Examine each of the following statistics. Which sampling method was

Examine each of the following statistics. Which sampling method was most likely to have been used (simple random, systematic, stratified, cluster)?

a. A survey showed that 30 percent of U.S. businesses have fired an employee for inappropriate web surfing, such as gambling, watching porn, or shopping.

b. Surveyed doctors report that 59 percent of patients do not follow their prescribed treatment.

c. The Internal Revenue Service reports that, based on a sample of individual taxpayers, 80 percent of those who failed to pay what they owed did so through honest errors or misinterpretation of the tax code.

d. In Spain, per capita consumption of cigarettes is 1,265 compared with 1,083 in the United States.

Ergonomics is the science of making sure that human surroundings

Ergonomics is the science of making sure that human surroundings are adapted to human needs. How could statistics play a role in the following:

a. Choosing the height of an office chair so that 95 percent of the employees (male and female) will feel it is the “right height” for their legs to reach the floor comfortably.

b. Designing a drill press so its controls can be reached and its forces operated by an “average employee.”

c. Defining a doorway width so that a “typical” wheelchair can pass through without coming closer than 6 inches from either side.

d. Setting the width of a parking space to accommodate 95 percent of all vehicles at your local Walmart.

e. Choosing a font size so that a highway sign can be read in daylight at 100 meters by 95 percent of all drivers.

The Graduate Management Admission Test (GMAT) is used by many

The Graduate Management Admission Test (GMAT) is used by many graduate schools of business as one of their admission criteria. Using your own reasoning and concepts in this chapter, criticize each of the following conclusions.

a. “Last year, 7,573 computer science majors took the GMAT, compared with only 588 philosophy majors. Philosophy majors must not be interested in business because so few take the GMAT.”

b. “Last year, 29,688 engineering majors took the GMAT, compared with only 3,589 English majors. Clearly, more students major in engineering than in English.”

c. “Last year, physics majors averaged 100 points higher on the GMAT than marketing majors. If marketing students majored in physics, they would score better on the GMAT.”

d. “On average, physics majors score higher on the GMAT than accounting majors. Therefore, physics majors would make the best managers.”

The probability that a customer at a grocery store pays

The probability that a customer at a grocery store pays for their items with a credit or debit card (event C) is .78. The probability that the grocery bill for a customer is greater than $100 (event H) is .37. The probability that a customer pays with a credit or debit card given that his or her grocery bill was greater than $100 is .95.

(a) What is the probability that a customer pays with a credit or debit card and his or her grocery bill was greater than $100?

(b) What is the probability that a customer’s grocery bill was over $100 given that he or she paid with a credit or debit card?

(c) In this problem, are C and H independent? Explain.

A Realtor claims that no more than half of the

A Realtor claims that no more than half of the homes he sells are sold for less than the asking price. When reviewing a random sample of 12 sales over the past year, he found that actually 10 were sold below the asking price.

(a) Would we be justified in assuming that the sample proportion p is normally distributed? Explain.

(b) Calculate a p-value for the observed sample outcome, using the normal distribution. At the .05 level of significance in a right-tailed test, is the proportion of homes sold for less than the asking price greater than 50%?

(c) Use Excel to calculate the binomial probability P(X ≥ 10 | n = 12, π = .50) = 1 − P(X ≤ 9 | n = 12, π = .50).

Researchers at the Mayo Clinic have studied the effect of

Researchers at the Mayo Clinic have studied the effect of sound levels on patient healing and have found a significant association (louder hospital ambient sound level is associated with slower postsurgical healing). Based on the Mayo Clinic’s experience, Ardmore Hospital installed a new vinyl flooring that is supposed to reduce the mean sound level (decibels) in the hospital corridors. The sound level is measured at five randomly selected times in the main corridor.

(a) At α = .05, has the mean been reduced? Show the hypotheses, decision rule, and test statistic.

(b) At α = .05, has the variance changed? Show the hypotheses, decision rule, and test statistic.

New Flooring                       Old Flooring

44……………………………………………………..52
42……………………………………………………..48
41……………………………………………………..51
40……………………………………………………..44
37……………………………………………………..48

SAT scores are often used as a proxy for how

SAT scores are often used as a proxy for how well a state educates the students who reside in that state. However, not all students in a state actually take the SAT, and SAT participation rates vary across states. For example, some states require the SAT as an assessment test in high school. Those states will have higher participation rates than states that do not require the test in high school. If a student attends a high school that does not require the SAT, but the student plans to apply to a college that requires the SAT for admission, then that student will
choose to take the exam. Regression results from a regression using Y = state average SAT and X = state SAT participation are shown below.

(a) What do these regression results tell you about the relationship between state average SAT score and state SAT participation?

(b) Do you consider this a strong relationship? Explain.

(c) Can you suggest reasons why this relationship might exist?

A ski resort asked a random sample of guests to

A ski resort asked a random sample of guests to rate their satisfaction on various attributes of their visit on a scale of 1–5 with 1 = very unsatisfied and 5 = very satisfied. The estimated regression model was Y = overall satisfaction score, X1 = lift line wait, X2 = amount of ski trail grooming, X3 = safety patrol visibility, and X4 = friendliness of guest services.

(a) Write the fitted regression equation.

(b) Interpret each coefficient.

(c) Would the intercept seem to have meaning in this regression?

(d) Make a prediction for Overall Satisfaction when a guest’s satisfaction in all four areas is rated a 5.

Predictor                                          Coefficient
Intercept…………………………………………….2.8931
LiftWait………………………………………………0.1542
AmountGroomed……………………………….0.2495
SkiPatrolVisibility………………………………..0.0539
FriendlinessHosts…………………………….−0.1196

To see whether students who finish an exam first get

To see whether students who finish an exam first get the same grades as those who finish later, a professor kept track of the order in which papers were handed in. Of the first 25 papers, 10 received a “B” or better, compared with 8 of the last 24 papers handed in. Research question: At α = .10, is the grade independent of the order handed in? Because it is a 2 × 2 table, try also a two-tailed, two-sample z test for π1 = π2 (see Chapter 10), and verify that z2 is the same as your chi-square statistic. Which test do you prefer? Why?