In a world of get-rich-quick schemes, few are mentioned more frequently than lawsuits. One of the reasons is the infamous McDonald’s coffee case (Liebeck v. McDonald’s Restaurants). This is what happened in 1992 in Albuquerque, New Mexico. Stella Liebeck, seventy-nine, was riding in a car driven by her grandson. They stopped at a McDonald’s drive-through, where she purchased a Styrofoam cup of coffee. Wanting to add cream and sugar, she squeezed the cup between her knees and pulled off the plastic lid. The entire thing spilled back into her lap. The searing liquid left her with extensive third-degree burns. Eight days of hospitalization—which included skin grafts—were required. Initially, she sought $20,000 from McDonald’s, which was more or less the cost of her medical bills. McDonald’s refused. They went to court. There it came to light that about seven hundred claims had been made by consumers between 1982 and 1992 for similar incidents. This seems to indicate that McDonald’s knew—or at least should have known—that the hot coffee was a problem. Most of the rest of the case turned around temperature questions. McDonald’s admitted that they served their coffee at 185 degrees, which will burn the mouth and throat and is about 50 degrees higher than typical homemade coffee. More importantly, coffee served at temperatures up to 155 degrees won’t cause burns, but the danger rises abruptly with each degree above that limit. So why did McDonald’s serve it so hot? Most customers, the company claimed, bought on the way to work or home and would drink it on arrival. The high temperature would keep it fresh until then. Unfortunately, internal documents showed that McDonald’s knew their customers intended to drink the coffee in the car immediately after purchase. Next, McDonald’s asserted that their customers wanted their coffee hot. The restaurant conceded, however, that customers were unaware of the serious burn danger and that no adequate warning of the threat’s severity was provided. Finally, the jury awarded Liebeck $160,000 in compensatory damages and $2.7 million in punitive damages (about two days’ worth of McDonalds’ coffee sales). The judge, however, reduced the $2.7 million to $480,000. McDonald’s threatened to appeal, and the two sides eventually came to a private settlement agreement.
In ethical terms, justify the original jury award to Liebeck: $160,000 in compensatory damages and $2.7 million in punitive damages (about two days of McDonalds’ coffee sales).
Of these three ethical structures for conceiving of the coffee-buying consumer and her protections—caveat emptor, the implicit contract, and manufacturer liability—which do you believe is best? Why?
In: Accounting
A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. A normal probability plot suggests that the residuals are normally distributed. Complete parts (a) and (b) below. Height (inches), x 25 27.5 27 25.5 26 Head Circumference (inches), y 16.9 17.5 17.5 17.1 17.3 (a) Use technology to determine s Subscript b 1. s Subscript b 1equals nothing (Round to four decimal places as needed.) (b) Test whether a linear relation exists between height and head circumference at the alphaequals0.01 level of significance. State the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0: beta 0equals0 Upper H 1: beta 0not equals0 B. Upper H 0: beta 1equals0 Upper H 1: beta 1greater than0 C. Upper H 0: beta 0equals0 Upper H 1: beta 0greater than0 D. Upper H 0: beta 1equals0 Upper H 1: beta 1not equals0 Determine the P-value for this hypothesis test. P-valueequals nothing (Round to three decimal places as needed.) What is the conclusion that can be drawn? A. Reject Upper H 0 and conclude that a linear relation exists between a child's height and head circumference at the level of significance alphaequals0.01. B. Do not reject Upper H 0 and conclude that a linear relation exists between a child's height and head circumference at the level of significance alphaequals0.01. C. Do not reject Upper H 0 and conclude that a linear relation does not exist between a child's height and head circumference at the level of significance alphaequals0.01. D. Reject Upper H 0 and conclude that a linear relation does not exist between a child's height and head circumference at the level of significance alphaequals0.01. Click to select your answer(s).
In: Statistics and Probability
A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. A normal probability plot suggests that the residuals are normally distributed. Complete parts (a) and (b) below. Height (inches), x 27.75 24.5 27.5 27 26.5 Head Circumference (inches), y 17.6 17.1 17.5 17.5 17.3 (a) Use technology to determine s Subscript b 1. s Subscript b 1equals nothing (Round to four decimal places as needed.) (b) Test whether a linear relation exists between height and head circumference at the alphaequals0.01 level of significance. State the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0: beta 0equals0 Upper H 1: beta 0greater than0 B. Upper H 0: beta 0equals0 Upper H 1: beta 0not equals0 C. Upper H 0: beta 1equals0 Upper H 1: beta 1not equals0 D. Upper H 0: beta 1equals0 Upper H 1: beta 1greater than0 Determine the P-value for this hypothesis test. P-valueequals nothing (Round to three decimal places as needed.) What is the conclusion that can be drawn? A. Do not reject Upper H 0 and conclude that a linear relation exists between a child's height and head circumference at the level of significance alphaequals0.01. B. Do not reject Upper H 0 and conclude that a linear relation does not exist between a child's height and head circumference at the level of significance alphaequals0.01. C. Reject Upper H 0 and conclude that a linear relation exists between a child's height and head circumference at the level of significance alphaequals0.01. D. Reject Upper H 0 and conclude that a linear relation does not exist between a child's height and head circumference at the level of significance alphaequals0.01.
In: Statistics and Probability
A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 5 children and measures their height and head circumference. The data are summarized below. A normal probability plot suggests that the residuals are normally distributed. Complete parts (a) and (b) below. Height (inches), x 27.75 25 27 26 26.5 Head Circumference (inches), y 17.6 16.9 17.5 17.3 17.3 (a) Use technology to determine s Subscript b 1. s Subscript b 1equals nothing (Round to four decimal places as needed.) (b) Test whether a linear relation exists between height and head circumference at the alphaequals0.01 level of significance. State the null and alternative hypotheses for this test. Choose the correct answer below. A. Upper H 0: beta 0equals0 Upper H 1: beta 0not equals0 B. Upper H 0: beta 0equals0 Upper H 1: beta 0greater than0 C. Upper H 0: beta 1equals0 Upper H 1: beta 1not equals0 D. Upper H 0: beta 1equals0 Upper H 1: beta 1greater than0 Determine the P-value for this hypothesis test. P-valueequals nothing (Round to three decimal places as needed.) What is the conclusion that can be drawn? A. Reject Upper H 0 and conclude that a linear relation does not exist between a child's height and head circumference at the level of significance alphaequals0.01. B. Reject Upper H 0 and conclude that a linear relation exists between a child's height and head circumference at the level of significance alphaequals0.01. C. Do not reject Upper H 0 and conclude that a linear relation does not exist between a child's height and head circumference at the level of significance alphaequals0.01. D. Do not reject Upper H 0 and conclude that a linear relation exists between a child's height and head circumference at the level of significance alphaequals0.01.
In: Statistics and Probability
The data in the accompanying table represent the heights and weights of a random sample of professional baseball players. Complete parts (a) through (c) below.
Player Height_(inches)
Weight_(pounds)
Player_1 76 227
Player_2 75 197
Player_3 72 180
Player_4 82 231
Player_5 69 185
Player_6 74 190
Player_7 75 228
Player_8 71 200
Player_9 75 230
(b) Determine the least-squares regression line. Test whether there is a linear relation between height and weight at the
alphaαequals=0.05
level of significance.
Determine the least-squares regression line. Choose the correct answer below.
A.
ModifyingAbove y with caretyequals=4.1604.160xnegative 103.7−103.7
B.
ModifyingAbove y with caretyequals=8.160xnegative−101.7
C.
ModifyingAbove y with caretyequals=negative 101.7−101.7xplus+4.1604.160
D.
ModifyingAbove y with caretyequals=4.1604.160xnegative 101.7−101.7
Test whether there is a linear relation between height and weight at the
alphaαequals=0.05
level of significance.
State the null and alternative hypotheses. Choose the correct answer below.
A.
Upper H 0H0:
beta 1β1equals=0
Upper H 1H1:
beta 1β1not equals≠0
B.
Upper H 0H0:
beta 0β0equals=0
Upper H 1H1:
beta 0β0not equals≠0
C.
Upper H 0H0:
beta 0β0equals=0
Upper H 1H1:
beta 0β0greater than>0
D.
Upper H 0H0:
beta 1β1equals=0
Upper H 1H1:
beta 1β1greater than>0
Determine the P-value for this hypothesis test.
P-valueequals=nothing
(Round to three decimal places as needed.)
State the appropriate conclusion at the
alphaαequals=0.05
level of significance. Choose the correct answer below.
A.Do not reject
Upper H 0H0.
There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.
B.Do not reject
Upper H 0H0.
There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.
C.Reject
Upper H 0H0.
There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.
D.Reject
Upper H 0H0.
There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.
(c) Remove the values listed for Player 4 from the data table. Test whether there is a linear relation between height and weight. Do you think that Player 4 is influential?
Determine the P-value for this hypothesis test.
P-valueequals=nothing
(Round to three decimal places as needed.)
State the appropriate conclusion at the
alphaαequals=0.05
level of significance. Choose the correct answer below.
A.Reject
Upper H 0H0.
There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.
B.Do not reject
Upper H 0H0.
There is not sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.
C.Do not reject
Upper H 0H0.
There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.
D.Reject
Upper H 0H0.
There is sufficient evidence to conclude that a linear relation exists between the height and weight of baseball players.
Do you think that Player 4 is influential?
Yes
No
In: Statistics and Probability
A physiological experiment was concluded to study the effect of
various factors on a pulse rate. The participants took their own
pulse. They then were asked to flip a coin. If their coin came up
head, they were to run in place for 1 minute. Then everyone took
their own pulse again. The dataset pulse.txt, available from
Moodle, contains the following variables:
ROW- id numbers, from 1 to 92;
PULSE1- first pulse rate;
PULSE2- second pulse rate;
RAN-1=ran in place, 2 =did not run;
SMOKES-1=smokes regularly, 2=does not smoke regularly;
SEX-1=male, 2=female;
HEIGHT-height in inches;
WEIGHT-weight in pounds;
ACTIVITY-usual level of physical activity: 1=slight, 2=moderate, 3=a lot.
Use this data for the following questions.
(a) Find the histograms for pulse2, weight and height; Are they
symmetrically distributed?
(b) Find the sample mean and sample standard deviation for pulse1.
(c) Construct a scatter plot between weight and height, categorized by male and female. What pattern have you observed?
Pulse.dat:
-----------------------------------------------------------------------------------------------------------------------------------------------------
1 64 88 1 2 1 66.00 140 2
2 58 70 1 2 1 72.00 145 2
3 62 76 1 1 1 73.50 160 3
4 66 78 1 1 1 73.00 190 1
5 64 80 1 2 1 69.00 155 2
6 74 84 1 2 1 73.00 165 1
7 84 84 1 2 1 72.00 150 3
8 68 72 1 2 1 74.00 190 2
9 62 75 1 2 1 72.00 195 2
10 76 118 1 2 1 71.00 138 2
11 90 94 1 1 1 74.00 160 1
12 80 96 1 2 1 72.00 155 2
13 92 84 1 1 1 70.00 153 3
14 68 76 1 2 1 67.00 145 2
15 60 76 1 2 1 71.00 170 3
16 62 58 1 2 1 72.00 175 3
17 66 82 1 1 1 69.00 175 2
18 70 72 1 1 1 73.00 170 3
19 68 76 1 1 1 74.00 180 2
20 72 80 1 2 1 66.00 135 3
21 70 106 1 2 1 71.00 170 2
22 74 76 1 2 1 70.00 157 2
23 66 102 1 2 1 70.00 130 2
24 70 94 1 1 1 75.00 185 2
25 96 140 1 2 2 61.00 140 2
26 62 100 1 2 2 66.00 120 2
27 78 104 1 1 2 68.00 130 2
28 82 100 1 2 2 68.00 138 2
29 100 115 1 1 2 63.00 121 2
30 68 112 1 2 2 70.00 125 2
31 96 116 1 2 2 68.00 116 2
32 78 118 1 2 2 69.00 145 2
33 88 110 1 1 2 69.00 150 2
34 62 98 1 1 2 62.75 112 2
35 80 128 1 2 2 68.00 125 2
36 62 62 2 2 1 74.00 190 1
37 60 62 2 2 1 71.00 155 2
38 72 74 2 1 1 69.00 170 2
39 62 66 2 2 1 70.00 155 2
40 76 76 2 2 1 72.00 215 2
41 68 66 2 1 1 67.00 150 2
42 54 56 2 1 1 69.00 145 2
43 74 70 2 2 1 73.00 155 3
44 74 74 2 2 1 73.00 155 2
45 68 68 2 2 1 71.00 150 3
46 72 74 2 1 1 68.00 155 3
47 68 64 2 2 1 69.50 150 3
48 82 84 2 1 1 73.00 180 2
49 64 62 2 2 1 75.00 160 3
50 58 58 2 2 1 66.00 135 3
51 54 50 2 2 1 69.00 160 2
52 70 62 2 1 1 66.00 130 2
53 62 68 2 1 1 73.00 155 2
54 48 54 2 1 1 68.00 150 0
55 76 76 2 2 1 74.00 148 3
56 88 84 2 2 1 73.50 155 2
57 70 70 2 2 1 70.00 150 2
58 90 88 2 1 1 67.00 140 2
59 78 76 2 2 1 72.00 180 3
60 70 66 2 1 1 75.00 190 2
61 90 90 2 2 1 68.00 145 1
62 92 94 2 1 1 69.00 150 2
63 60 70 2 1 1 71.50 164 2
64 72 70 2 2 1 71.00 140 2
65 68 68 2 2 1 72.00 142 3
66 84 84 2 2 1 69.00 136 2
67 74 76 2 2 1 67.00 123 2
68 68 66 2 2 1 68.00 155 2
69 84 84 2 2 2 66.00 130 2
70 61 70 2 2 2 65.50 120 2
71 64 60 2 2 2 66.00 130 3
72 94 92 2 1 2 62.00 131 2
73 60 66 2 2 2 62.00 120 2
74 72 70 2 2 2 63.00 118 2
75 58 56 2 2 2 67.00 125 2
76 88 74 2 1 2 65.00 135 2
77 66 72 2 2 2 66.00 125 2
78 84 80 2 2 2 65.00 118 1
79 62 66 2 2 2 65.00 122 3
80 66 76 2 2 2 65.00 115 2
81 80 74 2 2 2 64.00 102 2
82 78 78 2 2 2 67.00 115 2
83 68 68 2 2 2 69.00 150 2
84 72 68 2 2 2 68.00 110 2
85 82 80 2 2 2 63.00 116 1
86 76 76 2 1 2 62.00 108 3
87 87 84 2 2 2 63.00 95 3
88 90 92 2 1 2 64.00 125 1
89 78 80 2 2 2 68.00 133 1
90 68 68 2 2 2 62.00 110 2
91 86 84 2 2 2 67.00 150 3
92 76 76 2 2 2 61.75 108 2
In: Statistics and Probability
The following comparative income statement (in thousands of dollars) for two recent fiscal years was adapted from the annual report of Speedway Motorsports, Inc., owner and operator of several major motor speedways, such as the Atlanta, Texas, and Las Vegas Motor Speedways.
| Current Year | Previous Year | |||||||
| Revenues: | ||||||||
| Admissions | $78,332 | $86,949 | ||||||
| Event-related revenue | 140,210 | 133,632 | ||||||
| NASCAR broadcasting revenue | 216,592 | 209,155 | ||||||
| Other operating revenue | 26,780 | 28,622 | ||||||
| Total revenues | $461,914 | $458,358 | ||||||
| Expenses and other: | ||||||||
| Direct expense of events | $101,876 | $98,973 | ||||||
| NASCAR event management fees | 123,212 | 119,101 | ||||||
| Other direct operating expenses | 18,502 | 18,782 | ||||||
| General and administrative | 164,949 | 177,132 | ||||||
| Total expenses and other | $408,539 | $413,988 | ||||||
| Income from continuing operations | $53,375 | $44,370 | ||||||
a. Prepare a comparative income statement for these two years in vertical form, stating each item as a percent of revenues. Enter all amounts as positive numbers. (Note: Due to rounding, amounts may not total 100%).
b. Overall revenue __________ some between the two years, accompanied by a slight change in the overall mix of revenue sources. The NASCAR broadcasting revenue _________ by 1.3% of total revenue, while event-related revenue _____________ by 1.2% of total revenue. NASCAR event management fees, ___________ by 0.7% of total revenue. General and administrative expenses, however, _____________ by over 2.9% of total revenue. It appears that _____________ has helped the company significantly improve its income from continuing operations.
In: Accounting
The radius of the wheel on a bike is 27 inches. If the wheel is revolving at 144 revolutions per minute, what is the linear speed of the bike, in miles per hour? Round your answer to the nearest tenth, and do not include units in your answer.
In: Math
A forester measured 27 of the trees in a large forest on property that is for sale. He found a mean diameter of 10.4 inches and a standard deviation of 4.7 inches. Suppose that these trees provide an accurate description of the whole forest and that a Normal model applies.Determine:a) the percent of trees that has a diameter between 10.4 and 16.0 inches.b) the percent of trees that has a diameter greater than 16.0 inches. c) the percent of trees that has a diameter between 8.0 and 13.25 inches.d) the percent of trees that has a diameter between 8.0 and 10.0 inches. e) Any tree which has a diameter less than 4.00 inches is considered to be a “Small Tree.” Determine the percent of trees that receive this designation.f) The largest 5% of trees is designated as a “Big Tree”. Determine the diameter that a tree would need to have in order to receive this designation.g) The smallest 5% of trees are given extra nutrients in order to grow. Determine the diameter that a tree would need to have in order to be given the extra nutrients.
In: Statistics and Probability
2. The joint pmf of ? and ? is given by
??,? (?, ?) = （x+y）/27 ??? ? = 0, 1,2; ? = 1, 2, 3,
and ??,? (?, ?) = 0 otherwise.
a. Find ?(?|? = ?) for all ? = 0,1, 2.
b. Find ?(3 + 0.2?|? = 2).
In: Statistics and Probability