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 |
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. W=786.5.z=3.2399, P-value=0.0006.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.
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
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).
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?
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
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 |
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. H=15.8994, P-value=0.0004.The data show that some hotdog types have systematically higher calories than others.
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.
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.
(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. H=4.7128, P-value=0.0948. The data do not show systematic differences among sodium content for different types of hotdogs.
16.60 House prices.
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
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
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. H=3.6386, P-value=0.1621.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. H=7.0163, P-value=0.0300.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.
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.
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