Statistics: The Art and Science of Learning from Data (4th Edition)
4th Edition
ISBN: 9780321997838
Author: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
Publisher: PEARSON
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Chapter 13.6, Problem 56PB
a.
To determine
Give an interpretation of the predictors, by considering the signs of the coefficients.
b.
To determine
(i) Find the estimated probability that a man having 16 years of education and an income of $40,000 will vote for the Republican.
(ii) Find the estimated probability that a woman having 16 years of education and an income of $40,000 will vote for the Republican.
Compare the estimated probabilities in order to elucidate the effect of gender on the probability.
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For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of
months unemployed and the values in the second column show the corresponding number of unemployed persons.
Months
Unemployed
Number
Unemployed
1
1029
2
1686
3
2269
4
2675
5
3487
6
4652
7
4145
8
3587
9
2325
10
1120
Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals).
(x)
f(x)
1
2
3
4
5
6
7
8
9
10
b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
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c. What is the probability that a…
West Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff.
Working with a consultant, the management of MCC has developed the following probability distribution for x = the number of new clients for marriage counseling for the next year.
Excel File: data05-19.xls
x
10
f(x)
.05
20
30
.10
.10
40
.20
50
60
.35
.20
a. Is this probability distribution valid?
- Select your answer-
Explain.
f(x)
Σf(x)
Select your answer
Select your answer
b. What is the probability MCC will obtain more than 30 new clients (to 2 decimals)?
c. What is the probability MCC will obtain fewer than 20 new clients (to 2 decimals)?
d. Compute the expected value and variance of x.
Expected value
Variance
clients per year
squared clients per year
For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of
months unemployed and the values in the second column show the corresponding number of unemployed persons.
Months
Unemployed
Number
Unemployed
1
1029
2
1686
3
2269
4
2675
5
3487
6
4652
7
4145
8
3587
9
2325
10
1120
Let x be a random variable indicating the number of months a person is unemployed.
a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals).
(x)
f(x)
1
2
3
4
5
6
7
8
9
10
b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution.
The input in the box below will not be graded, but may be reviewed and considered by your instructor.
c. What is the probability that a person…
Chapter 13 Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
Ch. 13.1 - Predicting weight For a study of female college...Ch. 13.1 - Prob. 2PBCh. 13.1 - Predicting college GPA For all students at Walden...Ch. 13.1 - Prob. 4PBCh. 13.1 - Does more education cause more crime? The FL Crime...Ch. 13.1 - Crime rate and income Refer to the previous...Ch. 13.1 - The economics of golf The earnings of a PGA Tour...Ch. 13.1 - Prob. 8PBCh. 13.1 - Controlling can have no effect Suppose that the...Ch. 13.1 - House selling prices Using software with the House...
Ch. 13.1 - Used cars The following data (also available from...Ch. 13.2 - Predicting sports attendance Keeneland Racetrack...Ch. 13.2 - Predicting weight Lets use multiple regression to...Ch. 13.2 - Prob. 14PBCh. 13.2 - Price of used cars For the 19 used cars listed in...Ch. 13.2 - Prob. 16PBCh. 13.2 - Softball data For the Softball data set on the...Ch. 13.2 - Slopes, correlations, and units In Example 2 on y...Ch. 13.2 - Predicting college GPA Using software with the...Ch. 13.3 - Predicting GPA For the 59 observations in the...Ch. 13.3 - Study time help GPA? Refer to the previous...Ch. 13.3 - Variability in college GPA Refer to the previous...Ch. 13.3 - Does leg press help predict body strength? Chapter...Ch. 13.3 - Prob. 24PBCh. 13.3 - Interpret strength variability Refer to the...Ch. 13.3 - Any predictive power? Refer to the previous three...Ch. 13.3 - Predicting pizza revenue Aunt Ermas Pizza...Ch. 13.3 - Prob. 28PBCh. 13.3 - Mental health again Refer to the previous...Ch. 13.3 - Prob. 30PBCh. 13.3 - House prices Use software to do further analyses...Ch. 13.4 - Body weight residuals Examples 47 used multiple...Ch. 13.4 - Strength residuals In Chapter 12, we analyzed...Ch. 13.4 - Prob. 34PBCh. 13.4 - Nonlinear effects of age Suppose you fit a...Ch. 13.4 - Prob. 36PBCh. 13.4 - Why inspect residuals? When we use multiple...Ch. 13.4 - College athletes The College Athletes data set on...Ch. 13.4 - House prices Use software with the House Selling...Ch. 13.4 - Prob. 40PBCh. 13.5 - U.S. and foreign used cars Refer to the used car...Ch. 13.5 - Prob. 42PBCh. 13.5 - Predict using house size and condition For the...Ch. 13.5 - Quality and productivity The table shows data from...Ch. 13.5 - Predicting hamburger sales A chain restaurant that...Ch. 13.5 - Prob. 46PBCh. 13.5 - House size and garage interact? Refer to the...Ch. 13.5 - Prob. 48PBCh. 13.5 - Comparing sales You own a gift shop that has a...Ch. 13.6 - Prob. 50PBCh. 13.6 - Prob. 51PBCh. 13.6 - Prob. 52PBCh. 13.6 - Prob. 53PBCh. 13.6 - Prob. 54PBCh. 13.6 - Prob. 55PBCh. 13.6 - Prob. 56PBCh. 13.6 - Prob. 57PBCh. 13.6 - Prob. 58PBCh. 13.6 - Prob. 59PBCh. 13 - House prices This chapter has considered many...Ch. 13 - Prob. 61CPCh. 13 - Prob. 62CPCh. 13 - Prob. 63CPCh. 13 - Prob. 64CPCh. 13 - Prob. 65CPCh. 13 - Prob. 66CPCh. 13 - Prob. 67CPCh. 13 - Prob. 68CPCh. 13 - Prob. 69CPCh. 13 - AIDS and AZT In a study (reported in the New York...Ch. 13 - Factors affecting first home purchase The table...Ch. 13 - Unemployment and GDP Refer to Exercise 13.67. When...Ch. 13 - Prob. 75CPCh. 13 - Prob. 76CPCh. 13 - Prob. 77CPCh. 13 - Prob. 78CPCh. 13 - Prob. 79CPCh. 13 - True or false: Slopes For data on y = college GPA,...Ch. 13 - Prob. 81CPCh. 13 - Lurking variable Give an example of three...Ch. 13 - Prob. 83CPCh. 13 - Prob. 84CPCh. 13 - Prob. 85CPCh. 13 - Logistic versus linear For binary response...Ch. 13 - Prob. 87CPCh. 13 - Prob. 88CPCh. 13 - Prob. 89CPCh. 13 - Prob. 90CPCh. 13 - Prob. 91CPCh. 13 - Prob. 92CPCh. 13 - Prob. 93CP
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- In Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained (Gallup website, August 6, 2012). Excel File: data05-23.xls Number of Cups per Day Number of Responses 0 365 264 193 3 4 or more 91 101 Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups. Round your answers to four decimal places. a. Develop a probability distribution for x. x 0 1 2 3 4 f(x) b. Compute the expected value of x. cups of coffee c. Compute the variance of x. cups of coffee squared d. Suppose we are only interested in adults that drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day. Compute the expected value of y. Compare it to the expected value of x. The…arrow_forwardIn Gallup's Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was "How many cups of coffee, if any, do you drink on an average day?" The following table shows the results obtained (Gallup website, August 6, 2012). Excel File: data05-23.xls Number of Cups per Day Number of Responses 0 365 264 193 2 3 4 or more 91 101 Define a random variable x = number of cups of coffee consumed on an average day. Let x = 4 represent four or more cups. Round your answers to four decimal places. a. Develop a probability distribution for x. x 0 1 2 3 f(x) b. Compute the expected value of x. cups of coffee c. Compute the variance of x. cups of coffee squared d. Suppose we are only interested in adults that drink at least one cup of coffee on an average day. For this group, let y = the number of cups of coffee consumed on an average day. Compute the expected value of y. Compare it to the expected value of x. The…arrow_forwardA technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency. Develop a probability distribution for the duration of a service call. Duration of Call x f(x) 1 2 3 4 Which of the following probability distribution graphs accurately represents the data set? Consider the required conditions for a discrete probability function, shown below.Does this probability distribution satisfy equation (5.1)?Does this probability distribution satisfy equation (5.2)? What is the probability a service call will take three hours? A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?arrow_forward
- A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patient's trust. The following probability function has been proposed. x f(x) for x = 1, 2, or 3 a. Consider the required conditions for a discrete probability function, shown below. f(x) ≥0 Σf(x) = 1 (5.1) (5.2) Does this probability distribution satisfy equation (5.1)? Select Does this probability distribution satisfy equation (5.2)? Select b. What is the probability that it takes exactly 2 sessions to gain the patient's trust (to 3 decimals)? c. What is the probability that it takes at least 2 sessions to gain the patient's trust (to 3 decimals)?arrow_forwardA technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency. Develop a probability distribution for the duration of a service call. Which of the following probability distribution graphs accurately represents the data set? Consider the required conditions for a discrete probability function, shown below.Does this probability distribution satisfy equation (5.1)?Does this probability distribution satisfy equation (5.2)? What is the probability a service call will take three hours? A service call has just come in, but the type of malfunction is unknown. It is 3:00 P.M. and service technicians usually get off at 5:00 P.M. What is the probability the service technician will have to work overtime to fix the machine today?arrow_forwardWest Virginia has one of the highest divorce rates in the nation, with an annual rate of approximately 5 divorces per 1000 people (Centers for Disease Control and Prevention website, January 12, 2012). The Marital Counseling Center, Inc. (MCC) thinks that the high divorce rate in the state may require them to hire additional staff. Working with a consultant, the management of MCC has developed the following probability distribution for x = the number of new clients for marriage counseling for the next year. Excel File: data05-19.xls 10 20 f(x) .05 .10 11 30 40 50 60 .10 .20 .35 .20 a. Is this probability distribution valid? Yes Explain. greater than or equal to 0 f(x) Σf(x) equal to 1 b. What is the probability MCC will obtain more than 30 new clients (to 2 decimals)? c. What is the probability MCC will obtain fewer than 20 new clients (to 2 decimals)? d. Compute the expected value and variance of x. Expected value Variance clients per year squared clients per yeararrow_forward
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