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Questions and Answers of
Statistics
According to a 2011 report for IFA Educational Foundation, 20.5% of all franchised businesses in the United States are minority owned. (This information is based on the U.S. Census Bureau's survey of
As worldwide air traffic volume has grown over the years, the problem of airplanes striking birds and other flying wildlife has increased dramatically. The International Journal for Traffic and
The most common injury that occurs among mountain climbers is trauma to the lower extremity (leg). Consequently, rescuers must be proficient in immobilizing and splinting fractures. In High Altitude
Refer to the sample of 308 diamond stones that were listed for sale on the open market in Singapore's Business Times. Recall that the color of each diamond is classified as D, E, F, G, H, or I, while
Refer to the Nature (July 15, 2004) study of fish specimens labeled "red snapper," Exercise 3.75. Recall that federal law prohibits restaurants from serving a cheaper, look-alike variety of fish
Pigmented makeup products like mascara and eye shadow may contain metal (e.g., nickel) allergens. Is a nickel allergy more likely to occur in women who report cosmetic dermatitis from using eye
Explain what is meant by the statement, "We are 95% confident that an interval estimate contains μ."
If you wish to estimate a population mean with a sampling error of SE = .3 using a 95% confidence interval, and you know from prior sampling that σ2 is approximately equal to 7.2, how many
Suppose you wish to estimate a population mean correct to within .20 with probability equal to .90. You do not know σ2, but you know that the observations will range in value between 30 and 34. a.
The following is a 90% confidence interval for p: (.26, .54). How large was the sample used to construct this interval?
It costs you $10 to draw a sample of size n = 1 and measure the attribute of interest. You have a budget of $1,500. a. Do you have sufficient funds to estimate the population mean for the attribute
Suppose you wish to estimate the mean of a normal population using a 95% confidence interval, and you know from prior information that σ2 ≈ 1. a. To see the effect of the sample size on the width
Explain the difference between an interval estimator and a point estimator for μ.
Refer to the Heating/ Piping/Air Conditioning Engineering (April 2013) study of evaporation from occupied swimming pools, Exercise 6.34. The researchers desired an estimate of the mean absolute value
Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 6.48. Recall that you used a 99% confidence interval to estimate
Refer to the International Journal for Traffic and Transport Engineering (Vol. 3, 2013) study of aircraft bird strikes at a Nigerian airport, Exercise 6.54. Recall that an air traffic controller
Is the bottled water you drink safe? The Natural Resources Defense Council warns that the bottled water you are drinking may contain more bacteria and other potentially carcinogenic chemicals than
Refer to the International Journal of Retail and Distribution Management (Vol. 39, 2011) survey of Black Friday shoppers, Exercise 6.16. One question was, "How many hours do you usually spend
A large food-products company receives about 100,000 phone calls a year from consumers on its toll-free number. A computer monitors and records how many rings it takes for an operator to answer, how
Refer to the Journal of the European Academy of Dermatology and Venereology (June 2010) study of the link between nickel allergies and use of mascara or eye shadow, Exercise 6.58. Recall that two
Does the caffeine in coffee, tea, and cola induce an addiction similar to that induced by alcohol, tobacco, heroin, and cocaine? In an attempt to answer this question, researchers at Johns Hopkins
Calculate the percentage of the population sampled and the finite population correction factor for each of the following situations. a. n = 1,000, N = 2,500 b. n = 1,000, N = 5,000 c. n = 1,000, N =
Suppose the standard deviation of the population is known to be σ = 200. Calculate the standard error of x for each of the situations described in Exercise 6.80. a. n = 1,000, N = 2,500 b. n =
Suppose N = 5,000, n = 64, and s = 24. a. Compare the size of the standard error of x computed with and without the finite population correction factor. b. Repeat part a, but this time assume n =
Suppose N = 10,000, n = 2,000, and s = 50. a. Compute the standard error of x using the finite population correction factor. b. Repeat part a assuming n = 4,000. c. Repeat part a assuming n =
Suppose you want to estimate a population mean, μ, and x̅ = 422, s = 14, N = 375, and n = 40. Find an approximate 95% confidence interval for μ.
Suppose you want to estimate a population proportion, p, and p̂ = .42, N = 6,000, and n = 1,600. Find an approximate 95% confidence interval for p.
A random sample of size n = 30 was drawn from a population of size N = 300. The following measurements were obtained:a. Estimate μ with an approximate 95% confidence interval. b.
Researchers at the University of Pennsylvania's Wharton Sports Business Initiative collaborated with the National Football League Players Association (NFLPA) to produce the first NFL Player Survey.
Each year, the trade magazine Quality Progress publishes a study of subscribers' salaries. One year, the 223 vice presidents sampled had a mean salary of $116,754 and a standard deviation of $39,185.
Traditionally, auditors have relied to a great extent on sampling techniques, rather than 100% audits, to help them test and evaluate the financial records of a client firm. When sampling is used to
Will a large-sample confidence interval be valid if the population from which the sample is taken is not normally distributed? Explain.
A brand name that consumers recognize is a highly valued commodity in any industry. To assess brand familiarity in the furniture industry, NPD (a market research firm) surveyed 1,333 women who head
In a study of invoice errors in a company's new billing system, an auditor randomly sampled 35 invoices produced by the new system and recorded actual amount (A), invoice amount (I), and the
The U.S. Environmental Protection Agency (EPA) bans use of the cancer-causing pesticide ethylene dibromide (EDB) as a fumigant for grain- and flour-milling equipment. EDB was once used to protect
Given the following values of x̅, s, and n, form a 90% confidence interval for σ2.a. x̅ = 21, s = 2.5, n = 50b. x̅ = 1.3, s = .02, n = 15c. x̅ = 167, s = 31.6, n = 22d. x̅ = 9.4, s = 1.5, n = 5
The characteristics of sweet potato chips fried at different temperatures were investigated in the Journal of Food Engineering (September 2013). A sample of 6 sweet potato slices were fried at 130°
Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 6.12. Recall that the level of support for corporate sustainability (measured on a
Refer to the Psychological Science (Vol. 22, 2011) study of a chief executive officer's facial structure, Exercise 6.20. Recall that the facial width-to-height ratio (WHR) was determined by computer
The average size of single-family homes built in the United States is 2,600 square feet (U.S. Census Bureau, 2015). A random sample of 100 new homes sold in California yielded the following size
Refer to the Pew Internet & American Life Project Survey (January 2016) study of 250 store customers and their participation in a store loyalty card program, Exercise 7.69. Recall that a store owner
Refer to the Chance (Winter 2010) experiment to determine if color of a Gummi Bear is related to its flavor, Exercise 7.72. You tested the null hypothesis of p = .5 against the two-tailed alternative
Refer to Exercise 7.44, in which the performance of a particular type of laser-based inspection equipment was investigated. Assume that the standard deviation of the number of solder joints inspected
The national student loan default rate has fluctuated over the past several years. Recently (October 2015) the Department of Education reported the default rate (i.e., the proportion of college
Which of the elements of a test of hypothesis can and should be specified prior to analyzing the data that are to be used to conduct the test?
The National Center for Border Security and Protection has developed the "Embodied Avatar"-a kiosk with a computer-animated border guard that uses artificial intelligence to scan passports, check
Refer to Exercise 6.129 and the study of the accuracy of checkout scanners at Walmart stores in California. Recall that the National Institute for Standards and Technology (NIST) mandates that for
Refer to the Journal of Statistics Education data on diamonds saved in the file. In Exercise 6.122 you selected a random sample of 30 diamonds from the 308 diamonds and found the mean and standard
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
The Lincoln Tunnel (under the Hudson River) connects suburban New Jersey to midtown Manhattan. On Mondays at 8:30A.M., the mean number of cars waiting in line to pay the Lincoln Tunnel toll is 1,220.
Refer to the Chance (Fall 1998) study of point-spread errors in NFL games, Exercise 7.41. Recall that the difference between the actual game outcome and the point spread established by odds
Sales promotions that are used by manufacturers to entice retailers to carry, feature, or push the manufacturer's products are called trade promotions. A survey of 132 manufacturers conducted by
Shoplifting in the United States costs retailers about $35 million a day. Despite the seriousness of the problem, the National Association of shoplifting Prevention (NASP) claims that only 50% of all
Refer to Exercise 7.134. Shoplifting in the United States costs retailers about $35 million a day. Despite the seriousness of the problem, the National Association of shoplifting Prevention (NASP)
To instill customer loyalty, airlines, hotels, rental car companies, and credit card companies (among others) have initiated frequency marketing programs that reward their regular customers. A large
The EPA sets an airborne limit of 5 parts per million (ppm) on vinyl chloride, a colorless gas used to make plastics, adhesives, and other chemicals. It is both a carcinogen and a mutagen (New Jersey
Refer to Exercise 7.137. The EPA sets an airborne limit of 5 parts per million (ppm) on vinyl chloride, a colorless gas used to make plastics, adhesives, and other chemicals. It is both a carcinogen
Refer to Exercises 7.137 and 7.138. The EPA sets an airborne limit of 5 parts per million (ppm) on vinyl chloride, a colorless gas used to make plastics, adhesives, and other chemicals. It is both a
The interest rate at which London banks lend money to one another is called the London interbank offered rate, or Libor. The British Bankers Association regularly surveys international banks for the
In an effort to increase employment, France mandated in February 2000 that all companies with 20 or more employees reduce the workweek to 35 hours. The economic impact of the shortened workweek was
It is essential in the manufacture of machinery to use parts that conform to specifications. In the past, diameters of the ball bearings produced by a certain manufacturer had a variance of .00156.
Television commercials most often employ females or "feminized" males to pitch a company's product. Research published in Nature (August 27 1998) revealed that people are, in fact, more attracted to
In countries with a water shortage, converting salt water to potable water is big business. The standard method of water distillation is with a single-slope solar still. Several enhanced solar energy
Cable TV's Home Shopping Network (HSN) reports that the average age of its shoppers is 52 years. Suppose you want to test the null hypothesis, H0: μ = 52, using a sample of n = 50 cable TV
What factors inhibit the learning process in the classroom? To answer this question, researchers at Murray State University surveyed 40 students from a senior-level marketing class (Marketing
The placebo effect describes the phenomenon of improvement in the condition of a patient taking a placebo-a pill that looks and tastes real but contains no medically active chemicals. Physicians at a
Pharmaceutical companies spend billions of dollars per year on research and development of new drugs. The pharmaceutical company must subject each new drug to lengthy and involved testing before
Access to computers, email, and Facebook accounts is achieved via a password-a collection of symbols (usually letters and numbers) selected by the user. One problem with passwords is that persistent
The Journal of Research of the National Institute of Standards and Technology (November- December 2003) published a study of a computer intrusion detection system (IDS). The IDS is designed to
Consider the test of H0: μ = 7. For each of the following, find the p-value of the test: a. Ha: μ > 7, z = 1.20 b. Ha: μ < 7, z = -1.20 c. Ha: μ ≠ 7, z = 1.20
For each a and observed significance level (p-value) pair, indicate whether the null hypothesis would be rejected. a. α = .05, p-value = .10 b. α = .10, p-value = .05 c. α = .01, p-value = .001 d.
In a test of the hypothesis H0: μ = 50 versus Ha: μ > 50, a sample of n = 100 observations possessed mean x̅ = 49.4 and standard deviation s = 4.1. Find and interpret the p-value for this test.
In a test of H0: μ = 100 against Ha: μ > 100, the sample data yielded the test statistic z = 2.17. Find and interpret the p-value for the test.
In a test of H0: μ = 75 performed using the computer, SPSS reports a two-tailed p-value of .1032. Make the appropriate conclusion for each of the following situations: a. Ha: μ < 75, z = -1.63, α
Consider the test H0: μ = 70 versus Ha: μ > 70 using a large sample of size n = 400. Assume s = 20.a. Describe the sampling distribution of x̅.b. Find the value of the test statistic if ̅ =
Suppose you are interested in conducting the statistical test of H0: μ = 255 against Ha: μ > 255, and you have decided to use the following decision rule: Reject H0 if the sample mean of a
What is the level of significance of a test of hypothesis?
A random sample of 100 observations from a population with standard deviation 60 yielded a sample mean of 110.a. Test the null hypothesis that μ = 100 against the alternative hypothesis that μ >
Refer to the Business and Society (March 2011) study on the sustainability behaviors of CPA corporations, Exercise 6.12. Recall that the level of support for corporatesustainability (measured on a
Can packaging of a healthy food product influence children's desire to consume the product? This was the question of interest in an article published in the Journal of Consumer Behaviour (Vol. 10,
Refer to the ACS Medicinal Chemistry Letters (Vol. 1, 2010) study of the metabolic stability of drugs, Exercise 2.22. Recall that two important values computed from the testing phase are the fraction
Refer to the Psychological Science (Vol. 22, 2011) study on using a chief executive officer's facial structure to predict a firm's financial performance, Exercise 6.20 (p. 317). Recall that the
The trading skills of institutional stock investors were quantified and analyzed in The Journal of Finance (April 2011). The study focused on "round-trip" trades, i.e., trades in which the same stock
In quality-control applications of hypothesis testing, the null and alternative hypotheses are frequently specified asH0: The production process is performing satisfactorily.Ha: The process is
Refer to the Behavioral Research in Accounting (July 2015) study of unethical corporate conduct, Exercise 6.15 (p. 316). Recall that each in a sample of 86 accounting graduate students was asked to
When a person is asked, "How much time will you require to complete this task?" cognitive theory posits that people (e.g., a business consultant) will typically underestimate the time required. Would
Refer to the Journal of Interactive Marketing (February 2016) study of tipping points in online "daily deal" transactions, Exercise 6.11 (p. 315). Recall that a "tipping point" is the number of
During the National Football League (NFL) season, Las Vegas odds makers establish a point spread on each game for betting purposes. For example, the Carolina Panthers were established as 3.5-point
According to the National Funeral Directors Association (NFDA), the nation's 19,000 funeral homes collected an average of $7,180 per full-service funeral in 2014 (www.nfda.org). A random sample of 36
Refer to the Financial Analysts Journal (July/August 2008) study of earnings forecasts of buy-side and sell-side analysts, Exercise 2.86 (p. 88). Recall that data were collected on 3,526 forecasts
Current technology uses higher-solution X-rays and lasers for inspection of solder-joint defects on printed circuit boards (PCBs) (Global SMT & Packaging, April 2008). A particular manufacturer
In business, firms that both cooperate and compete with other firms are described as engaging in "coopetition." A study published in Industrial Marketing Management (February 2016) examined the level
The Economics of Education Review (Vol. 21, 2002) published a paper on the relationship between education level and earnings. The data for the research were obtained from the National Adult Literacy
a. Consider testing H0: μ = 80. Under what conditions should you use the t-distribution to conduct the test? b. In what ways are the distributions of the z-statistic and t-test statistic alike? How
For each of the following rejection regions, sketch the sampling distribution of t and indicate the location of the rejection region on your sketch: a. t > 1.440 where df = 6 b. t < -1.782 where df =
A random sample of n observations is selected from a normal population to test the null hypothesis that μ = 10. Specify the rejection region for each of the following combinations of Ha, a, and n:a.
List the four possible results of the combinations of decisions and true states of nature for a test of hypothesis.
A sample of five measurements, randomly selected from a normally distributed population, resulted in the following summary statistics: x̅ = 4.8, s = 1.3.a. Test the null hypothesis that the mean of
Refer to the Journal of Business Logistics (Vol. 36, 2015) study of the factors that lead to successful performance-based logistics projects, Exercise 2.45. Recall that opinions of a sample of
Recall, from Exercise 6.36, that stock screeners are automated tools used by investment companies to help clients select a portfolio of stocks to invest in. The data on the annualized percentage
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