Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 11.4, Problem 41E
a.
To determine
Test the significance of the regression at 5% level of significance.
Find the P-value of the test.
Check whether it can be concluded that the model specifies a useful relationship between these two variables.
b.
To determine
Estimate
c.
To determine
Find the standard error of the intercept in the model..
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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.
blank
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 11 Solutions
Applied Statistics and Probability for Engineers
Ch. 11.2 - 11-1. Diabetes and obesity are serious health...Ch. 11.2 - 11-2. On average, do people gain weight as they...Ch. 11.2 - Prob. 3ECh. 11.2 - 11-4. Regression methods were used to analyze the...Ch. 11.2 - 11-5. See Table E11-1 for data on the ratings of...Ch. 11.2 - 11-6. An article in Technometrics by S. C. Narula...Ch. 11.2 - 11-7. The number of pounds of steam used per month...Ch. 11.2 - 11-8. Go Tutorial Table E11-3 presents the highway...Ch. 11.2 - Prob. 9ECh. 11.2 - 11-10. An article in the Journal of Sound and...
Ch. 11.2 - Prob. 11ECh. 11.2 - 11-12. An article in the Journal of Environmental...Ch. 11.2 - 11-13. A rocket motor is manufactured by bonding...Ch. 11.2 - 11-14. Go Tutorial An article in the Journal of...Ch. 11.2 - 11-15 An article in the Journal of the...Ch. 11.2 - 11-16. An article in Wood Science and Technology...Ch. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - 11-20. Show that in a simple linear regression...Ch. 11.2 - 11-21. Consider the simple linear regression model...Ch. 11.2 - 11-22. Suppose that we wish to fit a regression...Ch. 11.4 - 11-23. Recall the regression of percent body fat...Ch. 11.4 - Prob. 24ECh. 11.4 - 11-25. Suppose that in Exercise 11-24 weight is...Ch. 11.4 - 11-26. Consider the simple linear regression model...Ch. 11.4 - Prob. 27ECh. 11.4 - Prob. 28ECh. 11.4 - Prob. 29ECh. 11.4 - Prob. 30ECh. 11.4 - 11-31. Consider the National Football League data...Ch. 11.4 - Prob. 32ECh. 11.4 - Prob. 33ECh. 11.4 - Prob. 34ECh. 11.4 - 11-35. Consider the data from Exercise 11-9 on y =...Ch. 11.4 - Prob. 36ECh. 11.4 - 11-37. Consider the data from Exercise 11-13, on y...Ch. 11.4 - 11-38. Consider the data from Exercise 11-12 on y...Ch. 11.4 - Prob. 39ECh. 11.4 - Prob. 40ECh. 11.4 - Prob. 41ECh. 11.4 - Prob. 42ECh. 11.4 - Prob. 44ECh. 11.6 - 11-45. Using the regression from Exercise...Ch. 11.6 - 11-46. Q Using the regression from Exercise...Ch. 11.6 - 11-47. Refer to the data in Exercise 11-3 on y =...Ch. 11.6 - 1-48. Exercise 11-4 presented data on roadway...Ch. 11.6 - 11-49. Refer to the NFL quarterback ratings data...Ch. 11.6 - Prob. 50ECh. 11.6 - 11-51. Exercise 11-7 presented data on y = steam...Ch. 11.6 - 11-52. Exercise 11-8 presented gasoline mileage...Ch. 11.6 - Prob. 53ECh. 11.6 - Prob. 54ECh. 11.6 - Prob. 55ECh. 11.6 - 11-56. Exercise 11-12 presented data on chloride...Ch. 11.6 - 11-57. Refer to the data in Exercise 11-13 on...Ch. 11.6 - Prob. 58ECh. 11.6 - Prob. 59ECh. 11.7 - 11-60. Consider the simple linear regression model...Ch. 11.7 - 11-61. Repeat Exercise 11-60 using an error term...Ch. 11.7 - 11-62. Refer to the compressive strength data in...Ch. 11.7 - 11-63. Refer to the NFL quarterback ratings data...Ch. 11.7 - 11-64. Refer to the data in Exercise 11-6 on...Ch. 11.7 - 11-65. Refer to the data in Exercise 11-7 on y =...Ch. 11.7 - 11-66. Refer to the gasoline mileage data in...Ch. 11.7 - Prob. 67ECh. 11.7 - Prob. 68ECh. 11.7 - 11-69. Refer to Exercise 11-12. which presented...Ch. 11.7 - Prob. 70ECh. 11.7 - 11-71. Consider the rocket propellant data in...Ch. 11.7 - 11-72. Consider the data in Exercise 11-9 on y =...Ch. 11.7 - Prob. 73ECh. 11.7 - Prob. 74ECh. 11.7 - Prob. 75ECh. 11.8 - 11-76. Suppose that data are obtained from 20...Ch. 11.8 - 11-77. Suppose that data are obtained from 20...Ch. 11.8 - Prob. 78ECh. 11.8 - 11-79. A random sample of 50 observations was made...Ch. 11.8 - 11-80. The data in Table E11-6 gave x = the water...Ch. 11.8 - Prob. 81ECh. 11.8 - 11-82. The weight and systolic blood pressure of...Ch. 11.8 - Prob. 83ECh. 11.8 - Prob. 84ECh. 11.8 - 11-85. Refer to the NFL quarterback ratings data...Ch. 11.8 - Prob. 86ECh. 11.9 - Prob. 87ECh. 11.9 - Prob. 88ECh. 11.9 - 11-89. An electric utility is interested in...Ch. 11.10 - Prob. 90ECh. 11.10 - 11-91. The compressive strength of an alloy...Ch. 11.10 - Prob. 92ECh. 11.10 - Prob. 93ECh. 11.10 - Prob. 94ECh. 11.10 - 11-95 Consider the propellant data is Exercise...Ch. 11 - Prob. 96SECh. 11 - Prob. 97SECh. 11 - 11-98. The strength of paper used in the...Ch. 11 - Prob. 99SECh. 11 - Prob. 100SECh. 11 - Prob. 101SECh. 11 - Prob. 102SECh. 11 - 11-103. An article in the Journal of Applied...Ch. 11 - 11-104. Two different methods can be used for...Ch. 11 - 11-105. The grams of solids removed from a...Ch. 11 - Prob. 106SECh. 11 - 11-107. The data in Table E11-20 related diamond...Ch. 11 - Prob. 108SECh. 11 - Prob. 109SECh. 11 - Prob. 110SECh. 11 - 11-111. Consider the simple linear regression...Ch. 11 - Prob. 112SECh. 11 - Prob. 113SECh. 11 - Prob. 114SECh. 11 - Prob. 115SECh. 11 - Prob. 116SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- 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
- Reconsider the patient satisfaction data in Table 1. Fit a multiple regression model using both patient age and severity as the regressors. (a) Test for significance of regression. (b) Test for the individual contribution of the two regressors. Are both regressor variables needed in the model? (c) Has adding severity to the model improved the quality of the model fit? Explain your answer.arrow_forwardThe output voltage of a power supply is assumed to be normally distributed. Sixteen observations taken at random on voltage are as follows: 10.35, 9.30, 10.00, 9.96, 11.65, 12.00, 11.25, 9.58, 11.54, 9.95, 10.28, 8.37, 10.44, 9.25, 9.38, and 10.85. (a) Test the hypothesis that the mean voltage equals 12 V against a two-sided alternative using a = 0.05. (b) Construct a 95% two-sided confidence interval on μ. (c) Test the hypothesis that σ² = 11 using α = 0.05. (d) Construct a 95% two-sided confidence interval on σ. (e) Construct a 95% upper confidence interval on σ. (f) Does the assumption of normality seem reasonable for the output voltage?arrow_forwardAnalyze the residuals from the regression model on the patient satisfaction data from Exercise 3. Comment on the adequacy of the regression model.arrow_forward
- Consider the hypotheses: Hop=po H₁ppo where 2 is known. Derive a general expression for determining the sample size for detecting a true mean of 1μo with probability 1-ẞ if the type I error is a.arrow_forwardSuppose we wish to test the hypotheses: Họ : | = 15 H₁: 15 where we know that o² = 9.0. If the true mean is really 20, what sample size must be used to ensure that the probability of type II error is no greater than 0.10? Assume that a = 0.05.arrow_forwardTable 1 contains the data from a patient satisfaction survey for a group of 25 randomly selected patients at a hospital. In addition to satisfaction, data were collected on patient age and an index that measured the severity of illness. (a) Fit a linear regression model relating satisfaction to patient age. (b) Test for significance of regression. (c) What portion of the total variability is accounted for by the regressor variable age? Table 1: Patient Satisfaction Data Severity Observation Age (21) (x2) Satisfaction (y) 1 55 50 2 46 24 3 30 46 4 35 48 5 59 58 6 61 60 7 74 65 8 38 42 9 27 42 10 51 50 11 53 38 12 41 30 13 37 31 88 14 24 34 15 42 30 16 50 48 17 58 61 18 60 71 19 62 62 20 68 38 21 70 41 22 79 66 23 63 31 24 39 42 25 49 40 BE225222222222222222 68 77 96 80 43 44 26 88 75 57 56 88 102 88 70 43 46 56 59 26 83 75arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Use of ALGEBRA in REAL LIFE; Author: Fast and Easy Maths !;https://www.youtube.com/watch?v=9_PbWFpvkDc;License: Standard YouTube License, CC-BY
Compound Interest Formula Explained, Investment, Monthly & Continuously, Word Problems, Algebra; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=P182Abv3fOk;License: Standard YouTube License, CC-BY
Applications of Algebra (Digit, Age, Work, Clock, Mixture and Rate Problems); Author: EngineerProf PH;https://www.youtube.com/watch?v=Y8aJ_wYCS2g;License: Standard YouTube License, CC-BY