Exam 19: Statistical Analysis Scenarios and Distributions

A Paso Robles wine producer wanted to forecast the cases of merlot wine sold. The number of cases of merlot wine sold in a 28-year period was collected. Which of the following would be the most appropriate analysis to perform?

A buyer for a manufacturing plant suspects that his primary supplier of raw materials is overcharging. In order to determine if his suspicion is correct, he contacts a second supplier and asks for the prices on various identical materials. He wants to compare these prices with those of his primary supplier. He collected data on 6 different materials from both suppliers. He believes that the differences are normally distributed. Which of the following tests will be the most appropriate?

A sample of 100 fuses from a very large shipment is found to have 10 that are defective. Based on this information, which of the following will you construct to learn about the proportion of fuses that are defective?

An economist is interested to see how consumption for an economy (in $ billions) is influenced by gross domestic product ($ billions) and aggregate price (consumer price index). Annual data from 30 years were collected. Which of the following would be the most appropriate analysis to perform?

A contractor wants to forecast the number of contracts in future quarters, using quarterly data on number of contracts during the 10-year period from 1997 to 2006. Which of the following would be the most appropriate analysis to perform?

A physician and president of a Tampa Health Maintenance Organization (HMO) are attempting to show the benefits of managed health care to an insurance company. The physician believes that certain types of doctors are more cost-effective than others. To investigate this, the president obtained independent random samples of 20 HMO physicians from each of 4 primary specialties - General Practice (GP), Internal Medicine (IM), Pediatrics (PED), and Family Physicians (FP) - and recorded the total charges per member per month for each. A second variable which the president believes influences total charges per member per month is whether the doctor is a foreign or USA medical school graduate. To investigate this, the president also collected data on 20 foreign medical school graduates in each of the 4 primary specialty types described above. So information on charges for 40 doctors (20 foreign and 20 USA medical school graduates) was obtained for each of the 4 specialties. Which of the following tests will be the most appropriate to find out if the primary specialty and the origin of medical school degree interact to affect the charges?

The quality control manager of Marilyn's Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the average number of chocolate chip parts per cookie is 1.. Suppose that the probability of a chocolate chip parts in a cookie is constant across cookies and the number of chocolate chip parts in one cookie is independent of the number in any other cookie. Which of the following distributions would you use to figure out the probability that any particular cookie being inspected has 4.0 chip parts?

Suppose the probability of producing a defective light bulb from a production line is the same over an interval of 90 minutes. Which of the following distributions would you use to figure out the probability that a defective light bulb will be produced in a 15 minutes interval?

The director of admissions at a state college is interested in seeing if admissions status (admitted, waiting list, denied admission) at his college is related to the type of community (urban, rural, suburban) in which an applicant resides. Which of the following tests will be the most appropriate?

The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test. She obtained the data on percentage of students passing the proficiency test (% Passing), daily average of the percentage of students attending class (% Attendance), average teacher salary in dollars (Salaries), and instructional spending per pupil in dollars (Spending) of 47 schools in the state. She believed that holding everything else constant, instructional spending per pupil had a positive but decreasing impact on percentage. Which of the following would be the most appropriate analysis to perform?

From an inventory of 48 new cars being shipped to local dealerships, corporate reports indicate that 12 have defective radios installed. Which of the following distributions would you use to figure out the probability that out of the 8 new cars it just received that, when each is tested, no more than 2 of the cars have defective radios?

An insurance company evaluates many variables about a person before deciding on an appropriate rate for automobile insurance. A representative from a local insurance agency selected a random sample of 100 insured drivers and recorded, X, the amount of claims each made in the last 3 years. A Pareto chart can be used to present this information.

An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. The airline will choose the package that bumps as few passengers, on the average, as possible during a month. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks. (A total of 20 weeks was included in the experiment.) Which of the following tests will be the most appropriate?

The weight of a randomly selected cookie from a production line can most likely be modeled by which of the following distributions?

An agronomist wants to compare the crop yield of 3 varieties of chickpea seeds. She plants all 3 varieties of the seeds on each of 5 different patches of fields. She then measures the crop yield in bushels per acre. Which of the following tests will be the most appropriate to find out if the different patches is advantageous in reducing the random error?

Suppose the probability of finding a bark beetles infested pine tree is the same anywhere over a piece of 100-acre national forest land. Which of the following distributions would you use to figure out the probability of finding a bark beetles infested pine tree in a piece of 10-acre national forest land?

A few years ago, Pepsi invited consumers to take the "Pepsi Challenge." Consumers were asked to decide which of two sodas, Coke or Pepsi, they preferred in a blind taste test. Pepsi was interested in determining what factors played a role in people's taste preferences. One of the factors studied was the gender of the consumer. Data on the percentage of men and women depicting preference for Pepsi were collected. Which of the following tests will you use to find out if there is any difference in preference between the different gender groups?

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Which of the following tests will you perform to help her make a decision?

Suppose students arrive at an advising office at a rate of 30 per hour. Which of the following distributions would you use to figure out the probability that the next two students will arrive 30 minutes apart?

A researcher randomly sampled 30 graduates, 18 males and 12 females, of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries. Statistics of the mean salaries of the females and males in the sample were computed. The sample standard deviations suggest that the variability of starting salaries of the two groups is almost the same. Suppose the starting salaries from both groups can be considered as normally distributed. Which of the following tests will be the most appropriate?