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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

Talk-show host Howard Stern moved his controversial radio program from free, over-the-air (AM/FM) radio to Sirius XM satellite radio. The move was perceived in the industry to boost satellite radio
Give an example of unethical statistical practice.
In industry, performance based logistics (PBL) strategies are increasingly popular ways to reduce cost, increase revenue, and attain customer satisfaction. The Journal of Business Logistics (Vol. 36,
Suppose you have to sort sample units into categories according to their region of origin. The regions are “Africa,” “Americas,” “Asia,” “Europe,” and “Oceania.” For further
Suppose that a production batch contains 1,000 units and you have to select 10 units for quality assurance. Use a random number generator to select a simple random sample of n = 10 from the
A group of cardiac physicians in southwest Florida have been studying a new drug designed to reduce blood loss in coronary artery bypass operations. Blood loss data for 114 coronary artery bypass
Parking at a large university has become a big problem. The university’s administrators want to determine the average parking time of its students. An administrator inconspicuously followed 250
A department store receives customer orders through its call center and website. These orders as well as any special orders received in the stores are forwarded to a distribution center where workers
A manufacturer of industrial wheels suspects that profitable orders are being lost because of the long time the firm takes to develop price quotes for potential customers. To investigate this
As part of an economics class project, students were asked to randomly select 500 New York Stock Exchange (NYSE) stocks from the Wall Street Journal. They were then asked to summarize the current
In recent years, the price of real estate in America’s major metropolitan areas has skyrocketed. Newspapers usually report recent real estate sales data in their Saturday editions, both hard copies
A qualitative variable is measured for 20 companies randomly sampled and the data are classified into three classes, small (S), medium (M), and large (L), based on the number of employees in each
Calculate the sample mean for the R&D expenditure percentages of the 50 companies given in Table 2.2 on page 76. Calculate the sample mean for the R&D expenditure percentages of the 50
Calculate the mean of the following five sample measurements: 5, 3, 8, 5, 6.
Calculate the median for the 50 R&D percentages given in Table 2.2. Compare the median to the mean found in Example 2.4. Data from table 2.2 Table 2.2 Company 123456TBAGHD3 10 11 Percentage of
Consider the following sample of n = 7 measurements: 5, 7, 4, 5, 20, 6, 2.a. Calculate the median m of this sample.b. Eliminate the last measurement (the 2) and calculate the median of the remaining
Each of 10 taste testers rated a new brand of barbecue sauce on a 10-point scale, where 1 = awful and 10 = excellent. Find the mode for the 10 ratings shown below. 8 7 9 6 8 10 9 9 5 7
Calculate the variance and standard deviation of the following sample: 2, 3, 3, 3, 4. (These data are entered into an Excel spreadsheet, shown in Figure 2.20.)Data from figure 2.20 1 2 3 4 5 96 A 7 8
Refer to Glassdoor Economic Research’s 2015 list of salaries for 441 CEOs whose firms filed salary reports with the Securities and Exchange Commission (SEC). The data set, saved in the CEOPAY file,
Use the computer to find the sample variance s2 and the sample standard deviation s for the 50 companies’ percentages of revenues spent on R&D, given in Table 2.2 Table 2.2 Percentage of Revenues
The 50 companies’ percentages of revenues spent on R&D are repeated in Table 2.6. We have previously shown (see Figure 2.21) that the mean and standard deviation of these data (rounded) are 8.49
Chebyshev’s Rule and the Empirical Rule are useful as a check on the calculation of the standard deviation. For example, suppose we calculated the standard deviation for the R&D percentages (Table
A manufacturer of automobile batteries claims that the average length of life for its grade A battery is 60 months. However, the guarantee on this brand is for just 36 months. Suppose the standard
Refer to the percentages spent on R&D by the 50 high-technology firms listed in Table 2.6. A portion of the SPSS descriptive statistics printout is shown in Figure 2.25. Locate the 25th percentile
In Example 2.2 we analyzed 50 processing times (listed in Table 2.4) for the development of price quotes by the manufacturer of industrial wheels. The intent was to determine whether the success or
Refer to Example 2.16. The box plot for the 50 processing times (Figure 2.30) does not explicitly reveal the differences, if any, between the set of times corresponding to the success and the set of
A random sample of 2,000 students who sat for the Graduate Management Admission Test (GMAT) is selected. For this sample, the mean GMAT score is x̄ = 540 points and the standard deviation is s = 100
A company is analyzing the prices at which its items are sold. Graph the relative frequency histogram for the 600 items summarized in the accompanying relative frequency table. Class Based on Item
Suppose a female bank employee believes that her salary is low as a result of sex discrimination. To substantiate her belief, she collects information on the salaries of her male counterparts in the
A medical item used to treat a hospital patient is called a factor. For example, factors can be intravenous (IV) tubing, IV fluid, needles, shave kits, bedpans, diapers, dressings, medications, and
Refer to Exercise 2.18 and calculate the number of the 600 items falling into each of the classes. Then graph a frequency histogram for these data.Data from Exercise 2.18A company is analyzing the
W. Edwards Deming was one of America’s most famous statisticians. He was best known for the role he played after World War II in teaching the Japanese how to improve the quality of their products
Consider the following stem-and-leaf display shown here.a. Identify the numbers in the original data set represented by the stem and its leaves. Assume that the data was not rounded.b. Construct a
Each year Forbes reports on the value of all teams in the National Football League. Although Spain’s soccer team, Real Madrid, is the most valuable team in the world ($3.3 billion), all 32 NFL
Suppose you’re considering working for a small law firm—one that currently has a senior member and three junior members. You inquire about the salary you could expect to earn if you join the
Calculate the mean and median of the following grade point averages: 3.2 2.5 2.1 3.7 2.8 2.0
Educators are constantly evaluating the efficacy of public schools in the education and training of American students. One quantitative assessment of change over time is the difference in scores on
Children out of School in America is a report on delinquency of school-age children prepared by the Children’s Defense Fund (CDF), a government-sponsored organization. Consider the following three
A group of researchers developed a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour (The Sport Journal, Winter 2007). The method
Parking at a university has become a problem. The university’s administrators are interested in determining the average time it takes a student to find a parking spot. An administrator
Calculate the mean, the median, and the mode for the following samples:a. -2, 0, 5, 5, 5, 10, 11b. 37, 98, 15, 38, 63, 19c. Five food tasters rated a new product either “awful” or
A society called Parents Against Watching Television (PAWT) is primarily concerned with the amount of television viewed by today’s youth. It asked 300 parents of elementary school aged children to
The long-run success of a business depends on its ability to market products with superior characteristics that maximize consumer satisfaction and that give the firm a competitive advantage (Kotler
Two coins are tossed, and their up faces are recorded. List all the sample points for this experiment.
Which of the following describe continuous random variables? Which describe discrete random variables?a. The number of cups of coffee sold in a cafeteria during lunchb. The height of a player on a
Warehouse clubs are retailers that offer lower prices than traditional retailers, but they sell only to customers who have purchased memberships and often merchandise must be purchased in large
A panel of 10 experts for the Wine Spectator (a national publication) is asked to taste a new white wine and assign a rating of 0, 1, 2, or 3. A score is then obtained by adding together the ratings
Collect data for at least 50 observations on a variable of interest to you (e.g., scores on a statistics exam, monthly sales of a pre-owned auto dealership, time spent preparing for the GMAT, number
Suppose the Environmental Protection Agency (EPA) takes readings once a month on the amount of pesticide in the discharge water of a chemical company. If the amount of pesticide exceeds the maximum
Refer to Example 4.2. A second random variable of interest is the amount x of pesticide (in milligrams per liter) found in the monthly sample of discharge waters from the chemical company. What
Refer to Glassdoor Economic Research’s list of the top-paid CEOs (Table 1.1). One variable saved in the file is the CEO’s compensation (in $ millions) in 2015.Is x a discrete or continuous random
A bottle contains 16 ounces of water. The variable x represents the volume, in ounces, of water remaining in the bottle after the first drink is taken. What are the natural bounds for the values of
Craps is a popular casino game in which a player throws two dice and bets on the outcome (the sum total of the dots showing on the upper faces of the two dice).Consider a $5 wager. On the first toss
Recall the experiment of tossing two coins (Section 4.1) and let x be the number of heads observed. Find the probability associated with each value of the random variable x, assuming the two coins
A drought is a period of abnormal dry weather that causes serious problems in the farming industry of the region. University of Arizona researchers used historical annual data to study the severity
Suppose you invest a fixed sum of money in each of five Internet business ventures.Assume you know that 70% of such ventures are successful, the outcomes of the ventures are independent of one
Suppose you work for an insurance company, and you sell a $10,000 oneyear term insurance policy at an annual premium of $290. Actuarial tables show that the probability of death during the next year
Suppose we set the Random Numbers applet to generate one number between 1 and 100, inclusive. We let the value of the random variable x be the number generated when the Sample button is clicked.
For the following examples, decide whether x is a binomial random variable.a. You randomly select 3 bonds out of a possible 10 for an investment portfolio.Unknown to you, 8 of the 10 will maintain
A machine that produces stampings for automobile engines is malfunctioning and producing 10% defectives. The defective and nondefective stampings proceed from the machine in a random manner. If the
Refer to Example 4.11 and find the values of p(0), p(1), p(2), p(4) and p(5). Graph p(x). Calculate the mean μ and standard deviation σ. Locate μ and the interval μ - 2σ to μ + 2σ on the
Suppose a poll of 20 employees is taken in a large company. The purpose is to determine x, the number who favor unionization. Suppose that 60% of all the company’s employees favor unionization.a.
Suppose the number, x, of a company’s employees who are absent on Mondays has (approximately) a Poisson probability distribution. Furthermore, assume that the average number of Monday absentees is
Consider the probability distribution shown here:a. Calculate μ, σ2, and σ.b. Graph p(x). Locate μ, μ - 2σ, and μ + 2σ on the graph.c. What is the probability that x is in the interval μ ±
Suppose a marketing professor randomly selects three new teaching assistants from a total of ten applicants—six male and four female students. Let x be the number of females who are hired.a. Find
Consider a standard normal random variable, z. Find the following “tail” probabilities:a. P(z > 1.64)b. P(z < .67)c. P( |z| > 1.96)
Consider the discrete probability distribution shown here:a. Find μ = E(x).b. Find σ = √E[(x - μ)2].c. Find the probability that the value of x falls within one standard deviation of the mean.
Assume that the length of time, x, between charges of a cellular phone is normally distributed with a mean of 10 hours and a standard deviation of 1.5 hours. Find the probability that the cell phone
The Environmental Protection Agency (EPA) performs extensive tests on all new car models to determine their mileage ratings. The results of 100 EPA tests on a certain new car model are displayed in
Suppose an automobile manufacturer introduces a new model that has an advertised mean in-city mileage of 27 miles per gallon. Although such advertisements seldom report any measure of variability,
Consider the standard normal distribution, z. Find a value of z, call it z0, such that:a. P(z 7 z0) = .10b. P( -z0 < z < z0) = .95
Suppose a paint manufacturer has a daily production, x, that is normally distributed with a mean of 100,000 gallons and a standard deviation of 10,000 gallons.Management wants to create an incentive
One problem with any product (e.g., a graphing calculator) that is mass produced is quality control. The process must somehow be monitored or audited to be sure the output of the process conforms to
Suppose the research department of a steel manufacturer believes that one of the company’s rolling machines is producing sheets of steel of varying thickness. The thickness is a uniform random
Compute the following: a. 7! 3! (7 - 3)! b. - (1) -(1) ₁ C. d. (4) e. (5)
Suppose the length of time (in hours) between emergency arrivals at a certain hospital is modeled as an exponential distribution with θ = 2. What is the probability that more than 5 hours pass
A manufacturer of microwave ovens is trying to determine the length of warranty period it should attach to its magnetron tube, the most critical component in the oven. Preliminary testing has shown
If x is a binomial random variable, compute p(x) for each of the following cases:a. n = 4, x = 2, p = .2b. n = 3, x = 0, p = .7c. n = 5, x = 3, p = .1d. n = 3, x = 1, p = .9e. n = 3, x = 1, q = .3f.
A recent study suggested that 70% of all eligible voters will vote in the next presidential election. Suppose 20 eligible voters are randomly selected from the population of all eligible voters.a.
Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 6, compute the following:a. P(x = 0)b. P(x = 1)c. P(x ≤ 1)d. P(x ≥ 2)
The following table reports the U.S. credit/debit card industry’s market share data for 2015. A random sample of 100 credit/debit card users is to be questioned regarding their satisfaction with
Applications of the Poisson distribution were discussed in the Journal of Case Research in Business and Economics (December 2014). In one case involving a hospital emergency room, 2 patients arrive
Find the following probabilities for the standard normal random variable z:a. P(0 < z < 2.25)b. P(-2.25 < z < 0)c. P(-2.25 < z < 1.25)d. P(-2.50 < z < 1.50)e. P(z > -2.33 or z > 2.33)
Identify the type of random variable—binomial, Poisson, or hypergeometric—described by each of the following probability distributions: a. p(x) b. p(x) .5% e-s x! = - (3) (-2)*(.8) 6-* = (x = 0,
Given that x is a binomial random variable, compute p(x) for each of the following cases:a. n = 7, x = 3, p = .5b. n = 4, x = 3, p = .8c. n = 15, x = 1, p = .1
Which of the following describe discrete random variables, and which describe continuous random variables?a. The number of damaged inventory itemsb. The average monthly sales revenue generated by a
Identify the type of continuous random variable—uniform, normal, or exponential—described by each of the following probability density functions: a. f(x) = (e-x/7)/7, x > 0 b. f(x)=1/20,5 < x <
Find the following probabilities for the standard normal random variable z:a. P(z ≤ 2.1)b. P(z ≥ 2.1)c. P(z ≥ -1.65)d. P( -2.13 ≤ z ≤ -.41)e. P( -1.45 ≤ z ≤ 2.15)f. P(z ≤ -1.43)
The random variable x has a normal distribution with μ = 75 and σ = 10. Find the following probabilities:a. P(x ≤ 80)b. P(x ≥ 85)c. P(70 ≤ x ≤ 75)d. P(x > 80)e. P(x = 78)f. P(x ≤ 110)
Assume that x is a binomial random variable with n = 100 and p = .5. Use the normal probability distribution to approximate the following probabilities:a. P(x ≤ 48)b. P(50 ≤ x ≤ 65)c. P(x ≥
The random variable x has a normal distribution with μ = 40 and σ2 = 36. Find a value of x, call it x0, such thata. P(x ≥ x0) = .10b. P(μ ≤ x < x0) = .40c. P(x < x0) = .05d. P(x ≥ x0) =
In a single toss of a fair coin, let x equal the number of heads observed. Now consider a sample of n = 2 tosses. Find the sampling distribution of x̄, the sample mean.
Consider the popular casino game of craps, in which a player throws two dice and bets on the outcome (the sum total of the dots showing on the upper faces of the two dice). we looked at the possible
Consider the length of time a student spends making a cell phone call, sending/retrieving a text message, or accessing e-mail on his/her cell phone. Let x represent the length of time, in seconds,
Refer to Example 4.24. Recall that the thickness of a steel sheet follows a uniform distribution with values between 150 and 200 millimeters. Suppose we perform the following experiment over and over
Suppose two statistics, A and B, exist to estimate the same population parameter θ (theta). (Note that θ could be any parameter: μ, σ2, σ, etc.) Suppose the two statistics have sampling
Refer to Example 5.2 and the outcome x of a $5 wager in craps. We found the sampling distributions of the sample mean x and the sample median m for random samples of n = 3 dice rolls from a
Refer to Example 5.5 and find the standard deviations of the sampling distributions of x̄ and m. Which statistic would appear to be a better estimator of μ?Example 5.5Refer to Example 5.2 and the
Suppose a population has the uniform probability distribution given in Figure 5.8. The mean and standard deviation of this probability distribution are μ = 175 and σ = 14.43. Now suppose a sample
Suppose we have selected a random sample of n = 36 observations from a population with mean equal to 80 and standard deviation equal to 6. It is known that the population is not extremely skewed.a.

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