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Statistics The Exploration & Analysis Of Data 7th Edition Roxy Peck, Jay L. Devore - Solutions

A pizza shop sells pizzas in four different sizes. The 1000 most recent orders for a single pizza gave the following proportions for the various sizes:With x denoting the size of a pizza in a single-pizza order, the given table is an approximation to the population distribution of x.a. Construct a
Airlines sometimes overbook flights. Suppose that for a plane with 100 seats, an airline takes 110 reservations. Define the variable x as the number of people who actually show up for a sold-out flight. From past experience, the population distribution of x is given in the following table:a. What
Homicide rate (homicides per 100,000 population) for each of the 50 states appeared in the 2010 Statistical Abstract (www.census.gov). A frequency distribution constructed from the 50 observations is shown in the following table: a. Calculate the relative frequency and density for
A company receives lightbulbs from two different suppliers. Define the variables x and y by x = lifetime of a bulb from Supplier 1 y = lifetime of a bulb from Supplier 2 Five hundred bulbs from each supplier are tested, and the lifetime of each bulb (in hours) is recorded. The density histograms in
A random sample is selected from a population with mean m = 100 and standard deviation s = 10. Determine the mean and standard deviation of the x sampling distribution for each of the following sample sizes: a. n 5 9 d. n 5 50 b. n 5 15 e. n 5 100 c. n 5 36 f. n 5 400
Explain the difference between σ and σx and between m and µ x.
Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5. a. What are the mean and standard deviation of the x sampling distribution? Describe the shape of the x sampling distribution. b. What is the approximate probability that x will be
The time that a randomly selected individual waits for an elevator in an office building has a uniform distribution over the interval from 0 to 1 minute. For this distribution m 5 0.5 and s 5 0.289.a. Let x be the sample mean waiting time for a random sample of 16 individuals. What are the mean and
Let x denote the time (in minutes) that it takes a fifth-grade student to read a certain passage. Suppose that the mean value and standard deviation of x are µ = 2 minutes and s = 0.8 minute, respectively. a. If x is the sample mean time for a random sample of n = 9 students, where is the x
In the library on a university campus, there is a sign in the elevator that indicates a limit of 16 persons. In addition, there is a weight limit of 2500 pounds. Assume that the average weight of students, faculty, and staff on campus is 150 pounds, that the standard deviation is 27 pounds, and
Suppose that the mean value of interpupillary distance (the distance between the pupils of the left and right eyes) for adult males is 65 mm and that the population standard deviation is 5 mm. a. If the distribution of interpupillary distance is normal and a random sample of n = 25 adult males is
Suppose that a sample of size 100 is to be drawn from a population with standard deviation 10. a. What is the probability that the sample mean will be within 1 of the value of µ? b. For this example (n = 100, σ = 10), complete each of the following statements by computing the appropriate value:
A manufacturing process is designed to produce bolts with a 0.5-inch diameter. Once each day, a random sample of 36 bolts is selected and the bolt diameters are recorded. If the resulting sample mean is less than 0.49 inches or greater than 0.51 inches, the process is shut down for adjustment. The
What is the difference between and µ? between s and σ?
College students with checking accounts typically write relatively few checks in any given month, whereas nonstudent residents typically write many more checks during a month. Suppose that 50% of a bank’s accounts are held by students and that 50% are held by nonstudent residents. Let x denote
An airplane with room for 100 passengers has a total baggage limit of 6000 pounds. Suppose that the total weight of the baggage checked by an individual passenger is a random variable x with a mean value of 50 pounds and a standard deviation of 20 pounds. If 100 passengers will board a flight, what
The thickness (in millimeters) of the coating applied to disk drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness (x) has a normal distribution with a mean of 2 mm and a standard deviation
A random sample is to be selected from a population that has a proportion of successes p = .65. Determine the mean and standard deviation of the sampling distribution of p^ for each of the following sample sizes: a. n 5 10 d. n 5 50 b. n 5 20 e. n 5 100 c. n 5 30 f. n 5 200
For which of the sample sizes given in Exercise 8.23 would the sampling distribution of p^ be approximately normal if p = .65? if p = .2?
The article “Unmarried Couples More Likely to Be Interracial” (San Luis Obispo Tribune, March 13, 2002) reported that 7% of married couples in the United States are mixed racially or ethnically. Consider the population consisting of all married couples in the United States.a. A random sample of
The article referenced in Exercise 8.25 reported that for unmarried couples living together, the proportion that are racially or ethnically mixed is .15. Answer the questions posed in Parts (a)– (e) of Exercise 8.25 for the population of unmarried couples living together. In Exercise 8.25 a. A
A certain chromosome defect occurs in only 1 in 200 adult Caucasian males. A random sample of n = 100 adult Caucasian males is to be obtained. a. What is the mean value of the sample proportion p^ , and what is the standard deviation of the sample proportion? b. Does p^ have approximately a normal
The article “Should Pregnant Women Move? Linking Risks for Birth Defects with Proximity to Toxic Waste Sites” (Chance [1992]: 40– 45) reported that in a large study carried out in the state of New York, approximately 30% of the study subjects lived within 1 mile of a hazardous waste site. Let
The article “Thrillers” (Newsweek, April 22, 1985) stated, “Surveys tell us that more than half of America’s college graduates are avid readers of mystery novels.” Let p denote the actual proportion of college graduates who are avid readers of mystery novels. Consider a sample proportion
For each of the following statements, identify the number that appears in boldface type as the value of either a population characteristic or a statistic: a. A department store reports that 84% of all customers who use the store’s credit plan pay their bills on time. b. A sample of 100 students
Suppose that a particular candidate for public office is in fact favored by 48% of all registered voters in the district. A polling organization will take a random sample of 500 voters and will use p^, the sample proportion, to estimate p. What is the approximate probability that p^ will be greater
A manufacturer of computer printers purchases plastic ink cartridges from a vendor. When a large shipment is received, a random sample of 200 cartridges is selected, and each cartridge is inspected. If the sample proportion of defective cartridges is more than .02, the entire shipment is returned
The nicotine content in a single cigarette of a particular brand has a distribution with mean 0.8 mg and standard deviation 0.1 mg. If 100 of these cigarettes are analyzed, what is the probability that the resulting sample mean nicotine content will be less than 0.79?
Let x1, x2, . . . , x̅ 100 denote the actual net weights (in pounds) of 100 randomly selected bags of fertilizer. Suppose that the weight of a randomly selected bag has a distribution with mean 50 pounds and variance 1 pound2. Let x̅ be the sample mean
Suppose that 20% of the subscribers of a cable television company watch the shopping channel at least once a week. The cable company is trying to decide whether to replace this channel with a new local station. A survey of 100 subscribers will be undertaken. The cable company has decided to keep
Water permeability of concrete can be measured by letting water flow across the surface and determining the amount lost (in inches per hour). Suppose that the permeability index x for a randomly selected concrete specimen of a particular type is normally distributed with mean value 1000 and
Newsweek (November 23, 1992) reported that 40% of all U.S. employees participate in “self-insurance” health plans (p = .40). a. In a random sample of 100 employees, what is the approximate probability that at least half of those in the sample participate in such a plan? b. Suppose you were told
The amount of money spent by a customer at a discount store has a mean of $100 and a standard deviation of $30. What is the probability that a randomly selected group of 50 shoppers will spend a total of more than $5300?
Suppose that the sampling experiment described in Example 8.1 had used samples of size 10 rather than size 5. If 50 samples of size 10 were selected, the x value for each sample computed, and a density histogram constructed, how do you think this histogram would differ from the density histogram
Consider the following population: {1, 2, 3, 4}. Note that the population mean isa. Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account):
Consider the following population: {2, 3, 3, 4, 4}. The value of m is 3.2, but suppose that this is not known to an investigator, who therefore wants to estimate m from sample data. Three possible statistics for estimating m are Statistic 1: the sample mean, x Statistic 2: the sample median
Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration:Which statistic would you recommend? Explain your choice.
For each of the following choices, explain which would result in a wider large-sample confidence interval for p: a. 90% confidence level or 95% confidence level b. n = 100 or n = 400
The formula used to compute a large-sample confidence interval for p isWhat is the appropriate z critical value for each of the following confidence levels?
The use of the intervalrequires a large sample. For each of the following combinations of n and p^, indicate whether the sample size is large enough for use of this interval to be appropriate. a. n = 50 and p^ = .30 b. n = 50 and p^ = .05 c. n = 15 and p^ = .45 d. n = 100 and p^ = .01 e. n = 100
Discuss how each of the following factors affects the width of the confidence interval for p:a. The confidence levelb. The sample sizec. The value of p̂
The article “Career Expert Provides DOs and DON’Ts for Job Seekers on Social Networking” (CareerBuilder.com, August 19, 2009) included data from a survey of 2667 hiring managers and human resource professionals. The article noted that many employers are using social networks to screen job
The article “Nine Out of Ten Drivers Admit in Survey to Having Done Something Dangerous” (Knight Ridder Newspapers, July 8, 2005) reported the results of a survey of 1100 drivers. Of those surveyed, 990 admitted to careless or aggressive driving during the previous 6 months. Assuming that it is
In a survey on supernatural experiences, 722 of 4013 adult Americans surveyed reported that they had seen or been with a ghost (“What Supernatural Experiences We’ve Had,” USA Today, February 8, 2010). a. What assumption must be made in order for it to be appropriate to use the formula of this
If a hurricane was headed your way, would you evacuate? The headline of a press release issued January 21, 2009 by the survey research company International Communications Research (icrsurvey.com) states, “Thirtyone Percent of People on High-Risk Coast Will Refuse Evacuation Order, Survey of
The study “Digital Footprints” (Pew Internet & American Life Project, www.pewinternet.org, 2007) reported that 47% of Internet users have searched for information about themselves online. The 47% figure was based on a random sample of Internet users. For purposes of this exercise, suppose that
The article “Kids Digital Day: Almost 8 Hours” (USA Today, January 20, 2010) summarized results from a national survey of 2002 Americans age 8 to 18. The sample was selected in a way that was expected to result in a sample representative of Americans in this age group. a. Of those surveyed,
Why is an unbiased statistic generally preferred over a biased statistic for estimating a population characteristic? Does unbiasedness alone guarantee that the estimate will be close to the true value? Explain. Under what circumstances might you choose a biased statistic over an unbiased statistic
The article “Students Increasingly Turn to Credit Cards” (San Luis Obispo Tribune, July 21, 2006) reported that 37% of college freshmen and 48% of college seniors carry a credit card balance from month to month. Suppose that the reported percentages were based on random samples of 1000 college
The article “CSI Effect Has Juries Wanting More Evidence” (USA Today, August 5, 2004) examines how the popularity of crime-scene investigation television shows is influencing jurors’ expectations of what evidence should be produced at a trial. In a survey of 500 potential jurors, one study
In a survey of 1000 randomly selected adults in the United States, participants were asked what their most favorite and what their least favorite subject was when they were in school (Associated Press, August 17, 2005). In what might seem like a contradiction, math was chosen more often than any
The report “2005 Electronic Monitoring & Surveillance Survey: Many Companies Monitoring, Recording, Videotaping—and Firing—Employees” (American Management Association, 2005) summarized the results of a survey of 526 U.S. businesses. The report stated that 137 of the 526 businesses had fired
In an AP-AOL sports poll (Associated Press, December 18, 2005), 394 of 1000 randomly selected U.S. adults indicated that they considered themselves to be baseball fans. Of the 394 baseball fans, 272 stated that they thought the designated hitter rule should either be expanded to both baseball
The article “Viewers Speak Out Against Reality TV” (Associated Press, September 12, 2005) included the following statement: “Few people believe there’s much reality in reality TV: a total of 82% said the shows are either ‘totally made up’ or ‘mostly distorted’.” This statement was
One thousand randomly selected adult Americans participated in a survey conducted by the Associated Press (June 2006). When asked “Do you think it is sometimes justified to lie or do you think lying is never justified?” 52% responded that lying was never justified. When asked about lying to
USA Today (October 14, 2002) reported that 36% of adult drivers admit that they often or sometimes talk on a cell phone when driving. This estimate was based on data from a sample of 1004 adult drivers, and a bound on the error of estimation of 3.1% was reported. Assuming a 95% confidence level, do
The Gallup Organization conducts an annual survey on crime. It was reported that 25% of all households experienced some sort of crime during the past year. This estimate was based on a sample of 1002 randomly selected households. The report states, “One can say with 95% confidence that the margin
The article “Hospitals Dispute Medtronic Data on Wires” (The Wall Street Journal, February 4, 2010) describes several studies of the failure rate of defibrillators used in the treatment of heart problems. In one study conducted by the Mayo Clinic, it was reported that failures were experienced
Based on a representative sample of 511 U.S. teenagers age 12 to 17, International Communications Research estimated that the proportion of teens who support keeping the legal drinking age at 21 is p^ = 0.64 (64%). The press release titled “Majority of Teens (Still) Favor the Legal Drinking
A discussion of digital ethics appears in the article “Academic Cheating, Aided by Cell Phones or Web, Shown to be Common” (Los Angeles Times, June 17, 2009). One question posed in the article is: What proportion of college students have used cell phones to cheat on an exam? Suppose you have
In spite of the potential safety hazards, some people would like to have an Internet connection in their car. A preliminary survey of adult Americans has estimated this proportion to be somewhere around .30 (USA Today, May 1, 2009).a. Use the given preliminary estimate to determine the sample size
A consumer group is interested in estimating the proportion of packages of ground beef sold at a particular store that have an actual fat content exceeding the fat content stated on the label. How many packages of ground beef should be tested to estimate this proportion to within .05 with 95%
Given a variable that has a t distribution with the specified degrees of freedom, what percentage of the time will its value fall in the indicated region? a. 10 df, between - 1.81 and 1.81 b. 10 df, between - 2.23 and 2.23 c. 24 df, between - 2.06 and 2.06 d. 24 df, between -2.80 and 2.80 e. 24 df,
What is the appropriate t critical value for each of the following confidence levels and sample sizes?a. 95% confidence, n = 17b. 90% confidence, n = 12c. 99% confidence, n = 24d. 90% confidence, n = 25e. 90% confidence, n = 13f. 95% confidence, n = 10
The two intervals (114.4, 115.6) and (114.1, 115.9) are confidence intervals (computed using the same sample data) for m = true average resonance frequency (in hertz) for all tennis rackets of a certain type. a. What is the value of the sample mean resonance frequency? b. The confidence level for
Samples of two different models of cars were selected, and the actual speed for each car was determined when the speedometer registered 50 mph. The resulting 95% confidence intervals for mean actual speed were (51.3, 52.7) and (49.4, 50.6). Assuming that the two sample standard deviations are
The authors of the paper “Deception and Design: The Impact of Communication Technology on Lying Behavior” (Proceedings of Computer Human Interaction [2004]) asked 30 students in an upper division communications course at a large university to keep a journal for 7 days, recording each social
In a study of academic procrastination, the authors of the paper “Correlates and Consequences of Behavioral Procrastination” (Procrastination, Current Issues and New Directions [2000]) reported that for a sample of 411 undergraduate students at a midsize public university preparing for a final
Data consistent with summary quantities in the article referenced in Exercise 9.3 on total calorie consumption on a particular day are given for a sample of children who did not eat fast food on that day and for a sample of children who did eat fast food on that day. Assume that it is reasonable to
How much money do people spend on graduation gifts? In 2007, the National Retail Federation (www.nrf.com) surveyed 2815 consumers who reported that they bought one or more graduation gifts that year. The sample was selected in a way designed to produce a sample representative of adult Americans who
In June 2009, Harris Interactive conducted its Great Schools Survey. In this survey, the sample consisted of 1086 adults who were parents of school-aged children. The sample was selected in a way that makes it reasonable to regard it as representative of the population of parents of school-aged
The authors of the paper “Driven to Distraction” (Psychological Science [2001]: 462–466) describe an experiment to evaluate the effect of using a cell phone on reaction time. Subjects were asked to perform a simulated driving task while talking on a cell phone. While performing this task,
Suppose that a random sample of 50 bottles of a particular brand of cough medicine is selected and the alcohol content of each bottle is determined. Let m denote the mean alcohol content (in percent) for the population of all bottles of the brand under study. Suppose that the sample of 50 results
Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for six specimens under specified conditions, and the resulting mean and standard deviation were 306.09 Newtons and 41.97
The article €œThe Association Between Television Viewing and Irregular Sleep Schedules Among Children Less Than 3 Years of Age€ (Pediatrics [2005]: 851€“ 856) reported the accompanying 95% confidence intervals for average TV viewing time (in hours per day) for three different age
The article “Most Canadians Plan to Buy Treats, Many Will Buy Pumpkins, Decorations and/or Costumes” (Ipsos-Reid, October 24, 2005) summarized results from a survey of 1000 randomly selected Canadian residents. Each individual in the sample was asked how much he or she anticipated spending on
Because of safety considerations, in May 2003 the Federal Aviation Administration (FAA) changed its guidelines for how small commuter airlines must estimate passenger weights. Under the old rule, airlines used 180 pounds as a typical passenger weight (including carry-on luggage) in warm months and
A Example 9.3 gave the following airborne times (in minutes) for 10 randomly selected flights from San Francisco to Washington Dulles airport: 270 256 267 285 274 275 266 258 271 281 a. Compute and interpret a 90% confidence interval for the mean airborne time for flights from San Francisco to
Fat content (in grams) for seven randomly selected hot dogs that were rated as very good by Consumer Reports (www.consumerreports.org) is shown below. Is it reasonable to use this data and the t confidence interval of this section to construct a confidence interval for the mean fat content of hot
Fat content (in grams) for seven randomly selected hot dogs that were rated as very good by Consumer Reports (www.consumerreports.org) is shown below. Is it reasonable to use this data and the t confidence interval of this section to construct a confidence interval for the mean fat content of hot
Five students visiting the student health center for a free dental examination during National Dental Hygiene Month were asked how many months had passed since their last visit to a dentist. Their responses were as follows:Assuming that these five students can be considered a random sample of all
The Bureau of Alcohol, Tobacco, and Firearms (BATF) has been concerned about lead levels in California wines. In a previous testing of wine specimens, lead levels ranging from 50 to 700 parts per billion were recorded. How many wine specimens should be tested if the BATF wishes to estimate the true
The formula described in this section for determining sample size corresponds to a confidence level of 95%. What would be the appropriate formula for determining sample size when the desired confidence level is 90%? 98%?
The following quote is from the article “Credit Card Debt Rises Faster for Seniors” (USA Today, July 28, 2009): The study, which will be released today by Demos, a liberal public policy group, shows that low- and middle-income consumers 65 and older carried $10,235 in average credit card debt
The paper “The Curious Promiscuity of Queen Honey Bees (Apis mellifera): Evolutionary and Behavioral Mechanisms” (Annals of Zoology Fennici [2001]:255– 265) describes a study of the mating behavior of queen honeybees. The following quote is from the paper: Queens flew for an average of 24.2
According to an AP-Ipsos poll (June 15, 2005), 42% of 1001 randomly selected adult Americans made plans in May 2005 based on a weather report that turned out to be wrong.a. Construct and interpret a 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an
“Tongue Piercing May Speed Tooth Loss, Researchers Say” is the headline of an article that appeared in the San Luis Obispo Tribune (June 5, 2002). The article describes a study of 52 young adults with pierced tongues. The researchers found receding gums, which can lead to tooth loss, in 18 of
In a study of 1710 schoolchildren in Australia (Herald Sun, October 27, 1994), 1060 children indicated that they normally watch TV before school in the morning. (Interestingly, only 35% of the parents said their children watched TV before school!) Construct a 95% confidence interval for the true
Suppose that each of 935 smokers received a nicotine patch, which delivers nicotine to the bloodstream but at a much slower rate than cigarettes do. Dosage was decreased to 0 over a 12-week period. Suppose that 245 of the subjects were still not smoking 6 months after treatment. Assuming it is
The article “Consumers Show Increased Liking for Diesel Autos” (USA Today, January 29, 2003) reported that 27% of U.S. consumers would opt for a diesel car if it ran as cleanly and performed as well as a car with a gas engine. Suppose that you suspect that the proportion might be different in
In the article “Fluoridation Brushed Off by Utah” (Associated Press, August 24, 1998), it was reported that a small but vocal minority in Utah has been successful in keeping fluoride out of Utah water supplies despite evidence that fluoridation reduces tooth decay and despite the fact that a
Seventy-seven students at the University of Virginia were asked to keep a diary of conversations with their mothers, recording any lies they told during these conversations (San Luis Obispo Telegram-Tribune, August 16, 1995). It was reported that the mean number of lies per conversation was 0.5.
An Associated Press article on potential violent behavior reported the results of a survey of 750 workers who were employed full time (San Luis Obispo Tribune, September 7, 1999). Of those surveyed, 125 indicated that they were so angered by a coworker during the past year that they felt like
The 1991 publication of the book Final Exit, which includes chapters on doctor-assisted suicide, caused a great deal of controversy in the medical community. The Society for the Right to Die and the American Medical Association quoted very different figures regarding the proportion of primary-care
A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor. If a handle is cracked, it is considered defective and must be discarded. A large shipment of plastic handles is received. The proportion of defective handles p is of interest. How many handles from
An article in the Chicago Tribune (August 29, 1999) reported that in a poll of residents of the Chicago suburbs, 43% felt that their financial situation had improved during the past year. The following statement is from the article: “The findings of this Tribune poll are based on interviews with
A manufacturer of college textbooks is interested in estimating the strength of the bindings produced by a particular binding machine. Strength can be measured by recording the force required to pull the pages from the binding. If this force is measured in pounds, how many books should be tested to
Recent high-profile legal cases have many people reevaluating the jury system. Many believe that juries in criminal trials should be able to convict on less than a unanimous vote. To assess support for this idea, investigators asked each individual in a random sample of Californians whether they
The confidence intervals presented in this chapter give both lower and upper bounds on plausible values for the population characteristic being estimated. In some instances, only an upper bound or only a lower bound is appropriate. Using the same reasoning that gave the large sample interval in
Given below are the sodium contents (in mg) for seven brands of hot dogs rated as €œvery good€ by Consumer Reports (www.consumerreports.org):a. Use the given data to produce a point estimate of m, the true mean sodium content for hot dogs. b. Use the given data to produce a

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