Exam 19: Statistical Analysis Scenarios and Distributions

Data on the amount of time spent studying for a particular exam at a high school were collected for 150 students. You want to know half of the students spent at least how much time studying for that exam. Which of the following would you compute?

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. The president has already found out that specialty types and origin of the medical degree do not interact to affect the charges. He has also found out special types do have an impact on average charges. Which of the following tests will be the most appropriate to find out which primary specialty has the highest charges?

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 15 insured drivers and recorded the amount of claims each made in the last 3 years. Based on this information, which of the following will you construct to learn about the average amount of claims made by the company's customer?

A political pollster randomly selects a sample of 100 voters each day for 8 successive days and asks how many will vote for the incumbent. The pollster wishes to see if the percentage favoring the incumbent candidate is too erratic. Which of the following would be the most appropriate analysis to perform?

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. She has found out that the different varieties do have an impact on crop yield. Which of the following tests will be the most appropriate to find out which variety will produce the highest yield?

Data on the amount of money made in a year by 1000 families in a small town were collected. You want to know if the money made is normally distributed. Which of the following would you use?

It was believed that the probability of being hit by lightning is the same during the course of a thunderstorm. Which of the following distributions would you use to figure out the probability of being hit by a lightning during the first half of a thunderstorm?

It was believed that the probability of a small business that declared bankruptcy per month was the same in any month. Also the number of small businesses that declared bankruptcy was the same every month. Which of the following distributions would you use to figure out the probability that more than 3 bankruptcies will occur next month?

Suppose the probability of a car accident taking place anywhere on a stretch of a 20- mile highway is the same. Which of the following distributions would you use to figure out the probability that a car accident will occur somewhere between the 5-mile and 15-mile posts of the highway?

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. Suppose the before and after exam scores are both normally distributed. Which of the following tests will be the most appropriate?

An airline wants to select a computer software package for its reservation system. Four software packages (1, 2, 3, and 4) are commercially available. An experiment is set up in which each package is used to make reservations for 5 randomly selected weeks and data on the number of passengers that are bumped over a month are collected. (A total of 20 weeks was included in the experiment.) The variability of the number of passengers that are bumped is found to be roughly the same for the 4 packages. The distribution on the number of passengers that are bumped has been found out to be right-skewed for package 1 and 4, left-skewed for package 2 and normal for package 3. Which of the following tests will be the most appropriate to find out if the average number of passengers being bumped over a month is the same across the 4 packages?

An investor wanted to forecast the price of a certain stock. He collected average daily price for the stock over the past 10 years. Which of the following would be the most appropriate analysis to perform?

The probability that a particular brand of smoke alarm will malfunction in the presence of smoke is

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. The president has already found out that specialty types and origin of the medical degree do not interact to affect the charges. Which of the following tests will be the most appropriate to find out if the primary specialty affects the charges?

A debate team of 4 members for a high school will be chosen randomly from a potential group of 15 students. Ten of the 15 students have no prior competition experience while the others have some degree of experience. Which of the following distributions would you use to figure out the probability that none of the members chosen for the team have any competition experience?

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 suspects that the differences are not normally distributed. Which of the following tests will be the most appropriate?

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States collected information on the endowment amount. Based on this information, which of the following will you construct to learn about the mean endowment of all private colleges in the United States?

The return of two different stocks has the following distribution depending on the market conditions. To decide on which is the best investment for an investor who prefers the highest average return bu the lowest risk, which of the following would be the most appropriate analysis to perform? Market Condition Probability Return of StockA Return of Stock B Bull 0.4 \ 200 -\ 200 Stable 0.3 \ 100 \ 150 Bear 0.3 -\ 100 \ 400

A certain type of new business succeeds 60% of the time. Suppose that 3 such businesses open (where they do not compete with each other, so it is reasonable to believe that their relative successes would be independent). Which of the following distributions would you use to figure out the probability that all of them will fail?

Suppose that past history shows that 60% of college students prefer coca-cola. A sample of 10 students is to be selected. Which of the following distributions would you use to figure out the probability that at least half of them will prefer coca-cola?