 67 Ha: µ > 67 These hypotheses _______________. a. Indicate a one-tailed to the right 27. The number of cars arriving at a toll booth in five-minute intervals is Poisson distributed with a mean of 3 cars arriving in five-minute time intervals. The probability of 5 cars arriving over a five-minute interval is _______. a. 0.1008 28. A market researcher is interested in determining the average income for families in San Mateo County, California. To accomplish this, she takes a random sample of 300 families from the county and uses the data gathered from them to estimate the average income for families of the entire county. This process is an example of _______. a. Inferential statistics 29. The expected (mean) life of a particular type of light bulb is 1,000 hours with a standard deviation of 50 hours. The life of this bulb is normally distributed. What is the probability that a randomly selected bulb would last fewer than 940 hours? a. 0.1151 30. Lucy Baker is analyzing demographic characteristics of two television programs, American Idol (population 1) and 60 Minutes (population 2). Previous studies indicate no difference in the ages of the two audiences (The mean age of each audience is the same.) Lucy plans to test this hypothesis using a random sample of 100 from each audience. Her null hypothesis is ____________. a. µ1 - µ2 = 0