Statistics (13th Edition)
13th Edition
ISBN: 9780134080215
Author: James T. McClave, Terry T Sincich
Publisher: PEARSON
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Chapter 7.4, Problem 71ACI
a.
To determine
Explain whether the
b.
To determine
Find and interpret the 95% confidence
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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.
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 7 Solutions
Statistics (13th Edition)
Ch. 7.2 - Define the target parameter.
Ch. 7.2 - What is the confidence coefficient in a 90%...Ch. 7.2 - 6.7 Explain the difference between an interval...Ch. 7.2 - 6.6 Explain what is meant by the statement, “We...Ch. 7.2 - 6.9 Will a large-sample confidence interval be...Ch. 7.2 - What conditions are required to form a valid...Ch. 7.2 - Find zα/2 for each of the following:
α = .10
α =...Ch. 7.2 - What is the confidence level of each of the...Ch. 7.2 - A random sample of n measurements was selected...Ch. 7.2 - 6.4 A random sample of 90 observations produced a...
Ch. 7.2 - A random sample of 100 observations from a...Ch. 7.2 - 6.8 The mean and standard deviation of a random...Ch. 7.2 - Use the applet entitled Confidence Intervals for a...Ch. 7.2 - Use the applet Confidence Intervals for a Mean...Ch. 7.2 - 6.10 Heart rate variability of police officers....Ch. 7.2 - Irrelevant speech effects. Refer to the Acoustical...Ch. 7.2 - Latex allergy in health care workers. Health care...Ch. 7.2 - Lipid profiles of hypertensive patients. People...Ch. 7.2 - Motivation of drug dealers. Refer to the Applied...Ch. 7.2 - Corporate sustainability of CPA firms. Corporate...Ch. 7.2 - Prob. 19ACBCh. 7.2 - Evaporation from swimming pools. A new formula for...Ch. 7.2 - 6.20 Facial structure of CEOs. In Psychological...Ch. 7.2 - 6.16 Shopping on Black Friday. The day after...Ch. 7.2 - Prob. 23ACICh. 7.2 - Prob. 24ACICh. 7.2 - Prob. 25ACICh. 7.2 - Speed training in football. Researchers at...Ch. 7.2 - Prob. 27ACACh. 7.2 - Prob. 28ACACh. 7.3 - State the two problems (and corresponding...Ch. 7.3 - Compare the shapes of the z- and t-distributions.
Ch. 7.3 - 6.24 Explain the differences in the sampling...Ch. 7.3 - Use the applet Confidence Intervals for a Mean...Ch. 7.3 - Use the applet Confidence Intervals for a Mean...Ch. 7.3 - Suppose you have selected a random sample of n = 7...Ch. 7.3 - Let t0 be a specific value of t. Use technology or...Ch. 7.3 - Let t0 be a particular value of t. Use technology...Ch. 7.3 - 6.27 The following random sample was selected from...Ch. 7.3 - 6.28 The following sample of 16 measurements was...Ch. 7.3 - Music performance anxiety. Refer to the British...Ch. 7.3 - Giraffes have excellent vision. Due to habitat,...Ch. 7.3 - Radon exposure in Egyptian tombs. Many ancient...Ch. 7.3 - Rainfall and desert ants. Refer to the Journal of...Ch. 7.3 - 6.29 Lobster trap placement. An observational...Ch. 7.3 - Shell lengths of sea turtles. Refer to the Aquatic...Ch. 7.3 - Duration of daylight in western Pennsylvania. What...Ch. 7.3 - 6.31 Do social robots walk or roll? Refer to the...Ch. 7.3 - Pitch memory of amusiacs. A team of psychologists...Ch. 7.3 - Shaft graves in ancient Greece. Refer to the...Ch. 7.3 - 6.35 Oxygen bubbles in molten salt. Molten salt is...Ch. 7.3 - Prob. 48ACICh. 7.3 - Reproduction of bacteria-infected spider mites....Ch. 7.3 - Antigens for a parasitic roundworm in birds....Ch. 7.3 - Prob. 51ACACh. 7.4 - 6.40 Describe the sampling distribution of based...Ch. 7.4 - Explain the meaning of the phrase “ is an unbiased...Ch. 7.4 - Prob. 54UPCh. 7.4 - Use the applet Confidence Intervals for a...Ch. 7.4 - Use the applet Confidence Intervals for a...Ch. 7.4 - A random sample of size n = 196 yielded .
Is the...Ch. 7.4 - A random sample of size n = 144 yielded .
Is the...Ch. 7.4 - For the binomial sample information summarized in...Ch. 7.4 - A random sample of 50 consumers taste-tested a new...Ch. 7.4 - Paying for music downloads. If you use the...Ch. 7.4 - Interactions in a children’s museum. Refer to the...Ch. 7.4 - Is Starbucks coffee overpriced? The Minneapolis...Ch. 7.4 - Nannies who work for celebrities. The...Ch. 7.4 - National Firearms Survey. Refer to the Harvard...Ch. 7.4 - Are you really being served red snapper? Refer to...Ch. 7.4 - What we do when we are sick at home. USA Today...Ch. 7.4 - Curbing street gang gun violence. Refer to the...Ch. 7.4 - Do social robots walk or roll? Refer to the...Ch. 7.4 - Study of aircraft bird strikes. As worldwide air...Ch. 7.4 - Prob. 69ACICh. 7.4 - Prob. 70ACICh. 7.4 - Prob. 71ACICh. 7.4 - Do you think you smell? If you falsely believe you...Ch. 7.4 - Prob. 73ACACh. 7.5 - How does the sampling error SE compare with the...Ch. 7.5 - True or false. For a specified sampling error SE,...Ch. 7.5 - True or false. For a fixed confidence level (1 −...Ch. 7.5 - Prob. 77LMCh. 7.5 - 6.66 If nothing is known about p. .5 can be...Ch. 7.5 - Suppose you wish to estimate a population mean...Ch. 7.5 - In each case, find the approximate sample size...Ch. 7.5 - The following is a 90% confidence interval for p:...Ch. 7.5 - Prob. 82LMCh. 7.5 - Suppose you wish to estimate the mean of a normal...Ch. 7.5 - Giraffes have excellent vision. Refer to the...Ch. 7.5 - Shaft graves in ancient Greece. Refer to the...Ch. 7.5 - Risk of home burglary in cul-de-sacs. Research...Ch. 7.5 - Prob. 87ACBCh. 7.5 - Aluminum cans contaminated by fire. A gigantic...Ch. 7.5 - Prob. 89ACBCh. 7.5 - Pitch memory of amusiacs. Refer to the Advances in...Ch. 7.5 - Shopping on Black Friday. Refer to the...Ch. 7.5 - Prob. 93ACICh. 7.5 - Prob. 94ACICh. 7.5 - Prob. 95ACICh. 7.5 - Caffeine content of coffee. According to a Food...Ch. 7.5 - Prob. 97ACICh. 7.5 - Preventing production of defective items. It costs...Ch. 7.6 - What sampling distribution is used to find an...Ch. 7.6 - Prob. 100UPCh. 7.6 - Prob. 101UPCh. 7.6 - Prob. 102LMCh. 7.6 - Given the following values of , s, and n, form a...Ch. 7.6 - Prob. 104LMCh. 7.6 - Prob. 105LMCh. 7.6 - Prob. 106ACBCh. 7.6 - Prob. 107ACBCh. 7.6 - Motivation of drug dealers. Refer to the Applied...Ch. 7.6 - Prob. 109ACBCh. 7.6 - Prob. 110ACBCh. 7.6 - Prob. 111ACBCh. 7.6 - Prob. 112ACICh. 7.6 - Prob. 113ACICh. 7.6 - Shell lengths of sea turtles. Refer to the Aquatic...Ch. 7.6 - Prob. 115ACICh. 7.6 - s6.105 Is honey a cough remedy? Refer to the...Ch. 7.6 - Prob. 117ACICh. 7 - Prob. 118UPCh. 7 - Prob. 119UPCh. 7 - In each of the following instances, determine...Ch. 7 - Prob. 121LMCh. 7 - Prob. 122LMCh. 7 - Prob. 123LMCh. 7 - Prob. 124LMCh. 7 - 6.113 General health survey. The Centers for...Ch. 7 - Prob. 126ACBCh. 7 - Prob. 127ACBCh. 7 - Prob. 128ACBCh. 7 - Scanning errors at Wal-Mart. Refer to the National...Ch. 7 - Prob. 130ACBCh. 7 - Assessing the bending strength of a wooden roof....Ch. 7 - Prob. 132ACBCh. 7 - Prob. 133ACBCh. 7 - Prob. 134ACBCh. 7 - Prob. 135ACBCh. 7 - Prob. 136ACBCh. 7 - Prob. 137ACICh. 7 - Prob. 138ACICh. 7 - Prob. 139ACICh. 7 - Prob. 140ACICh. 7 - Prob. 141ACICh. 7 - Prob. 142ACICh. 7 - Prob. 143ACICh. 7 - Prob. 144ACICh. 7 -
Salmonella in ice cream bars. Recently, a case...Ch. 7 - Prob. 146ACICh. 7 - Prob. 147ACICh. 7 - Jitter in a water power system. Jitter is a term...Ch. 7 - Prob. 149ACACh. 7 - Prob. 150ACACh. 7 - Prob. 151CTCCh. 7 - 6.138 A sampling dispute goes to court. Sampling...
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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
- 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
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