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Statistics Plus New Mylab Statistics With Pearson Etext Access Card Package 13th Edition James Mcclave ,Terry Sincich - Solutions
USGA golf ball tests. The United States Golf Association(USGA) tests all new brands of golf balls to ensure that they meet USGA specifications. One test conducted is intended to measure the average distance traveled when the ball is hit by a machine called “Iron Byron.” Suppose the USGA wishes
Studies on treating Alzheimer’s disease. Alzheimer’s disease is a progressive disease of the brain. The journal eCAM (Nov. 2006) published an article that critiqued the quality of the methodology used in studies on Alzheimer’s treatment. For each in a sample of 13 studies, the quality of the
Asthma drug study. The chemical benzalkonium chloride(BAC) is an antibacterial agent that is added to some asthma medications to prevent contamination. However, adding BAC to asthma drugs can cause airway constriction in patients. In a sample of 18 asthmatic patients, each of whom received a heavy
Training zoo animals. Refer to Exercise 2.193(p. 136) and the Teaching of Psychology (May 1998) study in which students assisted in the training of zoo animals. A sample of 15 psychology students rated “The Training Game” as a “great”method of understanding the animal’s perspective during
Salmonella in ice cream bars. 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 refused to purchase any brand of ice cream bars for some time after the
Salmonella in ice cream bars (cont’d). Refer to Exercise 7.145. Suppose it is now 1 year after the poisoning was traced to ice cream bars. The manufacturer wishes to estimate the proportion who still will not purchase bars to within .04, using a 90% confidence interval. How many consumers should
Latex allergy in health care workers. Refer to the Current Allergy & Clinical Immunology (Mar. 2004) study of health care workers who use latex gloves, presented in Exercise 7.15(p. 352). In addition to the 46 hospital employees who were diagnosed with a latex allergy on the basis of a skin-prick
Jitter in a water power system. Jitter is a term used to describe the variation in conduction time of a water power system. Low throughput jitter is critical to successful waterline technology. An investigation of throughput jitter in the opening switch of a prototype system (Journal of Applied
IMA salary survey. Each year, Management Accounting reports the results of a salary survey of the members of the Institute of Management Accountants (IMA). One year, the 2,112 members responding had a salary distribution with a 20th percentile of $35,100, a median of $50,000, and an 80th percentile
Air bags pose danger for children. By law, all new cars must be equipped with both driver-side and passengerside safety air bags. There is concern, however, over whether air bags pose a danger for children sitting on the passenger side. In a National Highway Traffic Safety Administration (NHTSA)
Scallops, sampling, and the law. Interfaces (Mar.–Apr.1995) discussed the case of a ship that fishes for scallops off the coast of New England. In order to protect baby scallops from being harvested, the U.S. Fisheries and Wildlife Service requires that “the average meat per scallop weigh at
A sampling dispute goes to court. Sampling of Medicare and Medicaid claims by the federal and state agencies who administer those programs has become common practice to determine whether providers of those services are submitting valid claims. (See the Statistics in Action for this chapter.)The
What is a sampling distribution of a sample statistic?
Simulate sampling from the population described in Exercise 6.3 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 coin, draw a second coin, and observe
Consider the population described by the probability distribution shown below. The random variable x is observed twice with independent observations.a. Complete the sampling distribution table. Type the values of x in ascending order.b. Construct a probability histogram for the sampling
Refer to Exercise 6.5 and find E1x2 = m. Then use the sampling distribution of x found in Exercise 6.5 to find the expected value of x. Note that E1x2 = m.
Consider a population that contains values of x equal to 00, 01, 02, 03,c, 96, 97, 98, 99. Assume that these values occur with equal probability. Use the computer to generate 500 samples, each containing n = 20 measurements, from this population. Calculate the sample mean x and sample variance s2
What are the properties of an ideal estimator?
Consider the following probability distribution: X p(x) 0 1 1/3 4 1/3
Consider the following probability distribution:a. Calculate m for this distribution.b. Find the sampling distribution of the sample mean x for a random sample of n = 3 measurements from this distribution, and show that x is an unbiased estimator of m.c. Find the sampling distribution of the sample
Use the computer to generate 750 samples, each containing n = 20 measurements, from a population that contains values of x equal to 1, 2, …, 48, 49, 50. Assume that these values of x are equally likely. Calculate the sample mean x and median M for each sample. Construct relative frequency
Refer to Exercise 6.5.a. Show that x is an unbiased estimator of m.b. Find s 2x.c. Find the probability that the x will fall within 2sxm
Refer to Exercise 6.5.a. Find the sampling distribution of s2.b. Find the population variance s2.c. Show that s2 is an unbiased estimator of s2.d. Find the sampling distribution of the sample standard deviation s.e. Show that s is a biased estimator of s.
Refer to Exercise 6.7, in which we found the sampling distribution of the sample median. Is the median an unbiased estimator of the population mean m?
What do the symbols mx and sx represent?
Another name given to the standard deviation of x is the ____________. (Fill in the blank.)
Suppose a random sample of n measurements is selected from a population with mean m = 225 and variance s2= 225. For each of the following values of n, give the mean and standard deviation of the sampling distribution of the sample mean x. a. n = 9 c. n = 225 e. n = 1,000 b. n = 49 d. n = 500 f. n =
Suppose a random sample of n = 16 measurements is selected from a population with mean m and standard deviation s. For each of the following values of m and s, give the values of mx and sx. 2. == = 12, = 3 b. p 144, = 16 . = 24, 24, = 28 d. = 12, = 96
Consider the following probability distribution: x 3 4 6 9 .3 .1 .5 .1 p(x) a. Find , o, and . b. Find the sampling distribution of x for random samples of n = 2 measurements from this distribution by listing all possible values of x, and find the probability associ- ated with each. c. Use the
A random sample of n = 64 observations is drawn from a population with a mean equal to 20 and standard deviation equal to 16.a. Give the mean and standard deviation of the (repeated)sampling distribution of x.b. Describe the shape of the sampling distribution of x.Does your answer depend on the
A random sample of n = 100 observations is selected from a population with m = 31 and s = 25.a. Find mx and sx.b. Describe the shape of the sampling distribution of x.c. Find P1x Ú 282. d. Find P(22.1 x 26.8). e. Find P(X 28.2). f. Find P(x27.0).
A random sample of n = 2,500 observations is selected from a population with m = 500 and s = 150.a. What are the largest and smallest values of x that you would expect to see?b. How far, at the most, would you expect x to deviate from m?c. Did you have to know m to answer part b? Explain.
Consider a population that contains values of x equal to 0, 1, 2,c, 97, 98, 99. Assume that the values of x are equally likely. For each of the following values of n, use the computer to generate 500 random samples and calculate x for each sample. For each sample size, construct a relative
Corporate sustainability of CPA firms. Refer to the Business and Society (Mar. 2011) study on the sustainability behaviors of CPA corporations, Exercise 1.26(p. 50).Recall that corporate sustainability refers to business practices designed around social and environmental considerations.The level of
Voltage sags and swells. Refer to the Electrical Engineering(Vol. 95, 2013) study of the power quality (sags and swells)of a transformer, Exercise 2.127(p. 110). For transformers built for heavy industry, the distribution of the number of sags per week has a mean of 353 with a standard deviation of
Phishing attacks to e-mail accounts. In Exercise 2.47(p. 81), you learned that phishing describes an attempt to extract personal/financial information from unsuspecting people through fraudulent e-mail. Data from an actual phishing attack against an organization were presented in Chance (Summer
Physical activity of obese young adults. In a study on the physical activity of young adults, pediatric researchers measured overall physical activity as the total number of registered movements (counts) over a period of time and then computed the number of counts per minute (cpm) for each subject
Cost of unleaded fuel. According to the American Automobile Association (AAA), the average cost of a gallon of regular unleaded fuel at gas stations in May 2014 was $3.65 (AAA Fuel Gauge Report). Assume that the standard deviation of such costs is $.15. Suppose that a random sample of n = 100 gas
Requests to a Web server. In Exercise 5.10(p. 266) you learned that Brighton Webs LTD modeled the arrival time of requests to a Web server within each hour using a uniform distribution. Specifically, the number of seconds x from the start of the hour that the request is made is uniformly
Shell lengths of sea turtles. Refer to the Aquatic Biology(Vol. 9, 2010) study of green sea turtles inhabiting the Grand Cayman South Sound lagoon, Exercise 2.85(p. 97). Research shows that the curved carapace (shell) lengths of these turtles has a distribution with mean m = 50 cm and standard
Tomato as a taste modifier. Miraculin is a protein naturally produced in a rare tropical fruit that can convert a sour taste into a sweet taste. Refer to the Plant Science(May 2010) investigation of the ability of a hybrid tomato plant to produce miraculin, Exercise 5.38(p. 279).Recall that the
Uranium in the Earth’s crust. Refer to the American Mineralogist (Oct. 2009) study of the evolution of uranium minerals in the Earth’s crust, Exercise 5.9(p. 266). Recall that researchers estimate that the trace amount of uranium x in reservoirs follows a uniform distribution ranging between 1
Critical part failures in NASCAR vehicles. Refer to The Sport Journal (Winter 2007) analysis of critical part failures at NASCAR races, Exercise 5.106(p. 299). Recall that researchers found that the time x (in hours) until the first critical part failure is exponentially distributed with m = .10
Motivation of drug dealers. Refer to the Applied Psychology in Criminal Justice (Sept. 2009) investigation of the personality characteristics of drug dealers, Exercise 2.102(p. 105). Convicted drug dealers were scored on the Wanting Recognition (WR) Scale—a scale that provides a quantitative
Is exposure to a chemical in Teflon-coated cookware hazardous?Perfluorooctanoic acid (PFOA) is a chemical used in Teflon®-coated cookware to prevent food from sticking.The Environmental Protection Agency is investigating the potential risk of PFOA as a cancer-causing agent(Science News Online,
Characteristics of antiwar demonstrators. Refer to the American Journal of Sociology (Jan. 2014) study of the characteristics of antiwar demonstrators in the United States, Exercise 2.106(p. 105). The researchers found that the mean number of protest organizations joined by antiwar demonstrators
Hand washing versus hand rubbing. Refer to the British Medical Journal (Aug. 17, 2002) study comparing the effectiveness of hand washing with soap and hand rubbing with alcohol, presented in Exercise 2.107(p. 106). Health care workers who used hand rubbing had a mean bacterial count of 35 per hand
Video game players and divided attention tasks. Human Factors (May 2014) published the results of a study designed to determine whether video game players are better than non-video game players at crossing the street when presented with distractions. Participants (college students)entered a street
Consider a sampling distribution with p = .14. and samples of size n each. For each value of n, give the mean and standard deviation of the sampling distribution of the sample proportion, pn.a. For a random sample of size n = 4,000.b. For a random sample of size n = 1,000.c. For a random sample of
Suppose a random sample of n = 591 measurements is selected from a binomial population with probability of success p. For each of the given values of p, give the mean and standard deviation of the sampling distribution of the sample proportion, pn.a. p = .2b. p = .5c. p = .8
A random sample of n = 70 measurements is drawn from a binomial population with probability of success .3.a. Give the mean and standard deviation of the sampling distribution of the sample proportion, pn.b. Describe the shape of the sampling distribution of pn.c. Calculate the standard normal
A random sample of n = 2,000 measurements is drawn from a binomial population with probability of success .25.What are the smallest and largest values of pn you would expect to see?
Consider a population with values of x equal to 0 or 1.Assume that the values of x are equally likely. For each of the following values of n, use a computer to generate 750 random samples and calculate the sample proportion of 1s observed for each sample. Then construct a histogram of the 750
Do social robots walk or roll? Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 2.7(p. 66).The researchers obtained a random sample of 106 social robots through a Web search and determined the number that were
Paying for music downloads. According to a recent Pew Internet & American Life Project Survey (Oct. 2010), 67%of adults who use the Internet have paid to download music. In a random sample of n = 1,000 adults who use the Internet, let pn represent the proportion who have paid to download music.a.
Working on summer vacation. According to an Adweek/Harris (July 2011) poll of U.S. adults, 35% do not work during their summer vacation. Assume that the true proportion of all U.S. adults that do not work during summer vacation is p = .35. Now consider a random sample of 500 U.S. adults.a. What is
Superstitions survey. A Harris (Feb. 2013) poll found that one-third of Americans (33%) believe finding and picking up a penny is good luck. Assume that the true proportion of all Americans who believe finding and picking up a penny is good luck is p = .33. In a random sample of 1,000 Americans,
Crop damage by wild boars. Refer to the Current Zoology(Apr. 2014) study of crop damage incurred by wild boars in southern Italy, Exercise 3.18(p. 158). If crop damage by wild boars occurs, the probability that the type of crop damaged is cereals is .45, legumes .20, and orchards .05. In a random
Downloading “apps” to your cell phone. Refer to Exercise 4.27(p. 221). The study found that 40% of adult cell phone owners have downloaded an application(“app”) to their cell phone. Assume this percentage applies to the population of all adult cell phone owners.a. In a random sample of 50
Hotel guest satisfaction. Refer to the results of the North American Hotel Guest Satisfaction Index Study referenced in Exercise 4.75(p. 241). Recall that 66% of hotel guests were aware of the hotel’s “green” conservation program; of these guests, 72% actually participated in the program by
Fingerprint expertise. Refer to the Psychological Science(Aug. 2011) study of fingerprint identification, Exercise 4.74(p. 240). Recall that when presented with prints from the same individual, a fingerprint expert will correctly identify the match 92% of the time. Consider a forensic database of
True or False. The sample mean, x, will always be equal to mx.
True or False. The sampling distribution of x is normally distributed, regardless of the size of the sample n.
True or False. The standard error of x will always be smaller than s.
True or False. The sampling distribution of pn is normally distributed for large n
A random sample of 50 observations is to be drawn from a large population of measurements. It is known that 40%of the measurements in the population are 1’s, 20% are 2’s, 30% are 3’s, and 10% are 4’s.a. Give the mean and standard deviation of the (repeated)sampling distribution of x, the
A random sample of n = 64 observations is selected from a population with m = 22.5 and s = 2.8. Approximate each of the following probabilities:a. P1x … 22.52b. P1x … 222c. P1x Ú 23.52d. P121.9 … x … 22.82
A random sample of n = 750 observations is selected from a binomial population with p = .45.a. Give the mean and standard deviation of the (repeated)sampling distribution of pn, the sample proportion of successes for the 750 observations.b. Describe the shape of the sampling distribution of pn.Does
A random sample of n = 300 observations is selected from a binomial population with p = .8. Approximate each of the following probabilities:a. P1pn 6 .662b. P1pn 7 .552c. P1.58 6 pn 6 .622
Use a statistical software package to generate 150 random samples of size n = 5 from a population characterized by a normal probability distribution with a mean of 75 and a standard deviation of 8. Compute x for each sample, and plot a frequency distribution for the 150 values of x.Repeat this
Use a statistical software package to generate 150 random samples of size n = 5 from a population characterized by a uniform probability distribution with c = 5 and d = 20. Compute x for each sample, and plot a frequency distribution for the 150 x values. Repeat this process for n = 10, 25, 50, and
Suppose x equals the number of heads observed when a single coin is tossed; that is, x = 0 or x = 1. The population corresponding to x is the set of 0’s and 1’s generated when the coin is tossed repeatedly a large number of times.Suppose we select n = 4 observations from this population.(That
A random sample of size n is to be drawn from a large population with mean 150 and standard deviation 20, and the sample mean x is to be calculated. To see the effect of different sample sizes on the standard deviation of the sampling distribution of x, plot s>2n against n for n = 1, 2, 5, 10, 25,
Salaries of travel managers. According to a 2012 Business Travel News survey, the average salary of a travel manager is $110,550. Assume that the standard deviation of such salaries is $25,000. Consider a random sample of 40 travel managers, and let x represent the mean salary for the sample.a.
Children’s attitudes toward reading. In the journal Knowledge Quest (Jan./Feb. 2002), education professors investigated children’s attitudes toward reading. One study measured third through sixth graders’ attitudes toward recreational reading on a 140-point scale (where higher scores indicate
Dentists’ use of laughing gas. According to the American Dental Association, 60% of all dentists use nitrous oxide in their practice. In a random sample of 100 dentists, let pn represent the proportion who use laughing gas in their practice.a. Find E1pn 2.b. Find spn .c. Describe the shape of the
Marital name changing. Refer to the Advances in Applied Sociology (Nov. 2013) study of marital name changing, Exercise 4.78(p. 241). According to the study, the probability that an American female will change her last name upon marriage is .9. Consider a sample of 250 American females. Let pn
Violence and stress. Interpersonal violence (e.g., rape)generally leads to psychological stress for the victim.Clinical Psychology Review (Vol. 15, 1995) reported on the results of all recently published studies of the relationship between interpersonal violence and psychological stress.The
Research on eating disorders. Refer to The American Statistician (May 2001) study of female students who suffer from bulimia, presented in Exercise 2.44(p. 80). Recall that each student completed a questionnaire from which a“fear of negative evaluation” (FNE) score was produced.(The higher the
Producing machine bearings. To determine whether a metal lathe that produces machine bearings is properly adjusted, a random sample of 36 bearings is collected and the diameter of each is measured.a. If the standard deviation of the diameters of the bearings measured over a long period of time is
Quality control. Refer to Exercise 6.84. The mean diameter of the bearings produced by the machine is supposed to be .5 inch. The company decides to use the sample mean to decide whether the process is in control(i.e., whether it is producing bearings with a mean diameter of .5 inch). The machine
Errors in filling prescriptions A large number of preventable errors (e.g., overdoses, botched operations, misdiagnoses) are being made by doctors and nurses in U.S. hospitals. A study of a major metropolitan hospital revealed that of every 100 medications prescribed or dispensed, 1 was in error,
Susceptibility to hypnosis. The Computer-Assisted Hypnosis Scale (CAHS) is designed to measure a person’s susceptibility to hypnosis. CAHS scores range from 0 (no susceptibility) to 12 (extremely high susceptibility).A study in Psychological Assessment (Mar. 1995) reported a mean CAHS score of
Supercooling temperature of frogs. Many species of terrestrial tree frogs can survive prolonged exposure to low winter temperatures during hibernation. In freezing conditions, the frog’s body temperature is called its supercooling temperature. A study in Science revealed that the supercooling
Levelness of concrete slabs. Geotechnical engineers use water-level “manometer” surveys to assess the levelness of newly constructed concrete slabs. Elevations are typically measured at eight points on the slab; of interest is the maximum differential between elevations. The Journal of
Machine repair time. [Note: This exercise refers to an optional section in Chapter 5.] An article in Industrial Engineering (Aug. 1990) discussed the importance of modeling machine downtime correctly in simulation studies. As an illustration, the researcher considered a single- machine-tool system
Flaws in aluminum siding. [Note: This exercise refers to an optional section in Chapter 4.] A building contractor has decided to purchase a load of factory-reject aluminum siding as long as the average number of flaws per piece of siding in a sample of size 45 from the factory’s reject pile is
Soft-drink bottles. A soft-drink bottler purchases glass bottles from a vendor. The bottles are required to have an internal pressure of at least 150 pounds per square inch(psi). A prospective bottle vendor claims that its production process yields bottles with a mean internal pressure of 155 psi
Fecal pollution at Huntington Beach. The state of California mandates fecal indicator bacteria monitoring at all public beaches. When the concentration of fecal bacteria in the water exceeds a certain limit (400 colony- forming units of fecal coliform per 100 milliliters), local health officials
True or False: The probability that the uniform random variable will assume a value in any interval of equal length is different for each interval.
The uniform distribution is a __________ distribution. (Fill in the blank.)
Suppose x is a random variable best described by a uniform probability distribution with c = 20 and d = 40.a. Find f(x).b. Find the mean and standard deviation of x.c. Graph f(x), and locate m and the interval m { 2s on the graph. Note that the probability that x assumes a value within the interval
Refer to Exercise 5.3. Find the following probabilities: a. P(15 x 30) c. P(x = 30) e. P(x 30) b. P(25 < x < 35) d. P(x = 20) f. P(25.5 x 30.5)
Suppose x is a random variable best described by a uniform probability distribution with c = 4 and d = 6. a. Find f(x). b. Find the mean and standard deviation of x. x p + ). c. Find P( d. Find P(x > 4.78). e. Find P(4.4 x 5.7). f. Find P(x < 4).
Refer to Exercise 5.5. Find the value of a makes each of the following probability statements true: 52 a. P(x = a) P(xa) = .5 b. P(x = a) = .2
The random variable x is best described by a uniform probability distribution with c = 100 and d = 200. Find the probability that x assumes a valuea. More than two standard deviations from mb. Less than three standard deviations from mc. Within two standard deviations of m
The random variable x is best described by a uniform probability distribution with mean 100 and standard deviation 10. Findc, d, and f(x). Graph the probability distribution.
Uranium in the Earth’s crust. The American Mineralogist(Oct. 2009) published a study of the evolution of uranium minerals in the Earth’s crust. Researchers estimate that the trace amount of uranium x in reservoirs follows a uniform distribution ranging between 1 and 3 parts per million.a. Find
Requests to a Web server. According to Brighton Webs LTD, a British company that specializes in data analysis, the arrival time of requests to a Web server within each hour can be modeled by a uniform distribution (http://www.brighton-webs.co.uk). Specifically, the number of seconds x from the
New method for detecting anthrax. Researchers at the University of South Florida Center for Biological Defense have developed a safe method for rapidly detecting anthrax spores in powders and on surfaces (USF Magazine, Summer 2002). Consider a powder specimen that has exactly 10 anthrax spores.
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