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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

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.
A manufacturer of automobile batteries claims that the distribution of the lengths of life of its best battery has a mean of 54 months and a standard deviation of 6 months. Recently, the manufacturer
Refer to Example 4.13 and the problem of sampling workers to determine whether they are in favor of unionization. We assumed that 60% of all workers at a large plant were, in fact, in favor of
Refer to Example 5.10. Again, assume that 60% of all workers at a large plant are in favor of unionization. In a random sample of 100 plant workers, what is the probability that fewer than half are
Consider the following three measurements: 0, 4, and 12. Find the z-score for each measurement if they are from a population with a following mean and standard deviation equal toa. µ = 2 and σ =
Refer to Exercise 2.141. Assuming all populations are approximately mound-shaped, for parts a–d, determine whether the values 0, 4, and 12 are outliers.Data from Exercise 2.141Consider the
The amount spent on textbooks for the fall term was recorded for a sample of five university students. The following data were observed: $400, $350, $600, $525, and $450.Calculate each of the
A statistician keeps track of every serve that a player hits during the U.S. Open Tennis Championship. The statistician reports that the mean serve speed was 100 miles per hour (mph) and the
To develop programs for business travelers staying at convention hotels, a major hotel chain commissioned a study of executives who play golf. The study revealed that 55% of the executives admitted
An investor in wheat futures is concerned with the following events:Based on available information, the investor believes that the probability is .01 that production of wheat will be profitable
Consider the experiment of tossing a fair die and letAre events A and B independent? A: (Observe B: {Observe an even number.} a number less than or equal to 4.}
A county welfare agency employs 10 welfare workers who interview prospective food stamp recipients. Periodically the supervisor selects, at random, the forms completed by 2 workers to audit for
Refer to the consumer product complaint study in Example 3.16. The percentages of complaints of various types during and after the guarantee period are shown in Table 3.6. Define the following
Refer to Example 3.5 (pp. 164–165). Recall that USA Today found that of all U.S. firms that use diversity training, 38% state that their primary reason for using it is to stay competitive.a. What
Electric wheelchairs are difficult to maneuver for many disabled people. In a paper presented at the 1st International Workshop on Advances in Service Robotics (March 2003), researchers applied
Australia has developed a General Purpose Water Accounting (GPWA)reporting system in an effort to provide a financial accounting of water use in the country. The perceptions of potential users of the
Refer to Exercise 2.27 and the data on state SAT scores. Construct a scatterplot for the data, with 2010 Math SAT score on the horizontal axis and 2014 Math SAT score on the vertical axis. What type
If the range of a set of data is 20, find a rough approximation to the standard deviation of the data set.
The American Bankruptcy Institute and the National Bankruptcy Research Center monitor the number of business bankruptcy filings each quarter. The table below lists the number of business bankruptcy
An experiment results in one of the following sample points: E1, E2, E3, or E4. Find P(E4) for each of the following cases. a. P(E₁) = .1, P(E₂) .2, and P(E3) b. P(E₁)=P(E₂) = P(E3) =
Consider an experiment in which two smartphones are randomly selected from an assembly line during manufacturing. The defective status—defective (D) or not (N)—of each is determined. The sample
Going Green is the term used to describe water conservation programs at hotels and motels. Many hotels now offer their guests the option of participating in these Going Green programs by reusing
Diversity training of employees is the latest trend in U.S. business. USA Today reported on the primary reasons businesses give for making diversity training part of their strategic planning process.
A fair die is tossed, and the up face is observed. If the face is even, you win $1. Otherwise, you lose $1. What is the probability that you win?
Three fair coins are tossed and either heads (H) or tails (T)is observed for each coin. a. List the sample points for this experiment.b. Assign probabilities to the sample points.c. Determine the
You have the capital to invest in two of four ventures, each of which requires approximately the same amount of investment capital. Unknown to you, two of the investments will eventually fail and two
Refer to Example 3.6, where we selected two ventures from four in which to invest. Use the Combinations Rule to determine how many different selections can be made.Data form Example 3.6You have the
Consider the die-toss experiment. Define the following events:a. Describe A ⋃ B for this experiment.b. Describe A ⋂ B for this experiment.c. Calculate P(A ⋃ B) and P(A ⋂ B) assuming the die
Suppose you plan to invest equal amounts of money in each of five business ventures. If you have 20 ventures from which to make the selection, how many different samples of five ventures can be
Many firms undertake direct marketing campaigns to promote their products. The campaigns typically involve mailing information to millions of households. The response rates are carefully monitored to
In an exit poll, 45% of voters said that the main issue affecting their choice of candidates was the economy, 35% said national security, and the remaining 20% were not sure. Suppose we select one of
Suppose you are interested in the probability of the sale of a large piece of earth moving equipment. A single prospect is contacted. Let F be the event that the buyer has sufficient money (or
Hospital records show that 12% of all patients are admitted for surgical treatment, 16% are admitted for obstetrics, and 2% receive both obstetrics and surgical treatment. If a new patient is
In a survey conducted by the International Nanny Association (INA) and reported at the INA Web site (www.nanny.org), 4,176 nannies were placed in a job in a given year. Only 24 of the nannies placed
The investigation of consumer product complaints by the Federal Trade Commission (FTC) has generated much interest by manufacturers in the quality of their products. A manufacturer of an
An unmanned monitoring system uses high-tech video equipment and microprocessors to detect intruders. A prototype system has been developed and is in use outdoors at a weapons munitions plant. The
A number between 1 and 10, inclusive, is randomly chosen, and the events A and B are defined as follows:a. Identify the sample points in the event A ⋃ b.b. Identify the sample points in the event A
The manager of an advertising department has asked her creative team to propose six new ideas for an advertising campaign for a major client. She will choose three of the six proposals to present to
The U.S. Census Bureau reports a growth in the percentage of mothers in the workforce who have infant children. The following table gives a breakdown of the marital status and working status of
Which of the following pairs of events are mutually exclusive? Justify your response.a. {The next customer entering a retail store is older than 30 years.}, {The next customer entering the same
A sample space consists of three sample points, S1, S2, and S3, with P(S1) = .1, and P(S2) = .2.a. Assign a probability to S3 in a way that the three sample points define a valid sample space obeying
For two events A and B, suppose P(A) = .7, P(B) = .5, and P(A ∩ B) = .4. Find P(A ∪ B).
Consider two events A and B, with P(A) = .1, P(B) = .2, and P(A ⋂ B) = 0.a. Are A and B mutually exclusive?b. Are A and B independent?
From a production batch with 16 items, 8 items are randomly selected for quality assurance. In how many different ways can the sample be drawn? Suggest an estimate before computing the exact number.
In agriculture, a main cause of fatal injuries is tractor rollover. To combat this problem, tractor manufacturers have installed foldable rollover protection structures (FROPS). Human Factors
Smart Insights reported on the “search” shares (i.e., percentage of all Internet searches) for the most popular search engines available on the Web. In Jan. 2020, Google accounted for 73% of all
For each of the following studies, give the parameter of interest and state any assumptions that are necessary for the inferences to be valid.a. Human Factors (December 2015) published a study on how
To improve quality, productivity, and timeliness, many American industries employ self-managed work teams (SMWTs). Because SMWTs require that employees be trained in interpersonal skills, they can
Consider dot plots 1 and 2 shown below. Assume that the two samples represent independent, random samples corresponding to two treatments in a completely randomized design.a. In which plot is the
The US Tobacco Control Act restricts cigarette advertisers from explicitly stating that their product is less harmful than others. However, marketers use terms like “organic” or “natural”
A randomized field experiment was carried out to determine how workers respond to wage cuts and the results published in Institute for the Study of Labor: Discussion Paper Series (March 2011). A
Long-haul truck drivers are often asked to drive while fatigued. Can a secondary task—such as a word association task—improve the performance of a fatigued driver? This was the question of
The performances of public bus depots in India were evaluated and ranked in the International Journal of Engineering Science and Technology (February 2011). A survey was administered to 150 customers
Consider a completely randomized design with k treatments. Assume all pairwise comparisons of treatment means are to be made using a multiple comparisons procedure. Determine the total number of
Define an experimentwise error rate.
What is the level of stress (if any) that cows undergo prior to being slaughtered? To answer this question, researchers designed an experiment involving cows bred in Normandy, France (Applied Animal
Define a comparisonwise error rate.
When planning for a new forest road to be used for tree harvesting, planners must select the location to minimize tractor skidding distance. In the Journal of Forest Engineering, researchers wanted
Recently, a case of salmonella (bacterial) poisoning was traced to a particular brand of ice cream bar, and the manufacturer removed the bars from the market. Despite this response, many consumers
When companies employ control charts to monitor the quality of their products, a series of small samples is typically used to determine if the process is “in control” during the period of time in
Acid has been found to be a primary cause of dental caries (cavities). It is theorized that oral mouthwashes contribute to the development of caries due to the antiseptic agent oxidizing into acid
The National Association of Realtors (NAR) reported the results of a July 2019 survey of home buyers. One question pertained to the first step in the home search process. In a random sample of 5,870
The potential of using solar panels constructed above national highways to generate energy was explored in the International Journal of Energy and Environmental Engineering (December 2013). Two-layer
The Washington Post (January 30, 2020) reported on a study conducted by the AAA Foundation for Traffic Safety to investigate a possible link between legalization of marijuana and fatal vehicle
“Take the Pepsi Challenge” was a famous marketing campaign used by the Pepsi-Cola Company. Coca-Cola drinkers participated in a blind taste test where they were asked to taste unmarked cups of
a. List three factors that will increase the power of a test.b. What is the relationship between b, the probability of committing a Type II error, and the power of a test?
If you select a very small value for α when conducting a hypothesis test, will b tend to be big or small? Explain.
The Academy of Management Journal (December 2019) published a study on how men and women differ in negotiating for career advancement. The researchers interviewed 49 civil servants (27 men and 22
If the rejection of the null hypothesis of a particular test would cause your firm to go out of business, would you want α to be small or large? Explain.
Merck Research Labs conducted an experiment to evaluate the effect of a new drug using the single-T swim maze. Nineteen impregnated dam rats were captured and allocated a dosage of 12.5 milligrams of
Will the 2020 US Census ask you if you are a US citizen? This was one of the questions of interest in a Pew Internet & American Life Project Survey (January 2020). The answer is “no,” but in
In 1894, druggist Asa Candler began distributing handwritten tickets to his customers for free glasses of Coca-Cola at his soda fountain. That was the genesis of the discount coupon. In 1975, it was
During periods of high electricity demand, especially during the hot summer months, the power output from a gas turbine engine can drop dramatically. One way to counter this drop in power is by
“Hot tamales” are chewy, cinnamon- flavored candies. A bulk vending machine is known to dispense, on average, 15 hot tamales per bag with a standard deviation of 3 per bag. Chance (Fall 2000)
In auction bidding, the “winner’s curse” is the phenomenon of the winning (or highest) bid price being above the expected value of the item being auctioned. The Review of Economics and
Many companies now use text messaging on cell phones as a means of marketing their products. One way to do this is to send a redeemable discount coupon (called an m-coupon) via a text. The redemption

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