APPLIED STAT.IN BUS.+ECONOMICS
6th Edition
ISBN: 9781259957598
Author: DOANE
Publisher: RENT MCG
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Chapter 4, Problem 14ERQ
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y of 45 home-
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Suppose that you have a loaded die. You roll
it several times and record the outcomes,
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Histogram for Loaded Die
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Calculate the mean for Study Hours and Test Scores.
Compute the covariance between the two variables using the formula:
Calculate the standard deviation for Study Hours (X) and Test Scores (Y).
Determine the correlation coefficient
Interpret the results: What does the calculated r-value indicate about the relationship between study hours and test scores?
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…
Chapter 4 Solutions
APPLIED STAT.IN BUS.+ECONOMICS
Ch. 4.2 - (a) For each data set, find the mean, median, and...Ch. 4.2 - For each data set, is the mode a good measure of...Ch. 4.2 - For each data set, is the mode a good measure of...Ch. 4.2 - For each data set, which best indicates a typical...Ch. 4.2 - For each data set, which best indicates a typical...Ch. 4.2 - Days on the market are shown for the 36 most...Ch. 4.2 - Scores are shown for the most recent state civil...Ch. 4.2 - A vehicle emissions testing facility can process...Ch. 4.2 - CitiBank recorded the number of customers to use a...Ch. 4.2 - Prob. 10SE
Ch. 4.2 - Prob. 11SECh. 4.2 - Prob. 12SECh. 4.2 - (a) Write the Excel function for the 10 percent...Ch. 4.2 - Prob. 14SECh. 4.2 - Prob. 15SECh. 4.2 - Spirit Airlines kept track of the number of empty...Ch. 4.2 - CitiBank recorded the number of customers to use a...Ch. 4.2 - On Friday night, the owner of Chez Pierre in...Ch. 4.2 - Prob. 19SECh. 4.2 - The number of internet users in Latin America grew...Ch. 4.3 - (a) Find the mean and standard deviation for each...Ch. 4.3 - For each data set: (a) Find the mean. (b) Find the...Ch. 4.3 - In fuel economy tests in city driving conditions,...Ch. 4.3 - Over the past month, Bobs bowling score mean was...Ch. 4.3 - Prob. 25SECh. 4.3 - Prob. 26SECh. 4.3 - (a) Find the coefficient of variation for prices...Ch. 4.3 - Prob. 28SECh. 4.3 - Noodles and Company tested consumer reaction to...Ch. 4.4 - (a) By Chebyshevs Theorem, at least how many...Ch. 4.4 - An exam has a mean of 70 with a standard deviation...Ch. 4.4 - Prob. 32SECh. 4.4 - The mean collection period for accounts receivable...Ch. 4.4 - Convert each individual data value to a...Ch. 4.4 - Prob. 35SECh. 4.4 - Prob. 36SECh. 4.4 - Find the original data value corresponding to each...Ch. 4.4 - CitiBank recorded the number of customers to use a...Ch. 4.4 - Prob. 39SECh. 4.5 - Scores on an accounting exam ranged from 42 to 96,...Ch. 4.5 - In 2007, total compensation (in thousands of...Ch. 4.5 - Waiting times (minutes) for a table at Joeys BBQ...Ch. 4.5 - Coffee temperatures (degrees Fahrenheit) at a...Ch. 4.5 - Prob. 44SECh. 4.5 - On San Martin Boulevard, embedded sensors kept...Ch. 4.5 - Prob. 46SECh. 4.5 - Prob. 47SECh. 4.6 - For each X-Y data set (n = 12): (a) Make a scatter...Ch. 4.6 - Closing prices of two stocks are recorded for 50...Ch. 4.6 - Prob. 50SECh. 4.6 - Prob. 51SECh. 4.7 - Estimate the mean from this table of grouped data...Ch. 4.7 - Estimate the mean from the following table of...Ch. 4 - What are descriptive statistics? How do they...Ch. 4 - Explain each concept: (a) center, (b) variability,...Ch. 4 - Prob. 3CRCh. 4 - List strengths and weaknesses of each measure of...Ch. 4 - Prob. 5CRCh. 4 - (a) What is a bimodal distribution? (b) Explain...Ch. 4 - Prob. 7CRCh. 4 - Prob. 8CRCh. 4 - (a) Which standard deviation formula (population,...Ch. 4 - (a) To what kind of data does Chebyshevs Theorem...Ch. 4 - Prob. 11CRCh. 4 - Prob. 12CRCh. 4 - Prob. 13CRCh. 4 - Prob. 14CRCh. 4 - (a) Explain the method of medians for calculating...Ch. 4 - (a) What is a box plot? What does it tell us? (b)...Ch. 4 - Prob. 17CRCh. 4 - Prob. 18CRCh. 4 - Prob. 19CRCh. 4 - (a) What is kurtosis? (b) Sketch a platykurtic...Ch. 4 - Prob. 54CECh. 4 - If the mean asset turnover for retail firms is...Ch. 4 - Prob. 56CECh. 4 - During a rock concert, the noise level (in...Ch. 4 - Bags of jelly beans have a mean weight of 396 gm...Ch. 4 - Based on experience, the Ball Corporations...Ch. 4 - SAT scores for the entering class of 2010 at...Ch. 4 - Prob. 61CECh. 4 - The average time a Boulder High varsity lacrosse...Ch. 4 - Prob. 63CECh. 4 - Below are monthly rents paid by 30 students who...Ch. 4 - How many days in advance do travelers purchase...Ch. 4 - The durations (minutes) of 26 electric power...Ch. 4 - The U.S. Postal Service will ship a Priority Mail...Ch. 4 - Prob. 68CECh. 4 - Prob. 69CECh. 4 - Prob. 70CECh. 4 - Prob. 71CECh. 4 - A plumbing suppliers mean monthly demand for vinyl...Ch. 4 - Prob. 73CECh. 4 - Analysis of investment portfolio returns over a...Ch. 4 - Prob. 75CECh. 4 - Caffeine content in a 5-ounce cup of brewed coffee...Ch. 4 - Prob. 77CECh. 4 - Prob. 78CECh. 4 - Prob. 79CECh. 4 - Prob. 80CECh. 4 - Prob. 81CECh. 4 - Prob. 82CECh. 4 - Prob. 83CECh. 4 - The median waiting time for a liver transplant in...Ch. 4 - A small suburban community agreed to purchase...Ch. 4 - A companys contractual trigger point for a union...Ch. 4 - Prob. 87CECh. 4 - (a) Enter the Excel function...Ch. 4 - Note: In each of the following tables, the upper...Ch. 4 - This table shows the distribution of winning times...Ch. 4 - The self-reported number of hours worked per week...Ch. 4 - How long does it take to fly from Denver to...Ch. 4 - (a) Make an Excel scatter plot of X = 1990 assault...Ch. 4 - (a) Make an Excel scatter plot of X = airspeed...Ch. 4 - Prob. 97CECh. 4 - (a) Make an Excel scatter plot of X = weekly...Ch. 4 - Prob. 99CECh. 4 - Prob. 1ERQCh. 4 - Which is not an ethical obligation of a...Ch. 4 - Prob. 3ERQCh. 4 - Prob. 4ERQCh. 4 - Give the type of measurement (nominal, ordinal,...Ch. 4 - Prob. 6ERQCh. 4 - To choose a sample of 12 students from a...Ch. 4 - Which of the following is not a reason for...Ch. 4 - Which statement is correct? Why not the others? a....Ch. 4 - Prob. 10ERQCh. 4 - The management of a theme park obtained a random...Ch. 4 - Which one of the following is true? Why not the...Ch. 4 - Prob. 13ERQCh. 4 - Prob. 14ERQCh. 4 - Here are the ages of a random sample of 20 CEOs...Ch. 4 - Prob. 16ERQCh. 4 - Prob. 17ERQCh. 4 - Prob. 18ERQCh. 4 - Which is not a characteristic of using a log scale...
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- 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 yeararrow_forwardFor 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…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 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_forward
- 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 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_forwardA 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_forward
- A 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_forwardReconsider 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_forward
- The 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_forwardConsider 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_forward
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