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

The Associated Press (December 16, 1991) reported that in a random sample of 507 people, only 142 correctly described the Bill of Rights as the first 10 amendments to the U.S. Constitution. Calculate a 95% confidence interval for the proportion of the entire population that could give a correct
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 thepopulation distribution is normal iswhich can be estimated by 9.9 to obtain a 95% confidence interval for the true standard
The interval from 2.33 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 limitand upper limit Would you recommend using this 95% interval over the 95% interval discussed in the text? Explain.
The eating habits of 12 bats were examined in the article “Foraging Behavior of the Indian False Vampire Bat” (Biotropica [1991]: 63– 67). These bats consume insects and frogs. For these 12 bats, the mean time to consume a frog was x 5 21.9 minutes. Suppose that the standard deviation was s =
A random sample of n = 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:a. Compute a point estimate of s, the population standard deviation of main stem diameter. What statistic did
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:a. Let µJ denote the average gas usage during January by all
The AARP Bulletin (March 2010) included the following short news brief:“Older adults who did 1 hour of tai chi twice weekly cut their pain from knee osteoarthritis considerably in a 12-week study conducted at Tufts University School of Medicine.” Suppose you were asked to design a study to
The National Geographic Society conducted a study that included 3000 respondents, age 18 to 24, in nine different countries (San Luis Obispo Tribune, November 21, 2002). The society found that 10% of the participants could not identify their own country on a blank world map. a. Construct a 90%
“Heinz Plays Catch-up After Under-Filling Ketchup Containers” is the headline of an article that appeared on CNN.com (November 30, 2000). The article stated that Heinz had agreed to put an extra 1% of ketchup into each ketchup container sold in California for a 1-year period. Suppose that you
In a survey conducted by Yahoo Small Business, 1432 of 1813 adults surveyed said that they would alter their shopping habits if gas prices remain high (Associated Press, November 30, 2005). The article did not say how the sample was selected, but for purposes of this exercise, assume that it is
In an AP-AOL sports poll (Associated Press, December 18, 2005), 272 of 394 randomly selected baseball fans stated that they thought the designated hitter rule should either be expanded to both baseball leagues or eliminated. Based on the given information, is there sufficient evidence to conclude
The article “Americans Seek Spiritual Guidance on Web” (San Luis Obispo Tribune, October 12, 2002) reported that 68% of the general population belongs to a religious community. In a survey on Internet use, 84% of “religion surfers” (defined as those who seek spiritual help online or who
A survey of teenagers and parents in Canada conducted by the polling organization Ipsos (“Untangling the Web: The Facts About Kids and the Internet,” January 25, 2006) included questions about Internet use. It was reported that for a sample of 534 randomly selected teens, the mean number of
The same survey referenced in the previous exercise reported that for a random sample of 676 parents of Canadian teens, the mean number of hours parents thought their teens spent online was 6.5 and the sample standard deviation was 8.6.a. Do the sample data provide convincing evidence that the mean
The following graphical display appeared in USA Today (June 3, 2009). Write a few sentences critiquing this graphical display. Do you think it does a good job of creating a visual representation of the three percentages in the display?
The article €œFlyers Trapped on Tarmac Push for Rules on Release€ (USA Today, July 28, 2009) included the accompanying data on the number of flights with a tarmac delay of more than 3 hours between October 2008 and May 2009 for U.S. airlines.a. Construct a dotplot of the data
The article €œWait Times on Rise to See Doctor€ (USA Today, June 4, 2009) gave the accompanying data on average wait times in days to get an appointment with a medical specialist in 15 U.S. cities. Construct a boxplot of the average wait-time data. Are there any outliers in the
The report “New Study Shows Need for Americans to Focus on Securing Online Accounts and Backing up Critical Data” (PRNewswire, October 29, 2009) reported that only 25% of Americans change computer passwords quarterly, in spite of a recommendation from the National Cyber Security Alliance that
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 estimate the proportion of Canadians who
The National Association of Colleges and Employers carries out a student survey each year. A summary of data from the 2009 survey included the following information: • 26% of students graduating in 2009 intended to go on to graduate or professional school. • Only 40% of those who graduated in
It probably wouldn’t surprise you to know that Valentine’s Day means big business for florists, jewelry stores, and restaurants. But would it surprise you to know that it is also a big day for pet stores? In January 2010, the National Retail Federation conducted a survey of consumers who they
The article “Doctors Cite Burnout in Mistakes” (San Luis Obispo Tribune, March 5, 2002) reported that many doctors who are completing their residency have financial struggles that could interfere with training. In a sample of 115 residents, 38 reported that they worked moonlighting jobs and 22
Many older homes have electrical systems that use fuses rather than circuit breakers. A manufacturer of 40-amp fuses wants to make sure that the mean amperage at which its fuses burn out is in fact 40. If the mean amperage is lower than 40, customers will complain because the fuses require
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
The paper €œMRI 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
Medical personnel are required to report suspected cases of child abuse. Because some diseases have symptoms that mimic those of child abuse, doctors who see a child with these symptoms must decide between two competing hypotheses: H0: symptoms are due to child abuse Ha: symptoms are due to disease
Ann Landers, in her advice column of October 24, 1994 (San Luis Obispo Telegram-Tribune), described the reliability of DNA paternity testing as follows: “To get a completely accurate result, you would have to be tested, and so would (the man) and your mother. The test is 100% accurate if the man
A television manufacturer claims that (at least) 90% of its TV sets will need no service during the first 3 years of operation. A consumer agency wishes to check this claim, so it obtains a random sample of n = 100 purchasers and asks each whether the set purchased needed repair during the first 3
A manufacturer of hand-held calculators receives large shipments of printed circuits from a supplier. It is too costly and time-consuming to inspect all incoming circuits, so when each shipment arrives, a sample is selected for inspection. Information from the sample is then used to test H0: p =
Water samples 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 150-F, there will be no negative effects on the river’s ecosystem. To investigate whether
Occasionally, warning flares of the type contained in most automobile emergency kits fail to ignite. A consumer advocacy group wants to investigate a claim against a manufacturer of flares brought by a person who claims that the proportion of defective flares is much higher than the value of .1
For the following pairs, indicate which do not comply with the rules for setting up hypotheses, and explain why:
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 content. a.
The National Cancer Institute conducted a 2-year study to determine whether cancer death rates for areas near nuclear power plants are higher than for areas without nuclear facilities (San Luis Obispo Telegram-Tribune, September 17, 1990). A spokesperson for the Cancer Institute said, “From the
An automobile manufacturer is considering using robots for part of its assembly process. Converting to robots is an expensive process, so it will be undertaken only if there is strong evidence that the proportion of defective installations is lower for the robots than for human assemblers. Let p
Use the definition of the P-value to explain the following: a. Why H0 would be rejected if P-value = .0003 b. Why H0 would not be rejected if P-value = .350
For which of the following P-values will the null hypothesis be rejected when performing a test with a significance level of .05: a. .001 b. .021 c. .078 d. .047 e. .148
Pairs of P-values and significance levels, a, are given. For each pair, state whether the observed P-value leads to rejection of H0 at the given significance level. a. P-value = .084, a = .05 b. P-value = .003, a = .001 c. P-value = .498, a = .05 d. P-value = .084, a = .10 e. P-value = .039, a =
Let p denote the proportion of grocery store customers who use the store’s club card. For a largesample z test of H0: p = .5 versus Ha: p = .5, find the P-value associated with each of the given values of the test statistic: a. 1.40 b. 0.93 c. 1.96 d. 2.45 e. - 0.17
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 = .2, n = 25 b. H0: p = .6, n = 210 c. H0: p = .9, n = 100 d. H0: p = .05, n = 75
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
In a survey of 1000 women age 22 to 35 who work full time, 540 indicated that they would be willing to give up some personal time in order to make more money (USA Today, March 4, 2010). The sample was selected in a way that was designed to produce a sample that was representative of women in the
To determine whether the pipe welds in a nuclear power plant meet specifications, a random sample of welds is selected and tests are conducted on each weld in the sample. Weld strength is measured as the force required to break the weld. Suppose that the specifications state that the mean strength
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
“Most Like it Hot” is the title of a press release issued by the Pew Research Center (March 18, 2009, www.pewsocialtrends.org). The press release states that “by an overwhelming margin, Americans want to live in a sunny place.” This statement is based on data from a nationally
In a survey of 1005 adult Americans, 46% indicated that they were somewhat interested or very interested in having web access in their cars (USA Today, May 1, 2009). Suppose that the marketing manager of a car manufacturer claims that the 46% is based only on a sample and that 46% is close to half,
The article “Poll Finds Most Oppose Return to Draft, Wouldn’t Encourage Children to Enlist” (Associated Press, December 18, 2005) reports that in a random sample of 1000 American adults, 700 indicated that they oppose the reinstatement of a military draft. Is there convincing evidence that
The poll referenced in the previous exercise (“Military Draft Study,” AP-Ipsos, June 2005) also included the following question: “If the military draft were reinstated, would you favor or oppose drafting women as well as men?” Forty-three percent of the 1000 people responding said that they
The article “Irritated by Spam? Get Ready for Spit” (USA Today, November 10, 2004) predicts that “spit,” spam that is delivered via Internet phone lines and cell phones, will be a growing problem as more people turn to web-based phone services. In a 2004 poll of 5500 cell phone users
According to a Washington Post-ABC News poll, 331 of 502 randomly selected U.S. adults interviewed said they would not be bothered if the National Security Agency collected records of personal telephone calls they had made. Is there sufficient evidence to conclude that a majority of U.S. adults
According to a survey of 1000 adult Americans conducted by Opinion Research Corporation, 210 of those surveyed said playing the lottery would be the most practical way for them to accumulate $200,000 in net wealth in their lifetime (“One in Five Believe Path to Riches Is the Lottery,” San Luis
The article “Theaters Losing Out to Living Rooms” (San Luis Obispo Tribune, June 17, 2005) states that movie attendance declined in 2005. The Associated Press found that 730 of 1000 randomly selected adult Americans preferred to watch movies at home rather than at a movie theater. Is there
The article referenced in the previous exercise also reported that 470 of 1000 randomly selected adult Americans thought that the quality of movies being produced was getting worse.a. Is there convincing evidence that fewer than half of adult Americans believe that movie quality is getting worse?
Do state laws that allow private citizens to carry concealed weapons result in a reduced crime rate? The author of a study carried out by the Brookings Institution is reported as saying, “The strongest thing I could say is that I don’t see any strong evidence that they are reducing crime”
The report “2007 Electronic Monitoring & Surveillance Survey: Many Companies Monitoring, Recording, Videotaping—and Firing—Employees” (American Management Association, 2007) summarized the results of a survey of 304 U.S. businesses. Of these companies, 201 indicated that they monitor
The article “Fewer Parolees Land Back Behind Bars” (Associated Press, April 11, 2006) includes the fol- lowing statement: “Just over 38% of all felons who were released from prison in 2003 landed back behind bars by the end of the following year, the lowest rate since 1979.” Explain why it
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 = 8, t = 2.0b. Upper-tailed test, n = 14, t = 3.2c. Lower-tailed test, df = 10, t = - 2.4d. Lower-tailed test, n = 22, t = - 4.2e. Two-tailed test, df = 15, t = - 1.6f.
Give as much information as you can about the P-value of a t test in each of the following situations: a. Two-tailed test, df = 9, t = 0.73 b. Upper-tailed test, df = 10, t = - 0.5 c. Lower-tailed test, n = 20, t = - 2.1 d. Lower-tailed test, n = 20, t = - 5.1 e. Two-tailed test, n = 40, t = 1.7
Paint used to paint lines on roads must reflect enough light to be clearly visible at night. Let µ denote the mean reflectometer reading for a new type of paint under consideration. A test of H0: µ = 20 versus Ha: µ > 20 based on a sample of 15 observations gave t = 3.2. What conclusion is
wA certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hours. A random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data
The true average diameter of ball bearings of a certain type is supposed to be 0.5 inch. What conclusion is appropriate when testing H0: µ = 0.5 versus Ha: µ = 0.5 inch each of the following situations: a. n = 13, t = 1.6, a = .05 b. n = 13, t = - 1.6, a = .05 c. n = 25, t = - 2.6, a = .01 d. n =
The paper “Playing Active Video Games Increases Energy Expenditure in Children” (Pediatrics [2009]: 534–539) describes an interesting investigation of the possible cardiovascular benefits of active video games. Mean heart rate for healthy boys age 10 to 13 after walking on a treadmill at 2.6
A study of fast-food intake is described in the paper “What People Buy From Fast-Food Restaurants” (Obesity [2009]: 1369–1374). Adult customers at three hamburger chains (McDonald’s, Burger King, and Wendy’s) at lunchtime in New York City were approached as they entered the
The report “Highest Paying Jobs for 2009–10 Bachelor’s Degree Graduates” (National Association of Colleges and Employers, February 2010) states that the mean yearly salary offer for students graduating with a degree in accounting in 2010 is $48,722. Suppose that a random sample of 50
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 that get the MMR,’ said Tom Jefferson, one of the
The Economist collects data each year on the price of a Big Mac in various countries around the world. The price of a Big Mac for a sample of McDonald€™s restaurants in Europe in May 2009 resulted in the following Big Mac prices (after conversion to U.S. dollars):The mean price of a Big Mac in
A credit bureau analysis of undergraduate students credit records found that the average number of credit cards in an undergraduate’s wallet was 4.09 (“Undergraduate Students and Credit Cards in 2004,” Nellie Mae, May 2005). It was also reported that in a random sample of 132 undergraduates,
Medical research has shown that repeated wrist extension beyond 20 degrees increases 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 consistent
The international polling organization Ipsos reported data from a survey of 2000 randomly selected Canadians who carry debit cards (Canadian Account Habits Survey, July 24, 2006). Participants in this survey were asked what they considered the minimum purchase amount for which it would be
A comprehensive study conducted by the National Institute of Child Health and Human Development tracked more than 1000 children from an early age through elementary school (Ne York w Times, November 1, 2005). The study concluded that children who spent more than 30 hours a week in child care before
In a study of computer use, 1000 randomly selected Canadian Internet users were asked how much time they spend using the Internet in a typical week (1psos Reid, August 9, 2005). The mean of the sample observations was 12.7 hours.a. The sample standard deviation was not reported, but suppose that it
The paper titled “Music for Pain Relief” (The Cochrane Database of Systematic Reviews, April 19, 2006) concluded, based on a review of 51 studies of the effect of music on pain intensity, that “Listening to music reduces pain intensity levels. However, the magnitude of these positive effects
Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases. It is therefore important that the information on packages be accurate. A random sample of n = 12 frozen dinners of a certain type was selected from production during a particular period,
Much concern has been expressed regarding the practice of using nitrates as meat preservatives. In one study involving possible effects of these chemicals, bacteria cultures were grown in a medium containing nitrates. The rate of uptake of radio-labeled amino acid was then determined for each
A certain university has decided to introduce the use of plus and minus with letter grades, as long as there is evidence that more than 60% of the faculty favor the change. A random sample of faculty will be selected, and the resulting data will be used to test the relevant hypotheses. If
a. Explain why use of the z statistic is appropriate in this setting.b. Describe Type I and Type II errors in this context.c. The rejection of H0 when z ‰¥ 1.8 corresponds to what value of a? (That is, what is the area under the z curve to the right of 1.8?)d. Suppose that the actual value
a. What is a for the test procedure that rejects H0 if z = - 1.28? b. If the test procedure of Part (a) is used, calculate b when µ = 9.8, and interpret this error probability. c. Without doing any calculation, explain how b when m = 9.5 compares to b when µ = 9.8. Then check your assertion by
The city council in a large city has become concerned about the trend toward exclusion of renters with children in apartments within the city. The housing coordinator has decided to select a random sample of 125 apartments and determine for each whether children are permitted. Let p be the
The amount of shaft wear after a fixed mileage was determined for each of seven randomly selected internal combustion engines, resulting in a mean of 0.0372 inch and a standard deviation of 0.0125 inch.a. Assuming that the distribution of shaft wear is normal, test at level .05 the hypotheses H0:
Optical fibers are used in telecommunications to transmit light. Suppose current technology allows production of fibers that transmit light about 50 km. Researchers are trying to develop a new type of glass fiber that will increase this distance. In evaluating a new fiber, it is of interest to test
Let µ denote the mean diameter for bearings of a certain type. A test of H0: µ = 0.5 versus Ha: µ = 0.5 will be based on a sample of n bearings. The diameter distribution is believed to be normal. Determine the value of b in each of the following cases:a. n = 15, a = .05, σ = 0.02, µ = 0.52b.
In 2006, Boston Scientific sought approval for a new heart stent (a medical device used to open clogged arteries) called the Liberte. This stent was being proposed as an alternative to a stent called the Express that was already on the market. The following excerpt is from an article that appeared
The article “Boy or Girl: Which Gender Baby Would You Pick?” (LiveScience, March 23, 2005, www.livescience.com) summarized the findings of a study that was published in Fertility and Sterility. The LiveScience article makes the following statements: “When given the opportunity to choose the
In a representative sample of 1000 adult Americans, only 430 could name at least one justice who is currently serving on the U.S. Supreme Court (Ipsos, January 10, 2006). Using a significance level of .01, carry out a hypothesis test to determine if there is convincing evidence to support the claim
In a national survey of 2013 adults, 1590 responded that lack of respect and courtesy in American society is a serious problem, and 1283 indicated that they believe that rudeness is a more serious problem than in past years (Associated Press, April 3, 2002). Is there convincing evidence that less
A certain television station has been providing live coverage of a particularly sensational criminal trial. The station’s program director wishes to know whether more than half the potential viewers prefer a return to regular daytime programming. A survey of randomly selected viewers is
Students at the Akademia Podlaka conducted an experiment to determine whether the Belgium-minted Euro coin was equally likely to land heads up or tails up. Coins were spun on a smooth surface, and in 250 spins, 140 landed with the heads side up (New Scientist, January 4, 2002). Should the students
An article titled “Teen Boys Forget Whatever It Was” appeared in the Australian newspaper The Mercury (April 21, 1997). It described a study of academic performance and attention span and reported that the mean time to distraction for teenage boys working on an independent task was 4 minutes.
The authors of the article “Perceived Risks of Heart Disease and Cancer Among Cigarette Smokers” (Journal of the American Medical Association [1999]: 1019–1021) expressed the concern that a majority of smokers do not view themselves as being at increased risk of heart disease or cancer. A
A number of initiatives on the topic of legalized gambling have appeared on state ballots. Suppose that a political candidate has decided to support legalization of casino gambling if he is convinced that more than two thirds of U.S. adults approve of casino gambling. Suppose that 1523 adults
Although arsenic is known to be a poison, it also has some beneficial medicinal uses. In one study of the use of arsenic to treat acute promyelocytic leukemia (APL), a rare type of blood cell cancer, APL patients were given an arsenic compound as part of their treatment. Of those receiving arsenic,
Many people have misconceptions about how profitable small, consistent investments can be. In a survey of 1010 randomly selected U.S. adults (Associated Press, October 29, 1999), only 374 responded that they thought that an investment of $25 per week over 40 years with a 7% annual return would
The same survey described in the previous exercise also asked the individuals in the sample what they thought was their best chance to obtain more than $500,000 in their lifetime. Twenty-eight percent responded “win a lottery or sweepstakes.” Does this provide convincing evidence that more than
Speed, size, and strength are thought to be important factors in football performance. The article “Physical and Performance Characteristics of NCAA Division I Football Players” (Research Quarterly for Exercise and Sport [1990]: 395–401) reported on physical characteristics of Division I
Duck hunting in populated areas faces opposition on the basis of safety and environmental issues. In a survey to assess public opinion regarding duck hunting on Morro Bay (located along the central coast of California), a random sample of 750 local residents included 560 who strongly opposed
Past experience has indicated that the true response rate is 40% when individuals are approached with a request to fill out and return a particular questionnaire in a stamped and addressed envelope. An investigator believes that if the person distributing the questionnaire is stigmatized in some
An automobile manufacturer who wishes to advertise that one of its models achieves 30 mpg (miles per gallon) decides to carry out a fuel efficiency test. Six nonprofessional drivers are selected, and each one drives a car from Phoenix to Los Angeles. The resulting fuel efficiencies (in miles per
A student organization uses the proceeds from a particular soft-drink dispensing machine to finance its activities. The price per can had been $0.75 for a long time, and the average daily revenue during that period had been $75.00. The price was recently increased to $1.00 per can. A random sample
A hot tub manufacturer advertises that with its heating equipment, a temperature of 100-F can be achieved on average in 15 minutes or less. A random sample of 25 tubs is selected, and the time necessary to achieve a 100-F temperature is determined for each tub. The sample mean time and sample
Consider two populations for which µ1 = 30, σ1 = 2, µ2 = 25, and σ2 = 3. Suppose that two independent random samples of sizes n1 = 40 and n2 = 50 are selected. Describe the approximate sampling distribution of x̅1 x̅2 (center, spread, and shape).

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