A car manufacturer is interested in learning about the proportion of people purchasing one of its cars who plan to purchase another car of this brand in the future. A random sample of 400 of these people included 267 who said they would purchase this brand again. For each of the three statements below, indicate if the statement is correct or incorrect. If the statement is incorrect, explain what makes it incorrect. Statement 1: The estimate pˆ = 0.668 will never differ from the value of the actual population proportion by more than 0.046. Statement 2: It is unlikely that the estimate p ˆ = 0.668 differs from the value of the actual population proportion by more than 0.024. Statement 3: It is unlikely that the estimate p ˆ = 0.668 differs from the value of the actual population proportion by more than 0.046.
> According to the U.S. census bureau (www.census.gov), the percentage of U.S. residents living in poverty in 2015 was 12.2% for men and 14.8% for women. These percentages were estimates based on data from large representative samples of men and women. Sup
> An article titled “The Latest on Workplace Monitoring and Surveillance” (American Management Association, November 17, 2014) referred to the “2007 Electronic Monitoring & Surveillance Survey.” In a summary of survey results submitted by 304 U.S. business
> The article “Report: More Than Half of DC-Area Millennials Are Using Ride-Hailing Apps” (June 23, 2016, www .washingtonian.com/2016/06/23/report-half-dc-area -millennials-using-ride-hailing-apps/, retrieved May 4, 2017
> A survey on SodaHead (www.sodahead.com/survey /featured/anonymous-advice/?results51, retrieved May 13, 2016) reported that 603 out of 753 respondents replied “no” to the question “Should you be friend
> USA TODAY (January 24, 2012) reported that ownership of tablet computers and e-readers is soaring. Suppose you want to estimate the proportion of students at your college who own at least one tablet or e-reader. What sample size would you use in order to
> Data from a representative sample were used to estimate that 32% of all computer users in 2011 had tried to get on a Wi-Fi network that was not their own in order to save money (USA TODAY, May 16, 2011). You decide to conduct a survey to estimate this pr
> 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 the proportion of adult Americans who would like Internet access in their car to be somewh
> 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 figu
> The article “Should Canada Allow Direct-to-Consumer Advertising of Prescription Drugs?” (Canadian Family Physician [2009]: 130–131) calls for the legalization of advertising of prescription drugs in Canada. Suppose you wanted to conduct a survey to estim
> A manufacturer of small appliances purchases plastic handles for coffeepots from an outside vendor. If a handle is cracked, it is considered defective and can’t be used. A large shipment of plastic handles is received. How many handles from the shipment
> In 2010, the online security firm Symantec estimated that 63% of computer users don’t change their passwords very often (www.cnet.com/news/survey-63-dont -change-passwords-very-often, retrieved November 19, 2016). Because this estimate may be outdated, s
> 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
> The report referenced in the previous exercise also indicated that 33% of those in a representative sample of 533 homeowners in southern states said that they had considered installing solar panels. a. Use the given information to construct and interpre
> The report “The Politics of Climate” (Pew Research Center, October 4, 2016, www.pewinternet.org/2016/10/04 /the-politics-of-climate, retrieved May 6, 2017) summarized data from a survey on public opinion of renewable and other energy sources. It was repo
> The report “The 2016 Consumer Financial Literacy Survey” (The National Foundation for Credit Counseling, www.nfcc.org, retrieved October 28, 2016) summarized data from a representative sample of 1668 adult Americans. Based on data from this sample, it wa
> The article referenced in the previous exercise also indicated that 811 of the 1001 students surveyed said that they would feel restricted if they could only work on digital devices. Would a 95% confidence interval for the proportion of students age 13 t
> The article “Write It by Hand to Make It Stick” (Advertising Age, July 27, 2016) summarizes data from a survey of 1001 students age 13 to 19 years. Of the students surveyed, 851 reported that they learn best using a mix of digital and nondigital tools. C
> 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 neve
> In 2010, the National Football League adopted new rules designed to limit head injuries. In a survey conducted in 2015 by the Harris Poll, 1216 of 2096 adults indicated that they were football fans and followed professional football. Of these football fa
> The article “Most Dog Owners Take More Pictures of Their Pet Than Their Spouse” (August 22, 2016, news.fastcompany.com/most-dog-owners-take-more-pictures-oftheir-pet-than-their-spouse-4017458, retrieved May 6, 2017) indicates that in a sample of 1000 dog
> The report “Job Seeker Nation Study 2016” (www .jobvite.com/wp-content/uploads/2016/03/Jobvite _Jobseeker_Nation_2016.pdf, retrieved May 6, 2017) summarized a survey of 2305 working adults. The report indicates that 484 of the working adults surveyed sai
> The USA Snapshot titled “Social Media Jeopardizing Your Job?” (USA TODAY, November 12, 2014) summarized data from a survey of 1855 recruiters and human resource professionals. The Snapshot indicted that 53% of the people surveyed had reconsidered a job c
> For the situation described in the previous exercise, use the five-step process for estimation problems (EMC3) to construct and interpret a 99% confidence interval for the proportion of mothers of children under the age of 2 years who post pictures of th
> The USA Snapshot titled “Baby’s First Photo Reveal” (USA TODAY, October 17, 2014) summarized data from a survey of 1001 mothers with children under the age of 2. The Snapshot includes the following statement: “83% of moms post new baby photos from the de
> The formula used to calculate a large-sample confidence interval for p is What is the appropriate z critical value for each of the following confidence levels? a. 95% b. 98% c. 85% P(1 – p) p + (z critical value)\
> Appropriate use of the interval requires a large sample. For each of the following combinations of n and p ˆ, indicate whether the sample size is large enough for this interval to be appropriate. a. n = 100 and p ˆ = 0.70 b. n =
> Based on data from a survey of 1200 randomly selected Facebook users (USA TODAY, March 24, 2010), a 98% confidence interval for the proportion of all Facebook users who say it is OK to ignore a coworker’s “friend” request is (0.35, 0.41). What is the mea
> For each of the following choices, explain which would result in a narrower large-sample confidence interval for p: a. 95% confidence level or 99% confidence level b. n = 200 or n = 500
> Suppose that a campus bookstore manager wants to know the proportion of students at the college who purchase some or all of their textbooks online. Two different people independently selected random samples of students at the college and used their sampl
> It probably wouldn’t surprise you to know that Valentine’s Day means big business for florists, jewelry stores, and restaurants. But did you know that it is also a big day for pet stores? In January 2015, the National Retail Federation conducted a survey
> In a survey of 800 college students in the United States, 576 indicated that they believe that a student or faculty member on campus who uses language considered racist, sexist, homophobic, or offensive should be subject to disciplinary action (“Listenin
> The Princeton Review 2016 College Hopes and Worries Survey Report (www.princetonreview.com/cms-content/final_cohowo2016survrpt.pdf, retrieved May 6, 2017) reported that 31% of students applying to college wanted to attend a college that was within 250 mi
> For the study described in the previous exercise, use the five-step process for estimation problems (EMC3) to construct and interpret a 95% confidence interval for the proportion of hiring managers and human resource professionals who use social network
> 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 more employers are
> The formula used to calculate a large-sample confidence interval for p is What is the appropriate z critical value for each of the following confidence levels? a.90% b. 99% c. 80% P(1 – p) p + (z critical value)\
> Appropriate use of the interval requires a large sample. For each of the following combinations of n and p ˆ, indicate whether the sample size is large enough for this interval to be appropriate. a. n = 50 and p ˆ = 0.30 b. n =
> Based on data from a survey of 1200 randomly selected Facebook users (USA TODAY, March 24, 2010), a 95% confidence interval for the proportion of all Facebook users who say it is OK for someone to “friend” his or her boss is (0.41, 0.47). What is the mea
> For each of the following choices, explain which one 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
> Suppose that a city planning commission wants to know the proportion of city residents who support installing streetlights in the downtown area. Two different people independently selected random samples of city residents and used their sample data to co
> 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
> Business Insider reported that a study commissioned by eBay Motors found that nearly 40% of millennials who drive a car that is more than 5 years old have named their cars (“Millennials Have an Odd Habit When It Comes to Their Cars,” April 14, 2016). a.
> The USA Snapshot titled “Have a Nice Trip” (USA TODAY, November 17, 2015) summarized data from a survey of 1000 U.S. adults who had traveled by air at least once in the previous year. The Snapshot includes the following statement: “38% admit to yelling a
> The article “Most Americans Don’t Understand the Cloud, But They Should” (foxbusiness.com, October 17, 2016, retrieved November 12, 2016) reported that in a sample of 1000 people, 22% said they have pretended to know what the cloud is or how it works. As
> USA TODAY reported that the proportion of Americans who prefer cheese on their burgers is 0.84 (USA TODAY, September 7, 2016). This estimate was based on a survey of a representative sample of 1000 adult Americans. Calculate and interpret a margin of err
> Suppose that 935 smokers each received a nicotine patch, which delivers nicotine to the bloodstream at a much slower rate than cigarettes do. Dosage was decreased to 0 over a 12-week period. Of these 935 people, 245 were still not smoking 6 months after
> The USA Snapshot titled “Big Bang Theory” (USA TODAY, October 14, 2016) summarized data from a sample of 1003 American parents of children age 6 to 11 years. It reported that 53% of these parents view science-oriented TV shows as a good way to expose the
> The use of the formula for margin of error requires a large sample. For each of the following combinations of n and pˆ, indicate whether the sample size is large enough for use of this formula to be appropriate. a. n = 100 and pˆ = 0.70 b. n = 40 and
> The report “Parents, Teens and Digital Monitoring” (Pew Research Center, January 7, 2016, www.pewinternet .org/2016/01/07/parents-teens-and-digital-monitoring, retrieved May 5, 2017) reported that 61% of parents of teens aged 13 to 17 said that they had
> Consider taking a random sample from a population with p 5 0.70. a. What is the standard error of p ˆ for random samples of size 100? b. Would the standard error of pˆ be smaller for samples of size 100 or samples of size 400? c. Does decreasing the s
> The report “The 2016 Consumer Financial Literacy Survey” (The National Foundation for Credit Counseling, www .nfcc.org, retrieved October 28, 2016) summarized data from a representative sample of 1668 adult Americans. When asked if they typically carry c
> The paper “Sleeping with Technology: Cognitive, Affective and Technology Usage Predictors of Sleep Problems Among College Students” (Sleep Health [2016]: 49–56) summarized data from a survey of a sample of college students. Of the 734 students surveyed,
> The use of the formula for margin of error requires a large sample. For each of the following combinations of n and pˆ, indicate whether the sample size is large enough for use of this formula to be appropriate. a. n = 50 and p ˆ = 0.30 b. n = 50 and p
> The report “2007 Electronic Monitoring & Surveillance Survey” (American Management Association) summarized a survey of 304 U.S. businesses. The report stated that 91 of the 304 businesses had fired workers for misuse of the Internet. Assume that this sam
> Consider taking a random sample from a population with p = 0.40. a. What is the standard error of pˆ for random samples of size 100? b. Would the standard error of pˆ be greater for samples of size 100 or samples of size 200? c. If the sample size wer
> A large online retailer is interested in learning about the proportion of customers making a purchase during a particular month who were satisfied with the online ordering process. A random sample of 600 of these customers included 492 who indicated they
> A researcher wants to estimate the proportion of property owners who would pay their property taxes one month early if given a $50 reduction in their tax bill. Would the standard error of the sample proportion pˆ be larger if the actual population propor
> A researcher wants to estimate the proportion of city residents who favor spending city funds to promote tourism. Would the standard error of the sample proportion pˆ be smaller for random samples of size n = 100 or random samples of size n = 200?
> A random sample will be selected from the population of all students enrolled at a large college. The sample proportion pˆ will be used to estimate p, the proportion of all students who use public transportation to travel to campus. For which of the foll
> If two statistics are available for estimating a population characteristic, under what circumstances might you choose a biased statistic over an unbiased statistic?
> A random sample will be selected from the population of all adult residents of a particular city. The sample proportion pˆ will be used to estimate p, the proportion of all adult residents who do not own a car. For which of the following situations will
> Use the formula for the standard error of pˆ to explain why increasing the sample size decreases the standard error.
> A researcher wants to estimate the proportion of students enrolled at a university who are registered to vote. Would the standard error of the sample proportion pˆ be larger if the actual population proportion was p = 0.4 or p = 0.8?
> 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. Statist
> 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 of these statistics are unbiased estimators of the population c
> For estimating a population characteristic, why is an unbiased statistic generally preferred over a biased statistic? Does unbiasedness alone guarantee that the estimate will be close to the actual value of the population characteristic? Explain.
> A random sample will be selected from the population of all adult residents of a particular city. The sample proportion pˆ will be used to estimate p, the proportion of all adult residents who are employed full time. For which of the following situations
> Use the formula for the standard error of pˆ to explain why a. the standard error is greater when the value of the population proportion p is near 0.5 than when it is near 1. b. the standard error of pˆ is the same when the value of the population prop
> A researcher wants to estimate the proportion of students enrolled at a university who eat fast food more than three times in a typical week. Would the standard error of the sample proportion pˆ be smaller for random samples of size n = 50 or random samp
> 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. Statist
> 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 of these statistics are unbiased estimators of the population ch
> For estimating a population characteristic, why is an unbiased statistic with a small standard error preferred over an unbiased statistic with a larger standard error?
> Determine the following standard normal (z) curve areas: a. The area under the z curve to the left of 1.75 b. The area under the z curve to the left of -0.68 c. The area under the z curve to the right of 1.20 d. The area under the z curve to the righ
> A business has six customer service telephone lines. Consider the random variable x 5 number of lines in use at a randomly selected time. Suppose that the probability distribution of x is as follows: a. Calculate the mean value and standard deviation of
> A company makes hardwood flooring, which it sells in boxes that will cover 500 square feet of floor. Let x = the number of boxes ordered by a randomly chosen customer. Suppose the probability distribution of x is as follows: a. Calculate and interpret th
> The probability distribution of x, the number of tires needing replacement on a randomly selected automobile checked at a certain inspection station, is given in the following table: The mean value of x is ux = 1.2. Calculate the values of σx
> A grocery store has an express line for customers purchasing at most five items. Consider the random variable x = the number of items purchased by a randomly selected customer using this line. Make two tables that represent two different possible probabi
> Suppose that for a given computer salesperson, the probability distribution of x 5 the number of systems sold in 1 week is given by the following table: a. Find the mean value of x (the mean number of systems sold). b. Find the variance and standard de
> A local television station sells 15-second, 30-s econd, and 60-second advertising spots. Consider the random variable x = length of a randomly selected commercial appearing on this station, and suppose that the probability distribution of x is given by t
> A grocery store has an express line for customers purchasing at most five items. Consider the random variable x = the number of items purchased by a randomly selected customer using this line. Make two tables that represent two different possible probabi
> An appliance dealer sells three different models of freezers having 13.5, 15.9, and 19.1 cubic feet of storage space. Consider the random variable x = the amount of storage space purchased by the next customer to buy a freezer. Suppose that x has the fol
> Consider the random variable y = the number of broken eggs in a randomly selected carton of one dozen eggs. Suppose the probability distribution of y is as follows: a. Calculate and interpret my. (Hint: See Example 6.13.) b. In the long run, for what
> Refer to the probability distribution given in the previous exercise. Put the following probabilities in order, from smallest to largest: P(2 < x < 3) P(2 ≤ x ≤ 3) P(x < 2) P(x > 7) Explain your reasoning.
> A particular professor never dismisses class early. Let x denote the amount of additional time (in minutes) that elapses before the professor dismisses class. Suppose that x has a uniform distribution on the interval from 0 to 10 minutes. The density cur
> Refer to the probabilities given in Parts (a)–(d) of the previous exercise. Which of these probabilities is smallest? Which is largest? Data from exercise 6.28: The continuous random variable x has the probability distribution shown he
> The continuous random variable x has the probability distribution shown here: Shade the area under the curve corresponding to each of the following probabilities. (Draw a new curve for each part.) a. P(x b. P(x > 3) c. P(1 d. P(2 3 4 2.
> The article “Probabilistic risk Assessment of infrastructure networks Subjected to hurricanes” (12th International Conference on Applications of Statistics and Probability in Civil Engineering, 2015) suggests a uniform distribution as a model for the act
> Suppose that the random variable x = weekly water usage (in gallons) for a randomly selected studio apartment in Los Angeles has the probability distribution described by the following density curve. a. What probability is represented by the shaded area
> An online store charges for shipping based on the weight of the items in an order. Define the random variable x = weight of a randomly selected order (in pounds) The density curve of x is shown here: Shade the area under the curve corresponding to each o
> Consider the population that consists of all soft contact lenses made by a particular manufacturer, and define the random variable x = thickness (mm). Suppose that a reasonable model for the probability distribution of x is the one shown in the following
> Let x denote the time (in seconds) necessary for an individual to react to a certain stimulus. Suppose the probability distribution of x is specified by the accompanying density curve. a. What is the height of the density curve above x = 0? (Hint: Tota
> Suppose that the random variable x = waiting time for service at a bank (in minutes) has the probability distribution described by the density curve pictured below. a. What probability is represented by the shaded area? b. Suppose the shaded area = 0.26
> Let x denote the lifetime (in thousands of hours) of a certain type of fan used in diesel engines. Suppose the density curve of x is as pictured. Shade the area under the curve corresponding to each of the following probabilities (draw a new curve for e
> A new battery’s voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. Suppose that 80% of all batteries have accep
> A contractor is required by a county planning department to submit anywhere from one to five forms (depending on the nature of the project) when applying for a building permit. Let y be the number of forms required of the next applicant. Suppose the prob
> A business has six customer service telephone lines. Let x denote the number of lines in use at any given time. Suppose that the probability distribution of x is as follows: Write each of the following events in terms of x, and then calculate the probab
> Suppose that a computer manufacturer receives computer boards in lots of five. Two boards are selected from each lot for inspection. You can represent possible outcomes of the selection process by pairs. For example, the pair (1, 2) represents the select
> Of all airline flight requests received by a certain ticket broker, 70% are for domestic travel (D) and 30% are for international flights (I). Define x to be the number that are for domestic flights among the next three requests received. Assuming indepe
> A pizza shop sells pizzas in four different sizes. The 1000 most recent orders for a single pizza resulted in the following proportions for the various sizes: With x = the size of a pizza in a single-pizza order, the given table is an approximation to t
> Suppose x = the number of courses a randomly selected student at a certain university is taking. The probability distribution of x appears in the following table: a. What is P(x = 4)? b. What is P(x ≤ 4)? c. What is the probability
> Suppose that 20% of all homeowners in an earthquake prone area of California are insured against earthquake damage. Four homeowners are selected at random. Define the random variable x as the number among the four who have earthquake insurance. a. Find
