Chapter 13 I Goodness-of-Fit Tests and Contingency Analysis
Chapter Exercises Conceptual Questions 13-35. Locate a journal article that uses either contingency Readmissions Last Year 0 analysis or a goodness-of-fit test. Discuss the article, paying particular attention to the reasoning behind 1 using the particular statistical test. 2 13-36.
Find a marketing research book (or borrow one from 3 a friend). Does it discuss either of the tests considered 4 in this chapter? If yes, outline the discussion. If no, 5 determine where in the text such a discussion would be 6 appropriate. 7 13-37.
One of the topics in Chapter 10 was hypothesis testing
for the difference between two population proportions. For the test to have validity, conditions were set on the sample sizes with respect to the sample proportions. A 2 X 2 contingency table may also be utilized to test the difference between proportions of two independent populations. This procedure has conditions placed on the expected value of each cell. Discuss the relationship between these two conditions.
13-38. A 2 X 2 contingency table and a hypothesis test of the difference between two population proportions can be used to analyze the same data set. However, besides all the similarities of the two methods, the hypothesis test of the difference between two proportions has two advantages. Identify these advantages. Business Applications 13-39.
The College Bookstore has four checkout stands. The store manager noticed that registers 3 and 4 served fewer students than registers I and 2. She is not sure whether the layout of the store channels customers into these registers, whether the checkout clerks in these lines are simply slower than in the other two, or whether she was just seeing random differences. The manager kept a record of which stands the next 1,000 students chose for checkout. The students checked out of the four stands according to the following pattern:
Stand 1 Stand 2 Stand 3 Stand 4
338 275 201 186
Based on these data, can the store manager conclude that the proportions of students who use the four checkout stands are equal? (Use an n = 0.05.) 13-40. A regional cancer treatment center has had success treating localized cancers with a linear accelerator. Whereas admissions for further treatment nationally average 2.1 per patient per year, the center’s director thinks that readmissions with the new treatment are Poisson distributed, with a mean of 1.2 patients per year. He has collected the following data on a random sample of 300 patients:
Patients
139 87 48 14 2 300
a. Adjust the data so that you can test the director’s claim using a test statistic whose sampling distribution can be approximated by a chi-square distribution.
b. Assume the Type I error rate is to be controlled at 0.05. Do you agree with the director’s claim? Why? Conduct a statistical procedure to support your opinion. 13-41.
Cooper Manufacturing has a contract with the U.S. Air Force to produce a part for a new fighter plane being manufactured. The part is a bolt with specifications requiring that the length be normally distributed with a an of 3.05 inches and a standard deviation of 0.015 inch. As part of the company’s quality-control efforts, each day Cooper’s engineers select a random sample of 100 bolts produced that day and carefully measure the bolts to determine whether they meet the specifications. The following data were collected yesterday:
Length (inches) Frequency
Under 3.030 5 3.030 and under 3.035 16 3.035 and under 3.040 7 3.040 and under 3.050 20 3.050 and under 3.060 36 3.060 and under 3.065 8 3.065 and over 8
Based on these sample data, what should Cooper’s engineers conclude about the production output ff they test using an a = 0.01? Discuss.
13-42. Suppose the Cooper Company, discussed in Exercise 13-41, has a second contract with a private firm for which it makes fuses for an electronic instrument. The quality-control department at Cooper periodically selects a random sample of five fuses and tests each fuse to determine whether it is defective. Based on these findings, the production process is either shut
