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.