Basic Business Statistics
14th Edition
ISBN: 9780134684840
Author: BERENSON, Mark L., Levine, David M., Szabat, Kathryn A.
Publisher: Pearson,
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Textbook Question
Chapter 1, Problem 31PS
A simple random sample of
a Give an example of possible coverage error.
b. Give an example of possible nonresponse error.
c. Give an example of possible sampling error.
d. Give an example of possible measurement error.
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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
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1
2
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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…
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
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per Day
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0
365
264
193
3
4 or more
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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…
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…
Chapter 1 Solutions
Basic Business Statistics
Ch. 1 - Four different beverages are sold at a fast-food...Ch. 1 - U. S. businesses are listed by size small medium,...Ch. 1 - The time it takes to download a video from the...Ch. 1 - For each of the following variables, determine...Ch. 1 - The following information is collected from...Ch. 1 - For each of the following variables, determine...Ch. 1 - For each of the following variables, determine...Ch. 1 - Suppose the following information is collected...Ch. 1 - One of the variables most often included in...Ch. 1 - If two students score a 90 on the same...
Ch. 1 - The director of market research at a large...Ch. 1 - The American Community Survey (www.census.gov/acs)...Ch. 1 - Visit the website of the Pew Research organization...Ch. 1 - Transportation engineers and planners want to...Ch. 1 - Visit the home page of the Statistics Portal...Ch. 1 - For a population containing N=902 individual, what...Ch. 1 - For a population of N=902, verify that by starting...Ch. 1 - Given a population of N=93, starting in row 29,...Ch. 1 - For a study that consists of personal interviews...Ch. 1 - You want to select a random sample of n=1 from a...Ch. 1 - A population has four members (called A, B, C, and...Ch. 1 - The registrar of a university with a population of...Ch. 1 - Prenumbered sales invoices are kept in a sales...Ch. 1 - Suppose that 10,000 customers in a retailer s...Ch. 1 - The cellphone brands owned by a sample of 20...Ch. 1 - The amount of monthly data usage by a sample of 10...Ch. 1 - An amusement park company owns three hotels on an...Ch. 1 - A hotel management company runs 10 hotels in a...Ch. 1 - A Survey indicates that the vast majority of...Ch. 1 - A simple random sample of n=300 full–time...Ch. 1 - Results of a 2017 Computer Service, Inc (CSI)...Ch. 1 - A recent PWC survey of 1,379 CEO s from a wide...Ch. 1 - A recent survey points to tremendous revenue...Ch. 1 - What is the difference between a sample and a...Ch. 1 - What is the difference between a statistic and...Ch. 1 - What is the difference between a categorical...Ch. 1 - What is the difference between a discrete...Ch. 1 - What is the difference between a nominal scaled...Ch. 1 - What is difference between an interval scaled...Ch. 1 - What is the difference between probability...Ch. 1 - What is difference between a missing value and an...Ch. 1 - What is the difference between unstack and stacked...Ch. 1 - What is the difference between coverage error and...Ch. 1 - What is the difference between sampling error and...Ch. 1 - Visit the official website for Microsoft Excel,...Ch. 1 - Results of a 2017 Computer Services, Inc (CSI)...Ch. 1 - The Gallup organization releases the results of...Ch. 1 - A recent PwC survey of 1,379 CEOs from a wide...Ch. 1 - The American community Survey (www.census.gov/acs)...Ch. 1 - Download and examine Zarca interactive’s Sample...Ch. 1 - Three professors examined awareness of four widely...Ch. 1 - Social media provides an enormous amount of data...
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- 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. 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_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_forward
- 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 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_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_forward
- Analyze 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_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_forward
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