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Business Statistics A First Course 7th Edition David M. Levine, Kathryn A. Szabat, David F. Stephan - Solutions

For a sample of n = 6, list the six Z values.
The file SUV contains the overall miles per gallon (MPG) of 2014 small SUVs (n = 20):Describe whether the data appear to be approximately normally distributed by a. Comparing data characteristics to theoretical properties. b. Constructing a normal probability plot.
As player salaries have increased, the cost of attending basketball games has increased dramatically. The file NBA Cost2013 contains the cost of four averaged- priced tickets, two beers, four soft drinks, four hot dogs, two game programs, two adult- sized caps, and one parking space at each of the
The file Property Taxes contains the property taxes per capita for the 50 states and the District of Columbia. Decide whether the data appear to be approximately normally distributed bya. Comparing data characteristics to theoretical properties. b. Constructing a normal probability plot.
Thirty companies comprise the DJIA. How big are these companies? One common method for measuring the size of a company is to use its market capitalization, which is computed by multiplying the number of stock shares by the price of a share of stock. On March 14, 2014, the market capitalization of
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E.2), what is the probability that a. Z is between – 1.57 and 1.84? b. Z is less than – 1.57 or greater than 1.84? c. What is the value of Z if only 2.5 percent of all possible Z
One operation of a mill is to cut pieces of steel into parts that will later be used as the frame for front seats in an automotive plant. The steel is cut with a diamond saw, and the resulting parts must be within ± 0.005 inch of the length specified by the automobile company. The data come from a
The file CD Rate contains the yields for a one- year certificate of deposit (CD) and a five- year CD for 22 banks in the United States, as of March 12, 2014. (Data extracted from www.Bankrate.com, March 12, 2014.) For each type of investment, decide whether the data appear to be approximately
The file Utility contains the electricity costs, in dollars, during July 2014 for a random sample of 50 one- bedroom apartments in a large city:Decide whether the data appear to be approximately normally distributed by a. Comparing data characteristics to theoretical properties. b. Constructing a
What are some of the distinguishing properties of a normal distribution?
How does the shape of the normal distribution differ from the shapes of the uniform and exponential distributions?
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearings can operate are 0.74 inch and 0.76 inch, respectively. Past experience has indicated that the actual diameter of the ball
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table E. 2), what is the probability that a. Z is less than 1.08? b. Z is greater than - 0.21? c. Z is less than - 0.21 or greater than the mean? d. Z is less than - 0.21 or greater than 1.08?
The fill amount in 2 liter soft drink bottles is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If bottles contain less than 95% of the listed net content (1.90 liters, in this case), the manufacturer may be subject to penalty by the state office of consumer
In an effort to reduce the number of bottles that contain less than 1.90 liters, the bottler in Problem 6.30 sets the filling machine so that the mean is 2.02 liters. Under these circumstances, what are your answers in Problem 6.30 (a) through (e)?a. Between 1.90 and 2.0 liters? b. Between 1.90 and
An Ipsos MediaCT study indicates that mobile device owners who used their mobile device while shopping for consumer electronics spent an average of $ 1,539 on consumer electronics in the past six months. (Data extracted from iab.net/ showrooming.) Assume that the amount spent on consumer
The file Domestic Beer contains the percentage alcohol, number of calories per 12 ounces, and number of carbohydrates (in grams) per 12 ounces for 156 of the best selling domestic beers in the United States. Determine whether each of these variables appears to be approximately normally
The evening manager of a restaurant was very concerned about the length of time some customers were waiting in line to be seated. She also had some concern about the seating times— that is, the length of time between when a customer is seated and the time he or she leaves the restaurant. Over the
The major stock market indexes had strong results in 2013. The mean one-year return for stocks in the S& P 500, a group of 500 very large companies, was $ 29.6%. The mean one year return for the NASDAQ, a group of 3,200 small and medium-sized companies, was $ 38.3%. Historically, the one-year
Interns report that when deciding on where to work, career growth, salary and compensation, location and commute, and company culture and values are important factors to them. According to the Glassdoor blog’s “25 Highest Paying Companies for Interns 2014,” bit.ly/1gx6vjx, the mean monthly
According to the same Glassdoor blog report mentioned in the previous question, the mean monthly pay for interns at Facebook is $ 6,213. Suppose that the intern monthly pay is normally distributed, with a standard deviation of $ 500. What is the probability that the monthly pay of an intern at
Given a standardized normal distribution determine the following probabilities:a. P(Z 7 1.08)b. P(Z 6 - 0.21)c. P(- 1.96 6 Z 6 - 0.21)d. What is the value of Z if only 15.87 percent of all possible Z values are larger?
Given a normal distribution with μ = 100 and σ = 10, what is the probability thata. X > 75?b. X < 70?c. X < 80 or X > 110?d. Between what two X values (symmetrically distributed around the mean) are eighty percent of the values?
Given a normal distribution with μ = 50 and σ = 4, what is the probability thata. X > 43?b. X < 42?c. Five percent of the values are less than what X value?d. Between what two X values (symmetrically distributed around the mean) are sixty percent of the values?
According to the “Bottled Water Trends for 2014” report (bit.ly/1gx5ub8), the U. S. per capita consumption of bottled water in 2013 was 31.8 gallons. Assume that the per capita consumption of bottled water in the United States is approximately normally distributed with a mean of 31.8 gallons
Toby’s Trucking Company determined that the distance traveled per truck per year is normally distributed, with a mean of 50 thousand miles and a standard deviation of 12 thousand miles.a. What proportion of trucks can be expected to travel between 34 and 50 thousand miles in a year?b. What
Consumers spent an average of $ 14.99 on a meal at a restaurant in 2013. (Data extracted from bit.ly/1hObH22.) Assume that the amount spent on a restaurant meal is normally distributed and that the standard deviation is $ 2.a. What is the probability that a randomly selected person spent more than
Given a normal distribution with μ = 100 and σ = 10, if you select a sample of n = 25, what is the probability that x isa. Less than 95?b. Between 95 and 97.5?c. Above 102.2?d. There is a 65% chance that X-bar is above what value?
A random sample of 50 households was selected for a phone (landline and cellphone) survey. The key question asked was, “ Do you or any member of your household own an Apple product (iPhone, iPod, iPad, or Mac computer)?” Of the 50 respondents, 20 said yes and 30 said no. a. Determine the sample
The following data represent the responses (Y for yes and N for no) from a sample of 40 college students to the question “ Do you currently own shares in any stocks?”a. Determine the sample proportion, p, of college students who own shares of stock.b. If the population proportion is 0.30,
A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a two- candidate election, if a specific candidate receives at least 55% of the vote in the sample, that candidate will be forecast as the winner of the election. If you select
You plan to conduct a marketing eX-bar periment in which students are to taste one of two different brands of soft drink. Their task is to correctly identify the brand tasted. You select a random sample of 200 students and assume that the students have no ability to distinguish between the two
Accenture’s Defining Success global research study found that the majority of today’s working women would prefer a better work–life balance to an increased salary. One of the most important contributors to work life balance identified by the survey was “ fleX-baribility,” with 80% of
The goal of corporate sustainability is to manage the environmental, economic, and social effects of a corporation’s operations so it is profitable over the long term while acting in a responsible manner toward society. A Hill $Knowlton Strategies survey found that 57% of U. S. respondents are
According to GMI Ratings’ 2013 Women on Boards Report, the percentage of women on U. S. boards has increased marginally in 2009– 2012 and now stands at 14%, well below the values for Nordic countries and France. A number of initiatives are underway in an effort to increase the representation.
The Chartered Financial Analyst (CFA) Institute reported that 49% of its U. S. members indicate that lack of ethical culture within financial firms has contributed the most to the lack of trust in the financial industry. (Source: “Global Market Sentiment Survey 2014,” cfa.is/Psk5O3.) Suppose
A Pew Research Center project on the state of news media showed that digital video consumption is growing and digital news video consumption is growing with it. According to Pew Research data, 36% of U. S. adults watch news videos.a. Suppose that you take a sample of 100 U. S. adults. If the
Given a normal distribution with μ = 50 and σ = 5, if you select a sample of n = 100, what is the probability that X-bar isa. Less than 47?b. Between 47 and 49.5?c. Above 51.1?d. There is a 35% chance that X-bar is above what value?
Why does the standard error of the mean decrease as the sample size, n, increases?
Why does the sampling distribution of the mean follow a normal distribution for a large enough sample size, even though the population may not be normally distributed?
An industrial sewing machine uses ball bearings that are targeted to have a diameter of 0.75 inch. The lower and upper specification limits under which the ball bearing can operate are 0.74 inch (lower) and 0.76 inch (upper). Past experience has indicated that the actual diameter of the ball
The fill amount of bottles of a soft drink is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If you select a random sample of 25 bottles, what is the probability that the sample mean will be a. Between 1.99 and 2.0 liters? b. Below 1.98 liters? c.
An orange juice producer buys oranges from a large orange grove that has one variety of orange. The amount of juice squeezed from these oranges is approximately normally distributed, with a mean of 4.70 ounces and a standard deviation of 0.40 ounce. Suppose that you select a sample of 25 oranges.a.
In Problem 7.26, suppose that the mean amount of juice squeezed is 5.0 ounces.a. What is the probability that the sample mean amount of juice will be at least 4.60 ounces?b. The probability is 70% that the sample mean amount of juice will be contained between what two values symmetrically
The stock market in France reported strong returns in 2013. The population of stocks earned a mean return of 15.23% in 2013. (Data extracted from The Wall Street Journal, January 2, 2014, p. R5.) Assume that the returns for stocks on the French stock market were distributed as a normal variable,
The article mentioned in Problem 7.28 reported that the stock market in China had a mean return of 3.17% in 2013. Assume that the returns for stocks on the Chinese stock market were distributed normally, with a mean of 3.17 and a standard deviation of 10. If you select an individual stock from this
For each of the following three populations, indicate what the sampling distribution for samples of 25 would consist of: a. Customer receipts for a supermarket for a year. b. Insurance payouts in a particular geographical area in a year. c. Call center logs of inbound calls tracking handling time
The following data represent the number of days absent per year in a population of six employees of a small company:1 3 6 7 9 10a. Assuming that you sample without replacement, select all possible samples of n = 2 and construct the sampling distribution of the mean. Compute the mean of all the
The diameter of a brand of tennis balls is approximately normally distributed, with a mean of 2.63 inches and a standard deviation of 0.03 inch. If you select a random sample of nine tennis balls,a. What is the sampling distribution of the mean?b. What is the probability that the sample mean is
The U. S. Census Bureau announced that the median sales price of new houses sold in 2013 was $ 265,900, and the mean sales price was $ 322,100 (www.census.gov/newhomesales, March 1, 2014). Assume that the standard deviation of the prices is $ 90,000.a. If you select samples of n = 4, describe the
According to a social media blog, time spent on Tumblr, a microblogging platform and social networking website, has a mean of 20 minutes per visit. (Source: “ 2014: The year of Tumblr,” bit.ly/QwM8ga.) Assume that time spent on Tumblr per visit is normally distributed and that the standard
Today, full- time college students report spending a mean of 27 hours per week on academic activities, both inside and outside the classroom. (Source: “ A Challenge to College Students for 2013: Don’t Waste Your 6,570,” Huffington Post, January 29, 2013, huff. to/ 13dNtuT.) Assume the
In a random sample of 64 people, 48 are classified as “successful.” a. Determine the sample proportion, p, of “successful” people. b. If the population proportion is 0.70, determine the standard error of the proportion.
If X-bar = 85, σ = 8, and n = 64, construct a 95% confidence interval estimate for the population mean, μ.
The operations manager at a compact fluorescent light bulb (CFL) factory needs to estimate the mean life of a large shipment of CFLs. The manufacturer’s specifications are that the standard deviation is 1,000 hours. A random sample of 64 CFLs indicated a sample mean life of 7,500 hours.a.
If X-bar = 75, S = 24, and n = 36, and assuming that the population is normally distributed, construct a 95% confidence interval estimate for the population mean, μ.
Determine the critical value of t in each of the following circumstances:a. 1 - α = 0.95, n = 10b. 1 - α = 0.99, n = 10c. 1 - α = 0.95, n = 32d. 1 - α = 0.95, n = 65e. 1 - α = 0.90, n = 16
Assuming that the population is normally distributed, construct a 95% confidence interval estimate for the population mean for each of the following samples:Sample A: 1 1 1 1 8 8 8 8Sample B: 1 2 3 4 5 6 7 8Explain why these two samples produce different confidence intervals even though
Assuming that the population is normally distributed, construct a 95% confidence interval for the population mean, based on the following sample of size n = 7:1 2 3 4 5 6 20Change the value of 20 to 7 and recalculate the confidence inter-val. Using these results, describe the effect of an outlier
A marketing researcher wants to estimate the mean savings ($) realized by shoppers who showroom. Showrooming is the practice of inspecting products in retail stores and then purchasing the products online at a lower price. A random sample of 100 shoppers who recently purchased a consumer
A survey of nonprofit organizations showed that online fundraising has increased in the past year. Based on a random sample of 55 nonprofits, the mean one- time gift do-nation in the past year was $ 75, with a standard deviation of $ 9.a. Construct a 95% confidence interval estimate for the
The U. S. Department of Transportation requires tire manufacturers to provide tire performance information on the sidewall of a tire to better inform prospective customers as they make purchasing decisions. One very important measure of tire performance is the tread wear index, which indicates the
The file FastFood contains the amount that a sample of 15 customers spent for lunch ($) at a fast- food restaurant:a. Construct a 95% confidence interval estimate for the population mean amount spent for lunch ($) at a fast- food restaurant, assuming a normal distribution. b. Interpret the interval
The file Sedans contains the overall miles per gallon (MPG) of 2014 midsized sedans:a. Construct a 95% confidence interval estimate for the population mean MPG of 2014 midsized sedans, assuming a normal distribution.b. Interpret the interval constructed in (a).c. Compare the results in (a) to those
If X-bar = 125, σ = 24, and n = 36, construct a 99% confidence interval estimate for the population mean, μ.
The file SUV contains the overall MPG of 2014 small SUVs:a. Construct a 95% confidence interval estimate for the population mean MPG of 2014 small SUVs, assuming a nor-mal distribution.b. Interpret the interval constructed in (a).c. Compare the results in (a) to those in Problem 8.19(a).
Is there a difference in the yields of different types of investments? The file CD Rate contains the yields for a one- year certificate of deposit (CD) and a five- year CD for 22 banks in the United States as of March 12, 2014. (Data extracted from www.Bankrate.com, March 12, 2014.)a. Construct a
One of the major measures of the quality of service pro-vided by any organization is the speed with which the organization responds to customer complaints. A large family-held department store selling furniture and flooring, including carpet, had under-gone a major expansion in the past several
A manufacturing company produces electric insulators. You define the variable of interest as the strength of the insulators. If the insulators break when in use, a short circuit is likely. To test the strength of the insulators, you carry out destructive testing to determine how much force is
The file Market Penetration contains Facebook penetration values (the percentage of the country population that are Facebook users) for 22 of the world’s largest economies:a. Construct a 95% confidence interval estimate for the population mean Facebook penetration.b. What assumption do you need
One operation of a mill is to cut pieces of steel into parts that are used in the frame for front seats in an automobile. The steel is cut with a diamond saw, and the resulting parts must be cut to be within ± 0.005 inch of the length specified by the automobile company. The measurement reported
If n = 200 and X-bar = 50, construct a 95% confidence interval estimate for the population proportion.
If n = 400 and X-bar = 25, construct a 99% confidence interval estimate for the population proportion.
A cellphone provider has the business objective of wanting to estimate the proportion of subscribers who would upgrade to a new cellphone with improved features if it were made available at a substantially reduced cost. Data are collected from a random sample of 500 subscribers. The results
In a survey of 529 travelers, 386 said that location was very important and 323 said that room quality was very important in choosing a hotel.a. Construct a 95% confidence interval estimate for the population proportion of travelers who said that location was very important for choosing a hotel.b.
Why is it not possible in Example 8.1 on page 253 to have 100% confidence? Explain.
Are you likely to purchase an item promoted by a celebrity on a social media site? According to a Brand Republic survey, 26% of social media users have made such a purchasea. Suppose that the survey had a sample size of n = 1,000. Construct a 95% confidence interval estimate for the population
In a Pew Research Center survey of 960 Facebook users, 452 cited “seeing photos or videos” as a major reason why they use Facebook, while 298 cited “keeping up with news and current events” as a major reason why they use Facebook.a. Construct a 95% confidence interval estimate for the
What are the global trends that technology CEOs believe will transform their business? According to a PwC white paper, 105 of 117 technology CEOs from around the world responded that technological advances will transform their business and 42 responded that resource scarcity and climate change will
If you want to be 95% confident of estimating the population mean to within a sampling error of ± 5 and the standard deviation is assumed to be 15, what sample size is required?
If you want to be 99% confident of estimating the population mean to within a sampling error of ± 20 and the standard deviation is assumed to be 100, what sample size is required?
If you want to be 99% confident of estimating the population proportion to within a sampling error of ± 0.04, what sample size is needed?
If you want to be 95% confident of estimating the population proportion to within a sampling error of ± 0.02 and there is historical evidence that the population proportion is approximately 0.40, what sample size is needed?
A survey is planned to determine the mean annual family medical expenses of employees of a large company. The management of the company wishes to be 95% confident that the sample mean is correct to within ± $50 of the population mean annual family medical expenses. A previous study indicates that
If the manager of a bottled water distributor wants to estimate, with 95% confidence, the mean amount of water in a 1 gallon bottle to within ± 0.004 gallon and also assumes that the standard deviation is 0.02 gallon, what sample size is needed?
If a light bulb manufacturing company wants to estimate, with 95% confidence, the mean life of compact fluorescent light bulbs to within ± 200 hours and also assumes that the population standard deviation is 1,000 hours, how many compact fluorescent light bulbs need to be selected?
If the inspection division of a county weights and measures department wants to estimate the mean amount of soft drink fill in 2 liter bottles to within ± 0.01 liter with 95% confidence and also assumes that the standard deviation is 0.05 liter, what sample size is needed?
An advertising executive wants to estimate the mean weekly amount of time consumers spend watching traditional television daily. Based on previous studies, the standard deviation is assumed to be 20 minutes. The executive wants to estimate, with 99% confidence, the mean weekly amount of time to
An advertising executive wants to estimate the mean amount of time that consumers spend with digital media daily. From past studies, the standard deviation is estimated as 45 minutes. a. What sample size is needed if the executive wants to be 90% confident of being correct to within ± 5
A growing niche in the restaurant business is gourmet- casual breakfast, lunch, and brunch. Chains in this group include Egg Spectation and Panera Bread. Suppose that the mean per- person check for breakfast at EggSpectation is approximately $ 14.50.a. Assuming a standard deviation of $ 2.00, what
What advertising medium gives a brand the most credibility in influencing brand decisions? According to an Adroit Digital survey, 35% of Millennials point to TV. (Source: “U. S. Millennials: TV is Most Influential Advertising Medium,” MC Marketing Charts, March 20, 2014.)a. To conduct a
A Nielsen Mobile Shopping Report looks at how consumers are using mobile devices throughout their purchase journey. In response to a survey question about shopping, 27% of tablet owners said they use mobile devices for payment, 21% said they use such devices to make social media comments about
In a study of 413 nonprofits nationwide, 83 indicated that turnover has been the biggest employment challenge at their organization. (Source: Nonprofit HR, 2014 Nonprofit Employment Practices Survey, available at bit.ly/1mfy2tJ.)a. Construct a 95% confidence interval for the population proportion
According to a study released by The Financial Brand, an online publication focusing on branding issues and advice affecting retail banks and credit unions, 68% of financial institutions use churn rate (attrition) to gauge the effectiveness of their marketing efforts.a. If you conduct a follow- up
What prevents consumers from sharing data with retailers? A recent Click Fo X-bar Consumer Behavior Survey (bit.ly/ 1fAfJAI) found that 32% of consumers responded “breaches of consumer data.” a. To conduct a follow-up study that would provide 99% confidence that the point estimate is
A market researcher selects a simple random sample of n = 100 Twitter users from a population of over 100 million Twitter registered users. After analyzing the sample, she states that she has 95% confidence that the mean time spent on the site per day is between 15 and 57 minutes. Explain the
Why can you never really have 100% confidence of correctly estimating the population characteristic of interest?
Why is the sample size needed to determine the proportion smaller when the population proportion is 0.20 than when the population proportion is 0.50?
The Pew Internet Project survey of 1,006 American adults found the following: 906 have a cell phone 584 have a smartphone 322 have an eBook reader 423 have a tablet computer Source: “Device Ownership Over Time,” bit.ly/1fvWYrL.a. Construct 95% confidence interval estimates for the population
What proposals for dealing with energy and the environment do Americans favor? Gallup conducted a survey of 1,048 adults, ages 18 $in all 50 U. S. states and the District of Columbia and found the following: Spending more government money on developing solar and wind power: 702 Setting higher

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