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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

Fraud survey of Asia-Pacific firms. The opinions of employees at Asia-Pacific firms regarding fraud, bribery, and corruption in the workplace were elicited in the 2017 Asia-Pacific (APAC) Fraud
Economic struggle. The chief executive of Queensland Council of Social Service (QCOSS) claims that one in four Queenslanders lost employment or faced a reduction in working hours in the year 2020. In
Number of Items of Interest 322 Sample Size 671 Intermediate Calculations Sample Proportion 0.4799 Standard Error 0.0167 Z Test Statistic 13.7519 Two-Tail Test Lower Critical Value -2.5758 Upper
Homeownership survey. A real estate agency conducted a survey to determine the proportion of homeownership in a residential area. The survey consists of 50 residents. Their current homeownership
Dehorning of dairy calves. For safety reasons, calf dehorning has become a routine practice at dairy farms. A report by Europe’s Standing Committee on the Food Chain and Animal Health (SANKO)
Effectiveness of skin cream. Pond’s Age-Defying Complex, a cream with alpha hydroxy acid, advertised that it could reduce wrinkles and improve the skin. In a study published in Archives of
Ride-hailing service. Refer to the service quality data provided by a ride-hailing service in Bangkok, Exercise
(p. 427). The research survey indicates that out of the total 563 respondents, 265 used the service for travel related to study, work, or business. The owner of the service claims that less than 50%
Ultra HD TVs. A 4K (also known as Ultra HD) television is a TV with four times as many pixels as a full high definition TV. According to a Leichtman Research Group report (May 2019), 22% of
Choosing portable grill displays. Refer to the Journal of Consumer Research (March 2003) experiment on influencing the choices of others by offering undesirable alternatives, Exercise
(p. 199). Recall that each of 124 college students selected three portable grills from five to display on the showroom floor. The students were instructed to include Grill #2 (a smaller-sized grill)
0.577589 Test Null hypothesis H0: p =
Alternative hypothesis H1: p 6
Z-Value P-Value -0.8485 0.1981
Brand store product. As of 2020, Adidas was the third largest apparel brand in the world, and it was also one of the most valuable athletic apparel, accessories, and footwear companies globally. The
Work from home during COVID-19. The McKinsey Global Business Executive Survey conducted in July 2020 included 800 respondents from the United States, Australia, Canada, China, France, Germany, India,
The Pepsi Challenge. “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
Which element of a test of hypothesis is used to decide whcther to reject the null hypothesis in Savor of the alternative hypothesis?
What is the difference between Type I and Type TI errors in hypothesis testing? How do a and /3 relate to Type I and Type I1 errors?65 List the four possible results of the combinations of decisions
We (generally) reject the null hypothesis when the test statistic falls in the rejection region, but we do not accept the null hypothesis when the test statistic does not fall in the rejection
If you test a hypothesis and reject the null hypothesis in favor of the alternative hypothesis, does your test prove that the alternative hypothesis is correct? Explain.Applying the Concepts
The interest rate at which London banks lend money to one another is called the London interbank offered mte, or Libor. According to The Wall Street Journal (Nov. 11, 1998). the British Bankers
The national student loan default rate has dropped steadily over the last decade. USF Magazine (Spring 1999) reported the default rate (i.e., the proportion of college students who default on their
According to the Journal of Psychology and Aging(May 1992), older workers (i.e., workers 45 years old or older) have a mean job satisfaction rating of 4.3 on a 5-point scale. (Higher scores indicate
Sometimes, the outcome of a jury trial defies the "commonsense" expectations of the general public (e.g., the 0. J. Simpson verdict in the "Trial of the Century"). Such a verdict is more acceptable
A group of physicians subjected the polygraph (or lie detector) to the same careful testing given to medical diagnostic tests. They found that if 1,000 people were subjected to the polygraph and 500
According to Chemical Marketing Reporter (Feb. 20, 1995), pharmaceutical companies spend $15 billion per year on research and development of new drugs. The pharmaceutical company must subject each
For each of the following rejection regions, sketch the sampling distribution for z and ind~cate the location of the rejection region.a. z > 1.96b. z > 1.645c. z > 2.575d. z < -1.28e. z < -1.645orz >
A random sample of 100 observations from a population with stardard deviation 60 yielded a sample mean of 110.a. Test the null hypothesis that p = 100 against the alternative hypothesis that p > 100
A random sample of 64 observations produced the following summary statistics: i = .323 and s2 = .034.a. Test the null hypothesis that p = .36 against the alternative hypothesis that p < .36 using a =
During the National Football League (NFL) season, Las Vegas oddsmakers establish a point spread on each game for betting purposes. For example, the St. Louis Rams were established as 7-point
According to the National Funeral Directors Association, the nation's 22,000 funeral homes collected an average $5,020 per full-service funeral in 1998, up from $4,780 in 1996 (Wall Street Journal
Most major corporations have psychologists available to help employees who suffer from stress. One problem that is difficult to diagnose is post-traumatic stress disorder (PTSD). Researchers studying
A study reported in the Journal of Occupational and Organizational Psychology (Dec. 1992) investigated the relationship of employment status to mental health. A sample of 49 unemployed men was given
In quality control applications of hypothesis testing, the null and alternative hypotheses are frequently specified as H,: The production process is performing satisfactorily Accordingly, a is
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
A company has devised a new ink-jet cartridge for its plain-paper fax machine that it believes has a longer lifetime (on average) than the one currently being produced. To investigate its length of
Nutritionists stress that weight control generally requires significant reduct~ons in the intake of fat. A random sample of 64 middle-aged men on weight control programs is selected to determine
It a hypothesis test were conducted using a = .05, for which of the following p-values would the null hypothesis be rejected?a..06 b..10 c..01d. ,001 e..251 f..042
For each a and observed significance level (p-value)pair, indicate whether the null hypothesis would be rejected.a. a = .05, p-value = .lob. a = .lo, p-value = .05c. a = .01, p-value = .001d. a =
An analyst tested the null hypothesis p 2 20 against the alternative hypothesis that p < 20. The analyst reported a p-value of .06. What is the smallest value of a for which the null hypothesis would
In a test of H,: p = 100 against Ha: p > 100, the sample data yielded the test statistic z = 2.17. Find thep-value for the test.
In a test of the hypothesis Ho: p = 10 versus Ha: p Z 10, a sample of n = 50 observations possessed mean i = 10.7 and standard deviation s = 3.1. Find and interpret the p-value for this test.
Consider a test of H,,: p = 75 performed using the computer. SAS reports a two-tailed p-value of .1032. Make the appropriate conclusion for each of the following situations:a. Ha: p < 75, z = -1.63,
According to USA Today (Dec. 30,1999), the average age of viewers of MSNBC cable television news programming is 50 years. A random sample of 50 U. S.households that receive cable television
Refer to the Wall Street JournaliNational Funeral Directors Association study of the average-fee charged for a full-service funeral during 1999, Exercise 6.20(p. 311). Recall that a test was
In Exercise 5.8(p. 266) we examined research about bicycle helmets reported in Public Health Reports(May-June 1992). One of the variables measured was the children's perception of the risk involved
An article published in the Journal of the American MedicalAssociation (Oct. 16,1995) calls smoking in China"a public health emergency." The researchers found that smokers in China smoke an average
In Exercise 6.23(p. 311) you tested H,: p = ,250 versus Ha: p f .250, where p is the population mean weight of plastic golf tees. A SAS printout for the hypothesis test is shown below. Locate the
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 = 6b. t < -1.782 where df =
For each of the rejection regions defined in Exercise 6.41, what is the probability that a Type I error will be made?
A random sample of n observations is selected from a normal population to test the null hypotheyis that p = 10. Specify the rejection region for each of the following combinations of H,,,a, and n:a.
A sample of five measurements, randomly selected from a normally distributed population, resulted in the following summary statistics: i = 4.8, s = 1.3.a. Test the null hypothesis that the mean of
MINITAB is used to conduct a t-test for the null hypothesis H,,: p = 1,000 versus the alternative hypothesis Ha: p > 1,000 based on a sample of 17 observations. The software's output is shown
Information Resources Inc., a Chicago-based research organization, tracks supermarket sales in 28 metropolitan markets in the United States. They convert their data for specific products to an index
A study was conducted to evaluate the effectiveness of a new mosquito repellent designed by the U.S. Army to be apphed a? camouflage face paint (Journal of [he Mosquzto Control Awoc~nt~on, June
The Cleveland Casting Plant is a large, highly automated producer of gray and nodular iron automotive castings for Ford Motor Company (Quality Engineering, Vol. 7, 1995). One process variable of
By law, the levels of toxic organic compounds in fish are constantly monitored. A technique, called matrix solid-phase dispersion (MSPD), has been developed for chemically extracting trace organic
The Occupational Safety and Health Act (OSHA)allows issuance of engineering standards to ensure safe workplaces for all Americans. The maximum allowable mean level of arsenic in smelters, herbicide
Suppose a random sample of 100 observations from a binomial population gives a value of a = .63 and you wish to test the null hypothesis that the popillation parameter p is equal to .70 against the
Refer to Exercise 5.26(p. 285), in which 50 consumer\taste tested a new snack food. Their responses (where 0 = do not like; 1 = like; 2 = indifferent) are reproduced below.a. Test H,: p = .5 against
A statistics student used a computer program to test the null hypothesis H,: p = .5 against the one-tailed alternative, Ha: p > .5. A sample of 500 observations are input into SPSS, which returns the
Pond's Age-Defying Complex, a cream with alphahydroxy acid, advertises that it can reduce wrinkles and improve the skin. In a study published in Archives of Dermatology (June 1996), 33 women over age
Shoplifting in the U. S. costs retailers about $15 billion a year. Those losses translate into higher prices for consumers. Despite the seriousness of the problem, Shoplifters Alternative of Jericho,
Refer to the Nature (Aug. 27, 1998) study of facial characteristics that are deemed attractive, Exercise 6.35(p. 318). In another experiment, 67 human subjects viewed side-by-side an image of a
Creative Good, a New York consulting firm, claimed that 39% of shoppers fail in their attempts to purchase merchandise on-line because Web sites are too complex. They estimated that this would
In 1895, 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
Consumer Reports (Sept. 1992) evaluated and rated 46 brands of toothpaste. One attribute examined in the study was whether or not a toothpaste brand carries an American Dental Association (ADA) seal
Use Table I1 of Appendix B to calculate the following binomial probabilities:a. P(x 2 7) when n = 8 and p = .5b. P(x 2 5) when n = 8 and p = .5c. P(x 2 8) when n = 8 and p = .5d. P(x 2 10) when n =
Consider the following sample of 10 measurements:Use these data to conduct each of the following sign tests using the binomial tables (Tablc 11, Appendix B)and a = .05:a. H,,: 7 = 9 versus Ha: 7 >
One way to assess the benefits of an MBA degree is to investigate the salaries received by MBA students several years after graduation. In 1998, the Graduate Management Admission Council estimated
The biting rate of a particular species of fly was investigated in a study reported in the Journal of the American Mosquito Control Association (Mar. 1995). Biting rate was defined as the number of
Reducing the size of a company's workforce in order to reduce costs is referred to as corporate downsizing or reductions in force (RIF) by the business community and media (Business Week, Feb. 24,
The Federal Aviation Administration (FAA) increased the frequency and thoroughness of its review of aircraft maintenance procedures in response to the admission by ValuJet Airlines that it had not
In Exercise 5.18(p. 276), the average 5-year revenue growth for the 500 fastest growing technology companies in 1999 (i.e., Forbes' Technology Fast 500) was investigated. The data are reproduced in
The trade publication Potentials in Marketing(Nov./Dec. 1995) surveyed its readers concerning their opinions of electronic marketing (i.e., marketing via the Internet, e-mail, CD-ROMs, etc.). A
The Lincoln Tunnel (under the Hudson River) connects suburban New Jersey to midtown Manhattan.On Mondays at 8:30 A.M., the mean number of cars waiting in line to pay the Lincoln Tunnel toll is
In order to be effective, the mean length of life of a certain mechanical component used in a spacecraft must be larger than 1,100 hours. Owing to the prohibitive cost of this component, only three
In Exercise 6.25(p. 312) you tested H,: p 2 10 versus Ha: p < 10, where p is the average number of solder joints inspected per second when the joints are spaced.1 inch apart. An SPSS printout of the
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 250 manufacturers conducted by
A consumer protection group is concerned that a ketchup manufacturer is filling its 20-ounce family-size containers with less than 20 ounces of ketchup. The group purchases 10 family-size bottles of
One way of evaluating a measuring instrument is to repeatedly measure the same item and compare the average of these measurements to the item's known measured value. The difference is used to assess
According to the National Restaurant Association, hamburgers are the number one selling fast-food item in the United States (Newark Star-Ledger, Mar. 17, 1997). An economist studying the fast-food
One study (Journal of Political Economy, Feb. 1988)of gambling newsletters that purport to improve a bettor's odds of winning bets on NFL football games indicates that the newsletters' betting
The "beta coefficient" of a stock is a measure of the stock's volatility (or risk) relative to the market as a whole. Stocks with beta coefficients greater than 1 generally bear greater risk (more
The manufacturer of an over-the-counter analgesic claims that its product brings pain relief to headache sufferers in less than 3.5 minutes, on average. In order to be able to make this claim in its
The probability distribution shown here describes a population of measurements that can assume values of 0, 2, 4, and 6, each of which occurs with the same relative frequency: x 0 2 4 6 p1x2 1 4 1 4
Simulate sampling from the population described in Exercise
by marking the values of x, one on each of four identical coins (or poker chips, etc.). Place the coins (marked 0, 2, 4, and 6) into a bag, randomly select one, and observe its value. Replace this
Consider the population described by the probability distribution shown below. x 1 2 3 4 5 p1x2 .2 .3 .2 .2 .1 The random variable x is observed twice. If these observations are independent, verify
or larger?d. Would you expect to observe a value of x equal to
or larger? Explain.
and find E1x2 = m. Then use the sampling distribution of x found in Exercise
to find the expected value of x. Note that E1x2 = m.
Refer to Exercise 5.3. Assume that a random sample of n = 2 measurements is randomly selected from the population.a. List the different values that the sample median m may assume and find the
In Example
we used a computer to generate 1,000 samples, each containing n = 11 observations, from a uniform distribution over the interval from 150 to 200. For this exercise, use a computer to generate 500
Consider the following probability distribution: x 0 1 4 p1x2 1 3 1 3 1 3a. Find m and s2 .b. Find the sampling distribution of the sample mean x for a random sample of n = 2 measurements from this
Consider the following probability distribution: x 2 4 9 p1x2 1 3 1 3 1 3a. Calculate m for this distribution.b. Find the sampling distribution of the sample mean x for a random sample of n = 3
Consider the following probability distribution: x 0 1 2 p1x2 1 3 1 3 1 3a. Find m.b. For a random sample of n = 3 observations from this distribution, find the sampling distribution of the sample

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