16.31 Online bookstore prices.

For more than 80 years, the New York Times has been publishing its weekly list of best-selling books in the United States. For certain book subcategories, the best-selling lists are done monthly. On the New York Times best-selling book website, there is a “buy” button next to each listed book. The button directs the viewer to one of two online bookstore options: Amazon or Barnes & Noble. Consider the following table of the online prices of the best-selling business books for September 2014. Note that older titles are paperback versus paperback comparisons, while newer titles are hardback versus hardback comparisons.¹¹

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Is there is a systematic difference in book prices between the two online booksellers? Formulate this question in terms of null and alternative hypotheses. Then compute the differences and find the value of the Wilcoxon signed rank statistic .

16.32 Significance test for online bookstore prices.

Refer to the previous exercise. Find , , and the Normal approximation for the -value for the Wilcoxon signed rank test. What do you conclude?

16.33 Potential insurance fraud?

Insurance adjusters are concerned about the high estimates they are receiving from Jocko’s Garage. To see if the estimates are unreasonably high, each of the 10 damaged cars was taken to Jocko’s and to another garage, and the estimates (in dollars) were recorded. Here are the results.

Test the null hypothesis that there is no difference between the two garages. Remember that zeros are dropped from the data before ranking, so that is the number of nonzero differences within pairs.

16.34 It’s all in the thumbs.

New mobile phone software is advertised as resulting in faster text message creation (measured in characters per second) when compared with traditional mobile phone software. The traditional software offers suggested word completions based on a list of commonly used words, while the new software uses a smartword completion algorithm that takes into account the context of the text message. Ten individuals are involved in an experiment to test the marketing claim. The following data are the differences in their text message creation speeds: a positive value indicates more characters per second with the new mobile phone software.

16.35 Oil-free frying comparison.

Exercise 7.10 (page 371) describes an experiment in which a group of food experts to compare foods made with hot oil and their oil-free fryer. Here are the data.

Using the signed rank test, is there a significant difference in taste? State appropriate hypotheses and carry out the test using .

16.36 Loss of product value.

In Example 16.6 (page 16-16), we considered the alternative hypothesis of vitamin C being systematically higher at the factory versus five months later when measured in Haiti. For the data provided in the example, the Wilcoxon signed rank statistic was found to be 34. On page 16-16, we noted that we could have equally used the sum of the ranks of the negative differences, which is 11.

16.37 Marketing a health aid.

Exercise that helps health and fitness should raise our heart rate for some period of time. A firm that markets a “Step Up to Health” apparatus consisting of a step and handrails for users to hold must tell buyers how to use their new device. The firm has subjects use the step at several stepping rates and measures their heart rates before and after stepping. Here are data for five subjects and two treatments: low rate (14 steps per minute) and medium rate (21 steps per minute). For each subject, we give the resting heart rate (beats per minutes) and the heart rate at the end of the exercise.¹²

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Does exercise at the low rate raise heart rate significantly? State hypotheses in terms of the median increase in heart rate and apply the Wilcoxon signed rank test. What do you conclude?

16.38 Marketing a health aid, continued.

Do the data from the previous exercise give good reason to think that stepping at the medium rate increases heart rates more than stepping at the low rate?

16.39 Executives learn Spanish.

A matched pairs study of the effect of a language institute on the ability of executives to comprehend spoken Spanish had these improvements in scores between the pretest and the posttest for 20 executives:

(Exercise 7.34, page 377, shows the actual pretest and posttest scores.) Show the assignment of ranks and the calculation of the signed rank statistic for these data.

16.40 Consumer perceptions of food safety.

CASE 16.2 Case 16.2 (page 16-10) describes a study of the attitudes of people attending outdoor fairs about the safety of the food served at such locations. In the associated data file, you will find the responses of 303 people to several questions. The variables in this data set are (in order)

The variable “sfair” contains responses to the safety question described in Case 16.2. The variable “srest” contains responses to the same question asked about food served in restaurants. We suspect that restaurant food will appear safer than food served outdoors at a fair. Do the data give good evidence for this suspicion? (Give descriptive measures, a test statistic and its -value, and your conclusion.)

16.41 Consumer perceptions of food safety.

CASE 16.2 The food safety survey data described in Case 16.2 (page 16-10) and Exercise 16.40 also contain the responses of the 303 subjects to the same question asked about food served at fast-food restaurants. These responses are the values of the variable “sfast.” Is there a systematic difference between the level of concern about food safety at outdoor fairs and at fast-food restaurants?

16.42 Home radon detectors.

How accurate are radon detectors of a type sold to homeowners? To answer this question, university researchers placed 12 detectors in a chamber that exposed them to 105 picocuries per liter (pCi/l) of radon.¹³ The detector readings are as follows:

We wonder if the median reading differs significantly from the true value 105.

To do this, apply the Wilcoxon signed rank statistic to the differences between the observations and 105. (This is the one-sample version of the test.) What do you conclude?

16.43 The Platinum Gasaver.

Platinum Gasaver is a device its maker says “may increase gas mileage by 22%.” An advertisement reports the results of a matched pairs study with 15 identical vehicles. The claimed percent changes in gas mileage with the Gasaver are

Is there good evidence that the Gasaver improves median gas mileage by 22% or more? (Apply the Wilcoxon signed rank test to the differences between the sample percents and the claimed 22%.)

16.44 Home radon detectors, continued.

Some software (Minitab, for example) calculates a confidence interval for the population median as part of the Wilcoxon signed rank test. Using software and the data in Exercise 16.42, give a 95% confidence interval for the median reading of home radon detectors when exposed to 105 picocuries per liter of radon.

16.45 Service call time.

Some software (Minitab, for example) calculates a confidence interval for the population median as part of the Wilcoxon signed rank test. Exercise 1.37 (page 26) gives the service times for 80 calls to a customer service center. Using software, find a 95% confidence interval for the median service call time.

16.46 Time to start a business.

CASE 1.2 Case 1.2 (page 23) provides World Bank data for 24 countries on the time, in days, to complete all the procedures required to start a business in the country. Some software (Minitab, for example) calculates a confidence interval for the population median as part of the Wilcoxon signed rank test. Using software, find a 95% confidence interval for the median time required to start a business.