ALEKS 360 ELEM STATISTICS
10th Edition
ISBN: 9781264241385
Author: Bluman
Publisher: MCG
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Chapter 9, Problem 7CQ
To determine
The approximate value that can be equal to the
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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 9 Solutions
ALEKS 360 ELEM STATISTICS
Ch. 9.1 - Home Runs For a sports radio talk show, you are...Ch. 9.1 - Explain the difference between testing a single...Ch. 9.1 - When a researcher selects all possible pairs of...Ch. 9.1 - What three assumptions must be met when you are...Ch. 9.1 - Show two different ways to state that the means of...Ch. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - For Exercises 5 through 16, perform each of the...
Ch. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - Prob. 13ECh. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - Self-Esteem Scores In a study of a group of women...Ch. 9.1 - Ages of College Students The dean of students...Ch. 9.1 - Working Breath Rate Two random samples of 32...Ch. 9.1 - Traveling Distances Find the 95% confidence...Ch. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Television Watching The average number of hours of...Ch. 9.1 - For Exercises 5 through 16, perform each of the...Ch. 9.1 - Prob. 23ECh. 9.1 - Home Prices According to the almanac, the average...Ch. 9.1 - Exam Scores at Private and Public Schools A...Ch. 9.1 - Sale Prices for Houses The average sales price of...Ch. 9.1 - Average Earnings for College Graduates The average...Ch. 9.2 - Too Long on the Telephone A company collects data...Ch. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - Prob. 9ECh. 9.2 - Find the 95% confidence interval for the...Ch. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Ages of Homes Whiting, Indiana, leads the Top 100...Ch. 9.2 - Prob. 17ECh. 9.2 - Out-of-State Tuitions The out-of-state tuitions...Ch. 9.2 - Gasoline Prices A random sample of monthly...Ch. 9.2 - For these exercises, perform each of these steps....Ch. 9.2 - Prob. 21ECh. 9.2 - Prob. 22ECh. 9.3 - Air Quality As a researcher for the EPA, you have...Ch. 9.3 - Classify each as independent or dependent samples....Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - Toy Assembly Test An educational researcher...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - For Exercises 2 through 12, perform each of these...Ch. 9.3 - Prob. 13ECCh. 9.4 - Smoking and Education You are researching the...Ch. 9.4 - Prob. 1ECh. 9.4 - Find p and q for each. a. n = 36, X = 20 b. n =...Ch. 9.4 - Prob. 3ECh. 9.4 - Find each X, given p. a. p = 0.24, n = 300 b. p =...Ch. 9.4 - Prob. 5ECh. 9.4 - Find p and q. a. X1 = 6, n1 = 15, X2 = 9, n2 = 15...Ch. 9.4 - For Exercises 7 through 27, perform these steps....Ch. 9.4 - Leisure Time In a sample of 150 men, 132 said that...Ch. 9.4 - Prob. 9ECh. 9.4 - For Exercises 7 through 27, perform each of these...Ch. 9.4 - Prob. 11ECh. 9.4 - For Exercises 7 through 27, perform each of these...Ch. 9.4 - Prob. 13ECh. 9.4 - For Exercises 7 through 27, perform each of these...Ch. 9.4 - Prob. 15ECh. 9.4 - Smoking Survey National statistics show that 23%...Ch. 9.4 - For Exercises 7 through 27, perform each of these...Ch. 9.4 - For Exercises 7 through 27, perform each of these...Ch. 9.4 - Prob. 19ECh. 9.4 - For Exercises 7 through 27, perform these steps....Ch. 9.4 - For Exercises 7 through 27, perform these steps....Ch. 9.4 - For Exercises 7 through 27, perform these steps....Ch. 9.4 - For Exercises 7 through 27, perform these steps....Ch. 9.4 - For Exercises 7 through 27, perform these steps....Ch. 9.4 - For Exercises 7 through 27, perform these steps....Ch. 9.4 - For Exercises 7 through 27, perform these steps....Ch. 9.4 - For Exercises 7 through 27, perform these steps....Ch. 9.4 - Prob. 28ECCh. 9.5 - Automatic Transmissions Assume the following data...Ch. 9.5 - When one is computing the F test value, what...Ch. 9.5 - Why is the critical region always on the right...Ch. 9.5 - What are the two different degrees of freedom...Ch. 9.5 - What are the characteristics of the F...Ch. 9.5 - Prob. 5ECh. 9.5 - Using Table H, find the critical value for each....Ch. 9.5 - Prob. 7ECh. 9.5 - Using Table H, find the P-value interval for each...Ch. 9.5 - Prob. 9ECh. 9.5 - For Exercises 9 through 24, perform the following...Ch. 9.5 - For Exercises 9 through 24, perform the following...Ch. 9.5 - For Exercises 9 through 24, perform the following...Ch. 9.5 - Prob. 13ECh. 9.5 - For Exercises 9 through 24, perform the following...Ch. 9.5 - For Exercises 9 through 24, perform the following...Ch. 9.5 - For Exercises 9 through 24, perform the following...Ch. 9.5 - Prob. 17ECh. 9.5 - For Exercises 9 through 24, perform the following...Ch. 9.5 - For Exercises 9 through 24, perform the following...Ch. 9.5 - For Exercises 9 through 24, perform the following...Ch. 9.5 - Prob. 21ECh. 9.5 - For Exercises 9 through 24, perform the following...Ch. 9.5 - For Exercises 9 through 24, perform the following...Ch. 9.5 - For Exercises 9 through 24, perform the following...Ch. 9 - For each exercise, perform these steps. Assume...Ch. 9 - Prob. 9.1.2RECh. 9 - Prob. 9.2.3RECh. 9 - Prob. 9.2.4RECh. 9 - For each exercise, perform these steps. Assume...Ch. 9 - For each exercise, perform these steps. Assume...Ch. 9 - High and Low Temperatures March is a month of...Ch. 9 - Testing After Review A statistics class was given...Ch. 9 - Lay Teachers in Religious Schools A study found a...Ch. 9 - Prob. 9.4.10RECh. 9 - Prob. 9.5.11RECh. 9 - Heights of World Famous Cathedrals The heights (in...Ch. 9 - Prob. 9.5.13RECh. 9 - Prob. 1DACh. 9 - Prob. 2DACh. 9 - Prob. 3DACh. 9 - Prob. 4DACh. 9 - Prob. 5DACh. 9 - Prob. 1CQCh. 9 - Prob. 2CQCh. 9 - Prob. 3CQCh. 9 - Prob. 4CQCh. 9 - Prob. 5CQCh. 9 - To test the equality of two proportions, you would...Ch. 9 - Prob. 7CQCh. 9 - Prob. 8CQCh. 9 - Complete these statements with the best answer. 9....Ch. 9 - Prob. 10CQCh. 9 - Prob. 11CQCh. 9 - Prob. 12CQCh. 9 - Prob. 13CQCh. 9 - Prob. 14CQCh. 9 - Prob. 15CQCh. 9 - Prob. 16CQCh. 9 - For these exercises, perform each of these steps....Ch. 9 - Prob. 18CQCh. 9 - Prob. 19CQCh. 9 - Mathematical Skills In an effort to improve the...Ch. 9 - Prob. 21CQCh. 9 - Prob. 22CQCh. 9 - Prob. 23CQCh. 9 - Prob. 24CQCh. 9 - Prob. 25CQ
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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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