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Business Statistics A First Course 7th Global Edition Kathryn A. Szabat, David M. Levine, David F. Stephan - Solutions
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
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:56 57 43 55 42 35 7 25 42 17 43 6 31 28 59 20 27 36 45 80 57 56 Source: Data extracted from slidesha.re/ODv6vG.a. Construct a
A manufacturing company produces chocolate bars. The table below contains the cost per ounce ($) for a sample of 14 dark chocolate bars. 0.63 0.79 0.95 1.19 1.45 0.94 0.78 0.53 1.58 0.53 0.61 0.73 1.52 0.81a. Construct a 99% confidence interval estimate for the population cost per ounce ($) of dark
One of the major measures of the quality of service provided 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 undergone a major expansion in the past several
New research shows that members of a certain youth generation have a great say in household purchases. Specifically, 70% of the people in the generation have a say in computer purchases. Suppose you select a sample of I 00 respondents from the generation.a. What is the probability that the sample
The data below represents the overall miles per gallon(MPG) of 2008 SUVs priced under $30,000.24, 18, 20, 22, 17, 19, 18, 18, 21, 19, 17, 18, 22, 19, 19, 17, 18, 18, 16, 20, 17, 24a. Construct a 95% confidence interval estimate for the population mean miles per gallon of 2008 priced under $30,000
The file Sedans contains the overall miles per gallon(MPG) of 2014 midsized sedans:38 26 30 26 25 27 24 22 27 32 39 26 24 24 23 24 25 31 26 37 22 33 Source: Data extracted from “Which Car Is Right for You,” Consumer Reports, April 2014, pp. 40–41.a. Construct a 95% confidence interval
The table below contains the amount that a sample of nine customers spent for lunch ($) at a fast-food restaurant: 4.88 5.01 5.79 6.35 7.39 7.68 8.23 8.71 9.88a. Construct a 99% confidence interval estimate for the population mean amount spent for lunch ($) at the fast-food restaurant, assuming a
A consumer organization wants to estimate the actual tread wear index of a brand name of tires that claims “graded 200” on the sidewall of the tire. A random sample of n = 19 indicates a sample mean tread wear index of 187.1 and a sample standard deviation of 26.4.a. Assuming that the
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 donation in the past year was $75, with a standard deviation of $9.a. Construct a 95% confidence interval estimate for the population
A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random sample of 64 greeting cards indicates a mean value of $2.89 and a standard deviation of $0.31.a. Assuming a normal distribution, construct a 99% confidence interval estimate of the
Assuming that the population is normally distributed, construct a 90% confidence interval for the population mean, based on the following sample size of n = 8:1, 2, 3, 4, 5, 6, 7, 29 Change the number 29 to 8 and recalculate the confidence interval.Using these results, describe the effect of an
Assuming that the population is normally distributed, construct a 95% confidence interval for the population mean for each of the samples below.
Determine the critical value of ta>2 in each of the following circumstances:a. 1 - a = 0.99, n = 40b. 1 - a = 0.90, n = 40c. 1 - a = 0.99, n = 24d. 1 - a = 0.99, n = 34e. 1 - a = 0.95, n = 68
If X = 99, S = 5, and n = 64, and assuming that the population is normally distributed, construct a 95% confidence interval estimate of the population mean, m.
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.
The manager of a paint supply store wants to estimate the actual amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer. The manufacturer’s specifications state that the standard deviation of the amount of paint is equal to 0.03 gallon. A random sample of 50
You are working as an assistant to the dean of institutional research at your university. The dean wants to survey members of the alumni association who obtained their baccalaureate degrees 5 years ago to learn what their starting salaries were in their first full-time job after receiving their
A market researcher collects a simple random sample of customers from its population of two million customers. After analyzing the sample, she states that she has 95% confidence that the mean annual income of its two million customers is between$68,000 and $85,000. Suppose that the population mean
Suppose that you are going to collect a set of data, either from an entire population or from a random sample taken from that population.a. Which statistical measure would you compute first: the mean or the standard deviation? Explain.b. What does your answer to (a) tell you about the
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
Is it true in Example 8.1 on page 275 that you do not know for sure whether the population mean is between 10.9941 and 11.0019 inches? Explain.
Why is it not possible in Example 8.1 on page 275 to have 100% confidence? Explain.
If X = 115, s = 21, and n = 35, construct a 95% confidence interval estimate of the population mean, m.
If X = 103, s = 22, and n = 39, construct a 99% confidence interval estimate of the population mean, m.
(Class Project) Suppose that step 3 of problem 7.33 uses the following rule: “If a random digit between 0 and 8 is selected, consider the ball to be white; if a random digit of 9 is selected, consider the ball to be red.” Compare and contrast the results in this problem and those in problem
(Class Project) Using a table of random numbers (Table E.1), simulate the selection of different-colored balls from a bowl, as follows:1. Start in the row corresponding to the day of the month in which you were born.2. Select one-digit numbers.3. If a random digit between 0 and 6 is selected,
(Class Project) The number of cars waiting in line at a car wash is distributed as follows:
(Class Project) Toss a coin 10 times and record the number of heads. If each student performs this experiment five times, a frequency distribution of the number of heads can be developed from the results of the entire class. Does this distribution seem to approximate the normal distribution?
(Class Project) The table of random numbers is an example of a uniform distribution because each digit is equally likely to occur. Starting in the row corresponding to the day of the month in which you were born, use a table of random numbers (Table E.1)to take one digit at a time.Select five
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
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, with
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
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.
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 bea. between 1.99 and 2.0 liters?b. below 1.98 liters?c. greater than
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
Under what circumstances does the sampling distribution of the proportion approximately follow the normal distribution?
What is the difference between a population distribution and a sampling distribution?
How would you define the standard error of the mean? For a sample of 100 with the standard error of the mean 30, why would we need to increase the sample size in order to cut the standard error of the mean to 15?
Why is the Central Limit Theorem important when analyzing population distributions?
Why is the sample mean an unbiased estimator of the population mean?
A survey of 2,250 adults found that 56% got news both online and offline during a typical day.a. Suppose that you take a sample of 50 adults. If the population proportion of adults who get news both online and offline in a typical day is 0.56, what is the probability that fewer than half in your
New research shows that members of a certain youth generation have a great say in household purchases. Specifically, 70% of the people in the generation have a say in computer purchases. Suppose you select a sample of I 00 respondents from the generation.a. What is the probability that the sample
According to a poll on consumer behavior, 36% of people say they will only consider cars manufactured in their country when purchasing a new car. Suppose you select a random sample of 100 respondents.a. What is the probability that the sample will have between 35%and 43% who say they will consider
In a recent survey of full-time female workers, 43% said that they would give up some of their salary for more personal time.Suppose you select a sample of 100 full-time female workers.a. What is the probability that in the sample, fewer than 50%would give up their salary for more personal time?b.
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 “flexibility,” with 80% of women
A marketing survey is conducted in which students are to taste two different brands of soft drink. Their task is to correctly identify the brand tasted. A random sample of 200 students is taken. Assume that the students have no ability to distinguish between the two brands.a. What is the
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 a
The following data represent the responses (Y for yes and N for no) from a sample of 20 college students to the question “Do you currently own shares in any stocks?”N Y Y N Y Y Y N N N N Y Y N N Y N N N Ya. Determine the sample proportion, p, of college students who own shares of stock.b. If
A random selection of 64 households was selected for a telephone survey. The key question asked was, “Do you or any member of your household own a cellular telephone that you can use to access the Internet?” Of the 64 respondents, 32 said yes and 32 said no.a. Determine the sample proportion,
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.
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 standard
Time spent using e-mail per session is normally distributed, with m = 9 minutes and s = 2 minutes. If you select a random sample of 25 sessions,a. what is the probability that the sample mean is between 8.8 and 9.2 minutes?b. what is the probability that the sample mean is between 8.5 and 9
A report announced that the median sales price of new houses sold one year was $211,000, and the mean sales price was $272,500. Assume that the standard deviation of the prices is$100,000.a. If you select samples of n = 2, describe the shape of the sampling distribution of X.b. If you select
inch. If you select a random sample of four pingpong balls,a. what is the sampling distribution of the mean?b. what is the probability that the sample mean is less than 1.27 inches?c. what is the probability that the sample mean is between 1.27 and 1.32 inches?d. The probability is 58% that the
inches and a standard deviation of
The diameter of a brand of ping-pong balls is approximately normally distributed, with a mean of
The following data represent the number of days absent per year in a population of six employees of a small company:1 3 4 7 8 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
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 for
Given a normal distribution with m = 101 and s = 15, if you select a sample of n = 9, what is the probability that X isa. less than 95?b. between 90 and 92.5?c. above 101.8?d. There is a 65% chance that X is above what value?
Given a normal distribution with m = 102 and s = 25, if you select a sample of n = 25, what is the probability that X isa. less than 90?b. between 90 and 92.5?c. above 103.6?d. There is a 61% chance that X is above what value?
(Class Project) One theory about the daily changes in the closing price of stock is that these changes follow a random walk—that is, these daily events are independent of each other and move upward or downward in a random manner—and can be approximated by a normal distribution. To test this
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
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
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 returns
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 file Domesticbeer 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 distributed.
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 electronics
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)?
In an effort to reduce the number of bottles that contain less than 1.90 liters, the bottler in Problem
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
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
How can you use the normal probability plot to evaluate whether a set of data is normally distributed?
What is the difference between normal distribution and exponential distribution?
What are the three main reasons that normal distribution is important in statistics?
How do you find the X value that corresponds to a given percentile of the normal distribution?
How do you find the area between two values under the normal curve?
Why is only one normal distribution table such as Table e.2 needed to find any probability under the normal curve?
The data set below contains the electricity costs in dollars during July 2014 for a random sample of 30 one-bedroom apartments in a large city.130 86 191 170 106 189 122 124 134 132 130 159 140 146 185 153 84 171 173 147 199 146 100 157 210 140 103 154 164 118 Decide whether the data appear to be
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
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
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
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.
As player salaries have increased, the cost of attending basketball games has increased dramatically. The file NbaCost2013 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 30
The file SuV contains the overall miles per gallon (MPG) of 2014 small SUVs 1n = 202:26 22 23 21 25 24 22 26 25 22 21 21 22 22 23 24 23 22 21 22 Source: Data extracted from “Which Car Is Right for You,” Consumer Reports, April 2014, pp. 60–61.Decide whether the data appear to be approximately
For a sample of n = 6, list the six Z values.
Show that for a sample of n = 37, the smallest and largest Z-values are -1.94 and +1.94 and the middle (that is, 19th) Z-value is 0.00.
Many manufacturing problems involve the matching of machine parts, such as shafts that fit into a valve hole. A particular design requires a shaft with diameters between 22.89 mm and 23.018 mm. Suppose that the manufacturing process yields shafts with diameters normally distributed, with a mean of
According to a speical issue of Beverage Digest (bit.ly/1e9ORS3), the U.S. per capita consumption of soft drinks in 2013 was 42.2 gallons. Assume that the per capita consumption of soft drinks in the United States is approximately normally distributed with a mean of 42.2 gallons and a standard
A Nielsen study indicates that 18- to 24- year olds spend a mean of 135 minutes watching video on their smartphones per month. (Data extracted bit.ly/1hF3BP2.) Assume that the amount of time watching video on a smartphone per month is normally distributed and that the standard deviation is 15
A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 78 and a standard deviation of 9.a. What is the probability that a student scored below 93 on this exam?b. What is the probability that a student scored between 69 and 103?c. The
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
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
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 and
Given a normal distribution with m = 50 and s = 4, what is the probability thata. X 7 43 ?b. X 6 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?
Given a normal distribution with m = 100 and s = 10, what is the probability thata. X 7 80?b. X 6 95 ?c. X 6 85 or X 7 105?d. Between what two X values (symmetrically distributed around the mean) are 90 percent of the values?
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1, as in Table e.2), determine the following probabilities:a. P1Z 7 1.082b. P1Z 6 -0.212c. P1-1.96 6 Z 6 -0.212d. What is the value of Z if only 15.87 percent of all possible Z values are larger?
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 thata. Z is less than 1.09?b. Z is greater than -0.26?c. Z is less than -0.26 or greater than the mean?d. Z is less than -0.26 or greater than 1.09?
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 thata. 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 values are larger?d.
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 thata. Z is less than 1.53?b. Z is greater than 1.89?c. Z is between 1.53 and 1.89?d. Z is less than 1.53 or greater than 1.89?
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