Answer all questions. Each answer must provide a managerial explanation of the outcomes.

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answer_all_the_question_in_the_files.docx

lawsuit.xlsx

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Answer all questions. Each answer must provide a managerial explanation of the outcomes.
1. One of the reasons health care costs have been rising rapidly in recent years is the
increasing cost of malpractice insurance for physicians. Also, fear of being sued causes
doctors to run more precautionary tests (possibly unnecessary) just to make sure they are
not guilty of missing something (Reader’s Digest, October 2012). These precautionary
tests also add to health care costs. Data in the DATAfile named LawSuit are consistent
with findings in the Reader’s Digest article and can be used to estimate the proportion of
physicians over the age of 55 who have been sued at least once.
a. Formulate hypotheses that can be used to see if these data can support a finding that more
than half of physicians over the age of 55 have been sued at least once.
b. Use Excel and the Datafile named LawSuit to compute the sample proportion of
physicians over the age of 55 who have been sued at least once. What is the p-value for
your hypothesis test?
c. At a = .01, what is your conclusion?
2. The College Board SAT college entrance exam consists of three parts: math, writing, and
critical reading. Sample data showing the math and writing scores for a sample of 12
students who took the SAT are presented in the Datafile named TestScores.
a. Use a .05 level of significance and test for a difference between the population mean for
the math scores and the population mean for the writing scores. What is the p-value and
what is your conclusion?
b. What is the point estimate of the difference between the mean score of the two tests?
What are the estimates of the population mean scores for the two tests? Which test
reports the higher mean score?
3. The average annual cost to attend a public college takes nearly a third of the annual
income of a typical family with college-age children. At private colleges, the average
annual income is equal to about 60% of the typical family’s income. The DATAfile
named CollegeCosts contains random samples of annual costs of attending private and
public colleges.
a. What is the point estimate of the difference between the two population mean? Interpret
this value in terms of the annual cost of attending private and public colleges. Use a =
.05.
b. Is there a significant difference between the mean annual cost of attending private
colleges and the mean annual cost of attending public colleges?
4. Four different paints are advertised as having the same drying time. To check the
manufacturer’s claims, five samples were tested for each of the paints. The time in
minutes until the paint was dry enough for a second coat to be applied was recorded. The
Datafile named Paint contains the samples.
At the a = .05 level of significance, test to see whether the mean drying time is the same
for each type of paint. Make sure to state your hypotheses clearly.
5. A 10-year study conducted by the American Heart Association provided data on how age,
blood pressure, and smoking habit relate to the risk of strokes. A random sample is taken
from the study and is given in the Datafile named Strokes. Risk is interpreted as the
probability (times 100) that the patient will have a stroke over the next 10-year period.
a. Develop an estimated regression equation that relates risk of a stroke to the person’s age,
blood pressure, and whether the person is a smoker.
b. Is smoking a significant factor in the risk of a stroke? Explain. Use a .05.
c. What is the probability of a stroke over the next 10 years for Art Speen, a 68-year-old
smoker who has blood pressure of 175? What action might the physician recommend for
this patient?
(Note: You must follow the procedures as outlined in the class for Problem 5).
Have you been
sued by a patient?
No
No
Yes
Yes
No
No
Yes
No
Yes
Yes
No
Yes
No
No
Yes
No
Yes
No
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
No
Yes
No
Yes
Yes
Yes
Yes
No
No
Yes
Yes
Yes
No
No
Yes
No
Yes
Yes
No
No
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
No
Yes
No
Yes
No
Yes
No
Yes
Yes
Yes
Yes
No
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
55
Yes
Yes
Yes
No
Yes
No
No
Yes
No
Yes
Yes
No
No
Yes
No
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
Yes
Yes
Yes
Yes
No
No
No
No
No
No
No
Yes
Yes
Yes
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
No
Yes
No
No
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Paint 1
128
137
135
124
141
Paint 2
144
133
142
146
130
Paint 3
133
143
137
136
131
Paint 4
150
142
135
140
153
Data
Risk
Age
12
24
13
56
28
51
18
31
37
15
22
36
15
48
15
36
8
34
3
37
57
67
58
86
59
76
56
78
80
78
71
70
67
77
60
82
66
80
62
59
Pressure
152
163
155
177
196
189
155
120
135
98
152
173
135
209
199
119
166
125
117
207
Smoker
No
No
No
Yes
No
Yes
Yes
No
Yes
No
No
Yes
Yes
Yes
No
Yes
No
Yes
No
Yes
Page 1
Math Score Writing Score
540
474
432
380
528
463
574
612
448
420
502
526
480
430
499
459
610
615
572
541
390
335
593
613
Private
52.8
43.2
45.0
33.3
44.0
30.6
45.8
37.8
50.5
42.0
Public
20.3
22.0
28.2
15.6
24.1
28.5
22.8
25.8
18.5
25.6
14.4
21.8
Have you been
sued by a patient?
No
No
Yes
Yes
No
No
Yes
No
Yes
Yes
No
Yes
No
No
Yes
No
Yes
No
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
No
Yes
No
Yes
Yes
Yes
Yes
No
No
Yes
Yes
Yes
No
No
Yes
No
Yes
Yes
No
No
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
No
Yes
No
Yes
No
Yes
No
Yes
Yes
Yes
Yes
No
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
55
Yes
Yes
Yes
No
Yes
No
No
Yes
No
Yes
Yes
No
No
Yes
No
No
Yes
No
Yes
No
Yes
No
Yes
No
Yes
Yes
Yes
Yes
Yes
No
No
No
No
No
No
No
Yes
Yes
Yes
No
No
No
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Yes
No
Yes
No
No
Yes
Yes
Yes
Yes
Yes
No
Yes
Yes
Paint 1
128
137
135
124
141
Paint 2
144
133
142
146
130
Paint 3
133
143
137
136
131
Paint 4
150
142
135
140
153
Data
Risk
Age
12
24
13
56
28
51
18
31
37
15
22
36
15
48
15
36
8
34
3
37
57
67
58
86
59
76
56
78
80
78
71
70
67
77
60
82
66
80
62
59
Pressure
152
163
155
177
196
189
155
120
135
98
152
173
135
209
199
119
166
125
117
207
Smoker
No
No
No
Yes
No
Yes
Yes
No
Yes
No
No
Yes
Yes
Yes
No
Yes
No
Yes
No
Yes
Page 1
Math Score Writing Score
540
474
432
380
528
463
574
612
448
420
502
526
480
430
499
459
610
615
572
541
390
335
593
613
Answer all questions. Each answer must provide a managerial explanation of the outcomes.
1. One of the reasons health care costs have been rising rapidly in recent years is the
increasing cost of malpractice insurance for physicians. Also, fear of being sued causes
doctors to run more precautionary tests (possibly unnecessary) just to make sure they are
not guilty of missing something (Reader’s Digest, October 2012). These precautionary
tests also add to health care costs. Data in the DATAfile named LawSuit are consistent
with findings in the Reader’s Digest article and can be used to estimate the proportion of
physicians over the age of 55 who have been sued at least once.
a. Formulate hypotheses that can be used to see if these data can support a finding that more
than half of physicians over the age of 55 have been sued at least once.
b. Use Excel and the Datafile named LawSuit to compute the sample proportion of
physicians over the age of 55 who have been sued at least once. What is the p-value for
your hypothesis test?
c. At a = .01, what is your conclusion?
2. The College Board SAT college entrance exam consists of three parts: math, writing, and
critical reading. Sample data showing the math and writing scores for a sample of 12
students who took the SAT are presented in the Datafile named TestScores.
a. Use a .05 level of significance and test for a difference between the population mean for
the math scores and the population mean for the writing scores. What is the p-value and
what is your conclusion?
b. What is the point estimate of the difference between the mean score of the two tests?
What are the estimates of the population mean scores for the two tests? Which test
reports the higher mean score?
3. The average annual cost to attend a public college takes nearly a third of the annual
income of a typical family with college-age children. At private colleges, the average
annual income is equal to about 60% of the typical family’s income. The DATAfile
named CollegeCosts contains random samples of annual costs of attending private and
public colleges.
a. What is the point estimate of the difference between the two population mean? Interpret
this value in terms of the annual cost of attending private and public colleges. Use a =
.05.
b. Is there a significant difference between the mean annual cost of attending private
colleges and the mean annual cost of attending public colleges?
4. Four different paints are advertised as having the same drying time. To check the
manufacturer’s claims, five samples were tested for each of the paints. The time in
minutes until the paint was dry enough for a second coat to be applied was recorded. The
Datafile named Paint contains the samples.
At the a = .05 level of significance, test to see whether the mean drying time is the same
for each type of paint. Make sure to state your hypotheses clearly.
5. A 10-year study conducted by the American Heart Association provided data on how age,
blood pressure, and smoking habit relate to the risk of strokes. A random sample is taken
from the study and is given in the Datafile named Strokes. Risk is interpreted as the
probability (times 100) that the patient will have a stroke over the next 10-year period.
a. Develop an estimated regression equation that relates risk of a stroke to the person’s age,
blood pressure, and whether the person is a smoker.
b. Is smoking a significant factor in the risk of a stroke? Explain. Use a .05.
c. What is the probability of a stroke over the next 10 years for Art Speen, a 68-year-old
smoker who has blood pressure of 175? What action might the physician recommend for
this patient?
(Note: You must follow the procedures as outlined in the class for Problem 5).

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