CHAPTER 16 Review Exercises

Question 16.53

16.53 Response times for telephone repair calls.

A study examined the time required for the telephone company Verizon to respond to repair calls from its own customers and from customers of a CLEC, another phone company that pays Verizon to use its local lines. Here are the data, which are rounded to the nearest hour:

trepair

Verizon
1 1 1 1 2 2 1 1 1 1 2 2
1 1 1 1 2 2 1 1 1 1 2 3
1 1 1 1 2 3 1 1 1 1 2 3
1 1 1 1 2 3 1 1 1 1 2 3
1 1 1 1 2 3 1 1 1 1 2 4
1 1 1 1 2 5 1 1 1 1 2 5
1 1 1 1 2 6 1 1 1 1 2 8
1 1 1 1 2 15 1 1 1 2 2
CLEC
1 1 5 5 5 1 5 5 5 5
  1. Does Verizon appear to give CLEC customers the same level of service as its own customers? Compare the data using graphs and descriptive measures and express your opinion.
  2. We would like to see if times are significantly longer for CLEC customers than for Verizon customers. Why would you hesitate to use a test for this purpose? Carry out a rank test. What can you conclude?
  3. Explain why a nonparametric procedure is appropriate in this setting.
calories h

16.53

(a) The CLEC customers generally have to wait longer than the Verizon customers for repairs. (b) The data are count data and far from normally distributed. , The CLEC customers have systematically higher repair wait times than the Verizon customers. (c) The CLEC group only has two values, 1 and 5. The Verizon group is strongly right skewed and has a large outlier.

Question 16.54

16.54 Design of controls.

Exercise 7.36 (page 378) contains data from a student project that investigated whether right-handed people can turn a knob faster clockwise than they can counterclockwise. Describe what the data show, then state hypotheses and do a test that does not require Normality. Report your conclusions carefully.

cntrols

Question 16.55

16.55 Retail sales.

Exercise 7.97 (page 411) gives monthly sales of 64GB flash drives at a sample of 50 retail stores. That exercise reports 95% confidence intervals for the mean sales in all stores obtained by the bootstrap method, which does not require Normality. Find a 95% confidence interval for the median sales and compare your results with those in Exercise 7.97.

retail

16.55

(25, 32). This is quite close to the confidence interval for the mean we found in Exercise 7.97, (26.06, 33.18).

Question 16.56

16.56 Drive-thru customer service.

Exercise 7.57 (page 395) considered data gathered by QSRMagazine .com in the assessment of drive-thru customer service for the fast-food chains Taco Bell and McDonald’s. Consider in this exercise the comparison between two competing burger fast-food chains: Burger King and Wendy’s.19 Responses ranged from “rude (1)” to “very friendly (5).” The following table breaks down the responses according to two of the chains studied.

burger

Rating
Chain 1 2 3 4 5
Burger King 11 28 92 117 51
Wendy’s 6 17 70 134 98

Is there evidence that one restaurant chain has systematically higher satisfaction ratings than the other?

Question 16.57

16.57 Calories in hot dog brands.

Table 16.1 presents data on the calorie and sodium content of selected brands of beef, meat, and poultry hot dogs.20 We regard these brands as random samples from all brands available in food stores.

hotdog

  1. Make stemplots of the calorie contents side by side, using the same stems for easy comparison. Give the five-number summaries for the three types of hot dog. What do the data suggest about the calorie content of different types of hot dog?
  2. Are any of the three distributions clearly not Normal? Which ones, and why?

    16-30

    Table 16.48: TABLE 16.1 Calories and sodium in three types of hot dogs
    Beef hot dogs Meat hot dogs Poultry hot dogs
    Calories Sodium Calories Sodium Calories Sodium
    186 495 173 458 129 430
    181 477 191 506 132 375
    176 425 182 473 102 396
    149 322 190 545 106 383
    184 482 172 496 94 387
    190 587 147 360 102 542
    158 370 146 387 87 359
    139 322 139 386 99 357
    175 479 175 507 170 529
    148 375 136 393 113 513
    152 330 179 405 135 426
    111 300 153 372 142 513
    141 386 107 144 86 358
    153 401 195 511 143 581
    190 645 135 405 152 588
    157 440 140 428 146 522
    131 317 138 339 144 545
    149 319
    135 298
    132 253
  3. Carry out a nonparametric test. Report your conclusions carefully.

16.57

(a) It looks like beef and meat hotdogs have more calories than poultry hotdogs.

Analysis Variable : Calories
Type Minimum Lower
Quartile		 Median Upper Quartile Maximum
Beef 111 140 152.5 178.5 190
Meat 107 139 153 179 195
Poultry 86 102 129 143 170

(b) None of the distributions look very normal. The beef and meat hotdogs have similar distributions: somewhat uniform with a gap in the 160s, creating a bimodal distribution. There also may be one low outlier in each. The poultry hotdogs also has a somewhat bimodal distribution with a low point around 120; it additionally may have a high outlier. (c) H0: Calories have the same distribution for all types of hotdogs. Ha: Calories are systematically higher for some types of hotdogs than in others. , The data show that some hotdog types have systematically higher calories than others.

Question 16.58

16.58 Comparative study of U.S. and Indian firms.

Are managerial efficiencies of similar U.S. and Indian firms comparable? A study was conducted to evaluate the relative managerial efficiencies of 14 match-paired U.S. and Indian firms.21 Each pair of firms chosen in the study consists of one U.S. firm and one Indian firm producing similar product and having approximately the same size. Here are the data on the cumulative return on assets (ROA) for each firm over a five-year span.

usin

Paired firms 1 2 3 4 5 6 7
U.S. 34.32 9.61 11.73 20.74 23.58 10.38 40.24
Indian 59.87 39.25 13.13 32.79 18.13 28.14 81.45
Paired firms 8 9 10 11 12 13 14
U.S. 84.55 9.95 16.3 0.50 7.42 9.38 43.53
Indian 58.27 37.14 9.73 6.61 3.22 0.18 43.74

Test the null hypothesis that there is no difference between the two countries in terms of managerial efficiency as measured by ROA.

Question 16.59

16.59 Sodium in hot dog brands.

Repeat the analysis of Exercise 16.57 for the sodium content of hot dogs.

hotdog

16.59

(a) It looks like poultry hotdogs have a slightly higher sodium content, followed by meat hotdogs; beef hotdogs have the lowest sodium content.

16-34

(b) The beef hotdogs have right-skewed distribution with maybe two potential high outliers with large sodium contents. The meat hotdogs category is roughly normal but has one extreme low outlier, with less than half the sodium of all other hotdogs. The poultry hotdogs have a bimodal distribution with two main groups, one with low sodium amounts and one with high sodium amounts. (c) H0: Sodium contents have the same distribution for all types of hotdogs. Ha: Sodium contents are systematically higher for some types of hotdogs than in others. , . The data do not show systematic differences among sodium content for different types of hotdogs.

Question 16.60

16.60 House prices.

CASE 11.3 Case 11.3 (page 566) provides data the selling prices of 504 houses in West Lafayette, Indiana. We wonder if there is a difference between the average prices of houses with three bathrooms and houses with more than three bathrooms in this community. In the provided data file, three bathroom houses are coded by “0” and houses with more than three bathrooms are coded by “1.”

baths

  1. Make a Normal quantile plot of the prices of three bathroom houses. What kind of deviation from Normality do you see?
  2. The tests are quite robust. State the hypotheses for the proper test, carry out the test, and present your results including appropriate data summaries.
  3. Carry out a nonparametric test. Once more, state the hypotheses tested and present your results for both the test and the data summaries that should go with it.
  4. Compare the nonparametric result of part (c) with the test result of part (b).

Question 16.61

16.61 French tourism economy.

Refer to Exercise 16.47 (page 16-27). The study also considered two other components of ski resort efficiency: technological change (TECH) and technical efficiency change (EFFCH).

ski

  1. With relationship to the TECH measure, the researcher states: “There is no reason to believe that size differences affect technological change.” Is this statement consistent with your results? Explain.
  2. With relationship to the EFFCH measure, the researcher states: “A relationship between size and technical efficiency change can be made.” Is this statement consistent with your results? Explain.
  3. With respect to the EFFCH measure, the researcher concludes: “These observations permit the conclusion that large ski resorts are better organized and ensure better management than medium and small ski resorts.” Explain how the data support this conclusion.

16.61

(a) This statement is correct. H0: TECH values have the same distribution in all groups. Ha: TECH values are systematically higher in some groups than in others. , The data do not show systematic differences in TECH values across resort sizes. (b) This statement is correct. H0: EFFCH values have the same distribution in all groups. Ha: EFFCH values are systematically higher in some groups than in others. , The data show systematic differences in EFFCH values across resort sizes. (c) The rank sum for the large resort size is much larger than expected under H0.

Question 16.62

16.62 Does the type of cooking pot affect iron content?

Iron-deficiency anemia is the most common form of malnutrition in developing countries, affecting about 50% of children and women and 25% of men. Iron pots for cooking foods had traditionally been used in many of these countries, but they have been largely replaced by aluminum pots, which are cheaper and lighter. Some research has suggested that food cooked in iron pots will contain more iron than food cooked in other types of pots. One study designed to investigate this issue compared the iron content of some Ethiopian foods cooked in aluminum, clay, and iron pots.22 One of the foods was yesiga wet’, beef cut into small pieces and prepared with several Ethiopian spices. The iron content of four samples of yesiga wet’ cooked in each of the three types of pots is given here. The units are milligrams of iron per 100 grams of cooked food.

16-31

Type of pot Iron content (mg/100 g food)
Aluminum 1.77 2.36 1.96 2.14
Clay 2.27 1.28 2.48 2.68
Iron 5.27 5.17 4.06 4.22

We want to know if the dish varies in iron content when cooked in aluminum, clay, and iron pots.

cook

  1. Check the requirements for one-way ANOVA. Which requirements are a bit dubious in this setting?
  2. Instead of ANOVA, do a nonparametric test. Summarize your conclusions about the effect of pot material on iron content, including both descriptive measures and your test result.