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Introduction To Statistics And Data Analysis 5th Edition Roxy Peck, Chris Olsen, Jay L Devore - Solutions

10.42 Give as much information as you can about the P-value of a t test in each of the following situations:a. Upper-tailed test, df 5 8, t 5 2.0b. Upper-tailed test, n 5 14, t 5 3.2c. Lower-tailed test, df 5 10, t 5 22.4d. Lower-tailed test, n 5 22, t 5 24.2e. Two-tailed test, df 5 15, t 5 21.6f.
10.39 Refer back to the previous exercise. The actual sample proportion observed in the study was p⁄5 0.33. Based on this sample proportion, is there convincing evidence that more than 25% of law enforcement agencies review social media activity as part of background checks, or is this sample
10.38 The article “Cops Get Screened for Digital Dirt” (USA Today, Nov. 12, 2010) summarizes a report of law enforcement agencies regarding the use of social media to screen applicants for employment. The report was based on a survey of 728 law enforcement agencies. One question on the survey
10.34 The report “How Teens Use Media” (Nielsen, June 2009) says that 37% of teens in the U.S. access the Internet from a mobile phone. Suppose you plan to select a random sample of 500 students at the local high school and will ask each student in the sample if he or she accesses the Internet
10.30 The paper “Debt Literacy, Financial Experiences and Over-Indebtedness” (Social Science Research Network, Working paper W14808, 2008) included analysis of data from a national sample of 1000 Americans.One question on the survey was:“You owe $3000 on your credit card. You pay a minimum
10.28 In a survey conducted by CareerBuilder.com, employers were asked if they had ever sent an employee home because they were dressed inappropriately(June 17, 2008, www.careerbuilder.com). A total of 2765 employers responded to the survey, with 968 saying that they had sent an employee home for
10.27 Assuming a random sample from a large population, for which of the following null hypotheses and sample sizes n is the large-sample z test appropriate:a. H0: p 5 .2, n 5 25b. H0: p 5 .6, n 5 210c. H0: p 5 .9, n 5 100d. H0: p 5 .05, n 5 75
10.26 Let p denote the proportion of students at a particular university that use the fitness center on campus on a regular basis. For a large-sample z test of H0: p 5 .5 versus Ha: p . .5, find the P-value associated with each of the given values of the test statistic:a. 1.40d. 2.45b. 0.93e.
10.25 Pairs of P-values and significance levels,a, are given. For each pair, state whether you would reject H0 at the given significance level.a. P-value 5 .084, a 5 .05b. P-value 5 .003, a 5 .001c. P-value 5 .498, a 5 .05d. P-value 5 .084, a 5 .10e. P-value 5 .039, a 5 .01f. P-value 5 .218, a 5 .10
10.24 For which of the following P-values will the null hypothesis be rejected when performing a test with a significance level of .05:a. .001d. .047b. .021e. .148c. .078
10.23 Use the definition of the P-value to explain the following:a. Why H0 would be rejected if P-value 5 .0003b. Why H0 would not be rejected if P-value 5 .350
10.20 Suppose that you are an inspector for the Fish and Game Department and that you are given the task of determining whether to prohibit fishing along part of the Oregon coast. You will close an area to fishing if it is determined that fish in that region have an unacceptably high mercury
10.19 Suppose that for a particular hypothesis test, the consequences of a Type I error are very serious.Would you want to carry out the test using a small significance level a (such as 0.01) or a larger significance level (such as 0.10)? Explain the reason for your choice. (Hint: See discussion
10.18 Water specimens are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 1508F, there will be no negative effects on the river’s ecosystem. To investigate
10.13 The paper “MRI Evaluation of the Contralateral Breast in Women with Recently Diagnosed Breast Cancer” (New England Journal of Medicine [2007]:1295–1303) describes a study of the use of MRI(Magnetic Resonance Imaging) exams in the diagnosis of breast cancer. The purpose of the study was
10.12 Researchers at the University of Washington and Harvard University analyzed records of breast cancer screening and diagnostic evaluations (“Mammogram Cancer Scares More Frequent than Thought,”USA Today, April 16, 1998). Discussing the benefits and downsides of the screening process, the
10.11 The report “How Teens Use Media” (Nielsen, June 2009)says that 83% of U.S. teens use text messaging. Suppose you plan to select a random sample of 400 students at the local high school and will ask each one if he or she uses text messaging. You plan to use the resulting data to decide if
10.10 A cruise ship charges passengers $3 for a can of soda. Because of passenger complaints, the ship manager has decided to try out a plan with a lower price. He thinks that with a lower price, more cans will be sold, which would mean that the ship would still make a reasonable total profit. With
10.9 A county commissioner must vote on a resolution that would commit substantial resources to the construction of a sewer in an outlying residential area. Her fiscal decisions have been criticized in the past, so she decides to take a survey of constituents to find out whether they favor spending
10.7 A study sponsored by the American Savings Education Council (“Preparing for Their Future: A Look at the Financial State of Gen X and Gen Y,” March 2008)included data from a survey of 1752 people age 19 to 36. One of the survey questions asked participants how satisfied they were with their
10.6 CareerBuilder.com conducted a survey to learn about the proportion of employers who had ever sent an employee home because they were dressed inappropriately (June 17, 2008, www.careerbuilder.com). Suppose you are interested in determining if the resulting data provided strong evidence in
10.5 The MMR vaccine is a measles-mumps-rubella vaccine. Consider the following quote from the article “Review Finds No Link Between Vaccine and Autism” (San Luis Obispo Tribune, October 19, 2005):“‘We found no evidence that giving MMR causes Crohn’s disease and/or autism in the children
10.2 For the following pairs, indicate which do not comply with the rules for setting up hypotheses, and explain why:a. H0: m 5 15, Ha: m 5 15b. H0: p 5 .4, Ha: p . .6c. H0: m 5 123, Ha: m , 123d. H0: m 5 123, Ha: m 5 125e. H0: p⁄5 .1, Ha: p⁄Þ .1
10.1 Explain why the statement x 5 50 is not a legitimate hypothesis.
●● describe the effect of the significance level and the sample size on the power of a test.
●● carry out a t test for a population mean and interpret the results in context.
●● carry out a large-sample z test for a population proportion and interpret the results in context.
●● describe Type I and Type II errors in context.
●● translate a research question into null and alternative hypotheses.
●● the reasoning used to reach a decision in a hypothesis test.
●● why failing to reject the null hypothesis does not imply strong support for the null hypothesis.
●● that rejecting the null hypothesis implies strong support for the alternative hypothesis.
9.68 The interval from 22.33 to 1.75 captures an area of .95 under the z curve. This implies that another large-sample 95% confidence interval for m has lower limit x 2 2.33 sÏn and upper limit x 1 1.75 sÏn.Would you recommend using this 95% interval over the 95% interval x 6 1.96 sÏn discussed
9.67 When n is large, the statistic s is approximately unbiased for estimating s and has approximately a normal distribution. The standard deviation of this statistic when the population distribution is normal is ss
9.66 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
9.54 Authors of the news release titled “Major Gaps Still Exist Between the Perception and the Reality of Americans’ Internet Security Protections, Study Finds”(The National Cyber Security Alliance) estimated the proportion of Americans who claim to have a firewall installed on their computer
9.51 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
9.50 ● 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:6 17 11 22 29 Assuming that these five students can be considered a
9.49 ● 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
9.48 ● 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 281a. Compute and interpret a 90% confidence interval for the mean airborne time for flights from San Francisco to
9.45 The article “The 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 groups.Age
9.42 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,
9.40 Medical research has shown that repeated wrist extensions beyond 20 degrees increase the risk of wrist and hand injuries. Each of 24 students at Cornell University used a proposed new computer mouse design, and while using the mouse, each student’s wrist extension was recorded. Data
9.39 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
9.36 The two intervals (114.4, 115.6) and (114.1, 115.9)are confidence intervals (computed using the same sample data) for m 5 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? (Hint: Where is the
9.35 The formula used to compute a confidence interval for the mean of a normal population when n is small is x 6 st critical valued sÏn What is the appropriate t critical value for each of the following confidence levels and sample sizes?a. 95% confidence, n 5 17b. 90% confidence, n 5 12c. 99%
9.34 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 21.81 and 1.81b. 10 df, between 22.23 and 2.23c. 24 df, between 22.06 and 2.06d. 24 df, between 22.80 and 2.80e. 24 df,
9.33 Data from a survey of a representative sample was used to estimate that 32% of 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).Suppose you decide to conduct a survey to estimate this proportion for the current
9.25 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
9.16 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
9.15 Based on data from a survey of 1200 randomly selected Facebook users (USA Today, March 24, 2010), the following is a 90% confidence interval for the proportion of all Facebook users who say it is not OK to “friend” someone who reports to you at work:(0.60, 0.64). What is the meaning of the
9.14 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
9.13 Discuss how each of the following factors affects the width of the confidence interval for p. (Hint: Consider the confidence interval formula.)a. The confidence levelb. The sample sizec. The value of p⁄
9.11 The formula used to compute a large-sample confidence interval for p is p⁄6 sz critical valuedÎp⁄s1 2p⁄d nWhat is the appropriate z critical value for each of the following confidence levels?a. 95%d. 80%b. 90%e. 85%c. 99%9.12 The use of the interval p⁄6 sz critical valuedÎp⁄s1
9.10 ▼ For each of the following choices, explain which would result in a wider large-sample confidence interval for p. (Hint: Consider the confidence interval formula.)a. 90% confidence level or 95% confidence levelb. n 5 100 or n 5 400
9.9 ● A random sample of 10 houses heated with natural gas in a particular area is selected, and the amount of gas (in therms) used during the month of January is determined for each house. The resulting observations are as follows:103 156 118 89 125 147 122 109 138 99a. Let mJ denote the average
9.8 ● A random sample of n 5 12 four-year-old red pine trees was selected, and the diameter (in inches) of each tree’s main stem was measured. The resulting observations are as follows:11.3 10.7 12.4 15.2 10.1 12.1 16.2 10.5 11.4 11.0 10.7 12.0a. Compute a point estimate of s, the population
9.7 ● Given below are the sodium contents (in mg) for seven brands of hot dogs rated as “very good” by Consumer Reports (www.consumerreports.org):420 470 350 360 270 550 530a. Use the given data to produce a point estimate of m, the true mean sodium content for hot dogs.b. Use the given data
9.4 ● Data consistent with summary quantities in the article referenced in the previous exercise 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
9.3 Consumption of fast food is a topic of interest to researchers in the field of nutrition. The article “Effects of Fast-Food Consumption on Energy Intake and Diet Quality Among Children” (Pediatrics [2004]: 112–118)reported that 1720 of those in a random sample of 6212 U.S. children
9.1 ▼ 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. (Hint: See the section on choosing a statistic.)
●● determine the sample size necessary to achieve a desired bound on error when estimating a population proportion or a population mean.
●● the meaning of the confidence level associated with a confidence interval.Students will be able to:
●● the factors that affect the width of a confidence interval.
●● the relationships between sample size, margin of error, and the width of a confidence interval.
●● what it means for a statistic to be an unbiased estimator of a population characteristic.
8.37 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? (Hint: The total will be more than$5300 when the sample mean exceeds what
8.36 Suppose that 40% of all U.S. employees contribute to a retirement plan (p 5 .40).a. In a random sample of 100 employees, what is the approximate probability that at least half of those in the sample contribute to a retirement plan?b. Suppose you were told that at least 60 of the 100 employees
8.32 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 randomly selected cigarettes of this brand are analyzed, what is the probability that the resulting sample mean nicotine content will be less than 0.79?
8.30 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
8.28 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
8.26 The article referenced in the previous exercise 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 the previous exercise for the population of unmarried couples living together.
8.25 ▼ 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.(Hint: See
8.24a. For which of the sample sizes given in the previous exercise would the sampling distribution of p⁄be approximately normal if p 5 .65?b. For which of the sample sizes given in the previous exercise would the sampling distribution be approximately normal if p 5 .2?
8.22 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 of 0.05 mm. Suppose that
8.21 ▼ 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
8.20 College students with checking accounts typically write relatively few checks in any given month, whereas adults who are not students 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 adults who are not
8.19 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.
8.18 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 m?b. For this example (n 5 100, s 5 10), complete each of the following statements by computing the appropriate
8.17 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 5 25 adult males
8.16 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
8.15 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 m 5 2 minutes and s 5 0.8 minutes, respectively.a. If x is the sample mean time for a random sample of n 5 9 students, where is the x
8.13 ▼ 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
8.12 Explain the difference between s and s x and between m and m x.
8.11 For which of the sample sizes given in the previous exercise would it be reasonable to think that the x sampling distribution is approximately normal in shape?
8.10 A random sample is selected from a population with mean m 5 100 and standard deviation s 5 10.Determine the mean and standard deviation of the x sampling distribution for each of the following sample sizes:a. n 5 9d. n 5 50b. n 5 15e. n 5 100c. n 5 36f. n 5 400
8.9 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. Three possible statistics for estimating m are Statistic 1: the sample mean, x Statistic 2: the sample median Statistic 3: the average of the largest and the smallest
8.8 Simulate sampling from the population of Exercise 8.7 by using four slips of paper individually marked 1, 2, 3, and 4. Select a sample of size 2 without replacement, and compute x. Repeat this process 50 times, and construct a density histogram of the 50 x values. How does this sampling
8.7 ▼ Consider the following population: {1, 2, 3, 4}.For this population the mean is m 5 1 1 2 1 3 1 4 45 2.5 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
8.6 Suppose that the sampling experiment described in Example 8.1 had used samples of size 10 rather than size 5.a. 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
8.5 Select 10 additional random samples of size 5 from the population of 20 students given in Example 8.1, and compute the mean amount spent on books for each of the 10 samples. Are the x values consistent with the results of the sampling experiment summarized in Figure 8.1?
8.4 Consider a population consisting of the following five values, which represent the number of DVD rentals during the academic year for each of five housemates:8 14 16 10 11a. Compute the mean of this population.b. Select a random sample of size 2 by writing the five numbers in this population on
8.2 What is the difference between x and m? between s and s?
8.1 Explain the difference between a population characteristic and a statistic.
●● use properties of the sampling distribution to reason informally about the value of a population mean or a population proportion.
● ● determine when the sampling distribution of x or p⁄is approximately normal.
● ● describe general properties of the sampling distribution of p⁄.
●● describe general properties of the sampling distribution of x.
● ● how the standard deviations of the sampling distributions of x and p⁄are related to sample size.
●● that sampling distribution describes sample-to-sample variability in the values of a statistic.

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