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Stats Data And Models 4th Edition Richard D. De Veaux, Paul D. Velleman, David E. Bock - Solutions

A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair shop has
Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items produced. If they find a significant increase in the proportion of items that must be rejected, they will halt the
As in Exercise 33, state regulators are checking up on repair shops to see if they are certifying vehicles that do not meet pollution standards. a) In this context, what is meant by the power of the test the regulators are conducting? b) Will the power be greater if they test 20 or 40 cars? Why? c)
Consider again the task of the quality control inspectors in Exercise 34. a) In this context, what is meant by the power of the test the inspectors conduct? b) They are currently testing 5 items each hour. Someone has proposed that they test 10 instead. What are the advantages and disadvantages of
A company is sued for job discrimination because only 19% of the newly hired candidates were minorities when 27% of all applicants were minorities. Is this strong evidence that the company's hiring practices are discriminatory? a) Is this a one-tailed or a two-tailed test? Why? b) In this context,
Highway safety engineers test new road signs, hoping that increased reflectivity will make them more visible to drivers. Volunteers drive through a test course with several of the new- and old-style signs and rate which kind shows up the best. a) Is this a one-tailed or a two-tailed test? Why? b)
A Statistics professor has observed that for several years’ students score an average Of 105 points out of 150 on the semester exam. A salesman suggests that he try a statistics software package that gets students more involved with computers, predicting that will increase students' scores. The
Which of the following are true? If false, explain briefly. a) A very low P-value provides evidence against the null hypothesis. b) A high P-value is strong evidence in favor of the null hypothesis. c) A P-value above 0.10 shows that the null hypothesis is true. d) If the null hypothesis is true,
A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 20% of the residents of the city have heard the ad and recognize the company's product. The radio station conducts a random phone survey of 400 people. a) What are the
203 students signed up for the Stats course ‘in Exercise 39. They used the software suggested by the salesman, and scored an average of 108 points on the final with a standard deviation of 8.7 points. a) Should the professor spend the money for this software? Support your recommendation with an
The company in Exercise 40 contacts 600 people selected at random, and only 133 remember the ads a) Should the company renew the contract? Support your recommendation with an appropriate test. b) Explain what your P-value means in this context.
The manufacturer of a metal stand for home TV sets must be sure that its product will not fail under the weight of the TV. Since some larger sets weigh nearly 300 pounds, the company's safety inspectors have set a standard of ensuring that the stands can support an average of over 500 pounds. Their
During an angiogram, heart problems can be examined via a small tube (a catheter) threaded into the heart from a vein in the patient's leg. It's important that the company that manufactures the catheter maintain a diameter of 2.00 mm. (The standard deviation is quite small.) Each day, quality
The manufacturer of the metal TV stands in Exercise 43 is thinking of revising its safety test. a) If the company's lawyers are worried about being sued for selling an unsafe product, should they increase or decrease the value of a? Explain. b) In this context, what is meant by the power of the
The catheter company in Exercise 44 is reviewing its testing procedure. a) Suppose the significance level is changed to ( = 0.01. Will the probability of a Type II error increase, decrease, or remain the same? b) What is meant by the power of the test the company conducts? c) Suppose the
In a drawer are two coins. They look the same, but one coin produces heads 90% of the time when spun while the other one produces heads only 30% of the time. You select one of the coins. You are allowed to spin it once and then must decide whether the coin is the 90%- or the 30%-head coin. Your
You are in charge of shipping computers to customers. You learn that a RAM chip was put into some of the machines. There's a simple test you can perform, but it's not perfect. All but 4% of the time, a good chip passes the test, but unfortunately, 35% of the bad chips pass the test, too. You have
A basketball player with a poor foul-shot record practices intensively during the off-season. He tells the coach that he has raised his proficiency from 60% to 80%. Dubious, the coach asks him to take 10 shots, and is surprised when the player hits 9 out of 10. Did the player prove that he has
For each of the following, write out the null and alternative hypotheses, being sure to state whether the alternative is one-sided or two-sided. a) A company reports that last year, 40% of their reports in accounting were on time. From a random sample this year, they want to know if that proportion
An artist experimenting with clay to create pottery with a special texture has been experiencing difficulty with these special pieces. About 40% break in the kiln during firing. Hoping to solve this problem, she buys some more expensive clay from another supplier. She plans to make and fire 10
For each of the following, write out the alternative hypothesis, being sure to indicate whether it is one-sided or two-sided. a) Consumer Reports discovered that 20% of a certain computer model had warranty problems over the first three months. From a random sample, the manufacturer wants to know
Which of the following statements are true? If false, explain briefly. a) Using an alpha level of 0.05, a P-value of 0.04 results in rejecting the null hypothesis. b) The alpha level depends on the sample size. c) With an alpha level of 0.01, a P-value of 0.10 results in rejecting the null
Which of the following statements are true? If false, explain briefly. a) It is better to use an alpha level of 0.05 than an alpha level of 0.01. b) If we use an alpha level of 0.01, then a P-value of 0.001 is statistically significant. c) If we use an alpha level of 0.01, then we reject the null
For each of the following situations find the critical value(s) for z or t. a) Ho: p = 0.5 vs. HA: p ≠ 0.5 at ( = 0.05. b) Ho: p = 0.4 vs. HA: p > 0.4 at ( = 0.05. c) Ho:( = 10 vs. HA: ( ≠ 10 at ( = 0.05; n = 36. d) Ho: p = 0.5 vs. HA: p > 0.5 at ( = 0.01; n = 345. e) Ho: ( = 20 vs. HA: ( <
Suppose an advocacy organization surveys 960 Canadians and 192 of them reported being born in another country (www.unitednorthamerica.org/simdiff.htm). Similarly, 170 out of 1250 Americans reported being foreign-born. Find the standard error of the difference in sample proportions.
The researchers from Exercise 2 want to test if the proportions of satisfied employees are the same at for-profit companies as at not-for-profit companies. In Exercise 2 Data collected from 422 employees at non-profit organizations revealed that 377 of them were "highly satisfied." From the
Do consumers spend more on a trip to Walmart or Target? Suppose researchers interested in this question collected a systematic sample from 85 Walmart customers and 80 Target customers by asking customers for their purchase amount as they left the stores. The data collected are summarized in the
A sports reporter suggests that professional baseball players must be, on average, older than professional football players, since football is a contact sport and players are more susceptible to concussions and serious injuries (www.sports.yahoo.com). One player was selected at random from each
The researchers in Exercise 11 decide to test the hypothesis that the means are equal. The degrees of freedom formula gives 162.75 df. Test the null hypothesis at ( = 0.05.In Exercise 11
The researchers in Exercise 12 decide to test the hypothesis. The degrees of freedom formula gives 51.83 df. Test the null hypothesis at ( = 0.05. Is the alternative one or two-sided?In Exercise 12
Repeat the test you did in Exercise 15, but assume that the variances of purchase amounts are the same at Target and Walmart. Did your conclusion change? Why do you think that is?
Repeat the test you did in Exercise 16, but assume that the variances of ages are the same in the two leagues. Did your conclusion change? Why do you think that is?
Looking back at Exercise 11, instead of comparing two very similar stores, suppose the researchers had compared purchases at two car dealerships: one that specializes in new Italian sports cars and another that carries used domestic vehicles. Would the pooled f-test be a good choice here? Why or
Do people who work for non-profit organizations differ from those who work at for-profit companies when it comes to personal job satisfaction? Separate random samples were collected by a polling agency to investigate the difference. Data collected from 422 employees at non-profit organizations
Looking back at Exercise 12, instead of comparing the ages of players in Major League Baseball to players in the National Football League, what if they had compared the ages in Major League Baseball to a Little League composed of third graders? Would the pooled r-test be a good choice here? Why or
In September 2013, the Pew Internet and American Life Project surveyed American adults on their Face book use. It found that 64% visited the site on a daily basis, up from 51 % in 2010. What does it mean to say that the difference in proportions is "significant"?
At the end of 2013, the Pew Project for Excellence in Journalism investigated where people are getting their news. In the study 22% of people 18-29 years old said they still read newspapers as one of their sources of news, while only 18% of people 30-49 said the same. What does it mean to say that
A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They'll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. Obviously, the staff can't know this, but suppose the
A consumer magazine plans to poll car owners to see if they are happy enough with their vehicles that they would purchase the same model again. They'll randomly select 450 owners of American-made cars and 450 owners of Japanese models. Obviously, the actual opinions of the entire population
The Centers for Disease Control and Prevention reported a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and I 535 of 1062 women suffered from some form of arthritis. a) Are the assumptions and conditions necessary for inference satisfied? Explain. b)
In October 2000, the U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females indicated that
Researchers at the National Cancer Institute released the results of a study that investigated the effect of weed-killing herbicides on house pets. They examined 827 dogs from homes where an herbicide was used on a regular basis, diagnosing malignant lymphoma in 473 of them. Of the 130 dogs from
If the information in Exercise 1 is to be used to make inferences about the proportion all Canadians and all Americans born in other countries, what conditions must be met before proceeding? Are they met? Explain.
The painful wrist condition called carpal tunnel syndrome can be treated with surgery or less invasive wrist splints. Recently, Time magazine reported on a study of 176 patients. Among the half that had surgery, 80% showed improvement after three months, but only 48% of those who used the wrist
There has been debate among doctors over whether surgery can prolong life among men suffering from prostate cancer, a type of cancer that typically develops and spreads very slowly. Recently, The New England Journal of Medicine published results of some Scandinavian research. Men diagnosed with
Data collected in 2013 by the Behavioral Risk Factor Surveillance System revealed that in the state of New Jersey, 14.7% of whites and 18.8% of blacks were cigarette smokers. Suppose these proportions were based on samples of 11,112 whites and 1916 blacks. a) Create a 90% confidence interval for
A new vaccine was recently tested to see if it could prevent the painful and recurrent ear infections that many infants suffer from. The Lancet, a medical journal, reported a study in which babies about a year old were randomly divided into two groups. One group received vaccinations; the other did
The Journal of the American Medical Association reported on an experiment intended to see if the drug Prozac® could be used as a treatment for the eating disorder anorexia nervosa. The subjects, women being treated for anorexia, were randomly divided into two groups. Of the 49 who received Prozac,
In Exercise 33, you used a confidence interval to examine the effectiveness of a vaccine against ear infections in babies. Suppose that instead you had conducted a hypothesis test. a) What hypotheses would you test? b) State a conclusion based on your confidence interval. c) If that conclusion is
In Exercise 34, you used a confidence interval to examine the effectiveness of Prozac in treating anorexia nervosa. Suppose that instead you had conducted a hypothesis test. a) What hypotheses would you test? b) State a conclusion based on your confidence interval. c) If that conclusion is wrong,
A Vermont study published by the American Academy of Pediatrics examined parental influence on teenagers' decisions to smoke. A group of students who had never smoked were questioned about their parents' attitudes toward smoking. These students were questioned again two years later to see if they
A study published in the Archives of General Psychiatry examined the impact of depression on a patient's ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients with no
The Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the 9/11 attack on New York's World Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who were exposed to heavy doses of soot and ash
If the information in Exercise 2 is to be used to make inferences about all people who work at non-profits and for-profit companies, what conditions must be met before proceeding? List them and explain if they are met.
One month before the election, a poll of 630 randomly selected voters showed 54% planning to vote for a certain candidate. A week later, it became known that he had had an extramarital affair, and a new poll showed only 51% of 1010 voters supporting him. Do these results indicate a decrease in
It's widely believed that regular mammogram screening may detect breast cancer early, resulting in fewer deaths from that disease. One study that investigated this issue over a period of 18 years was published during the 1970s. Among 30,565 women who had never had mammograms, 196 died of breast
In 2001, the conclusion of the study outlined in Exercise 41 was questioned. A new 9-year study was conducted in Sweden, comparing 21,088 women who had mammograms with 21,195 who did not. Of the women who underwent screening, 63 died of breast cancer, compared to 66 deaths among the control group.
Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain. They randomly divided these people into two groups, and then administered the pain killers. Of the 112 people in the group who received
Candidates for political office realize that different levels of support among men and women may be a crucial factor in determining the outcome of an election. One candidate finds that 52% of 473 men polled say they will vote for him, but only 45% of the 522 women in the poll express support. a)
Political pundits talk about the "bounce" that a presidential candidate gets after his party's convention. In the past 40 years, it has averaged about 6 percentage points. Just before the 2004 Democratic convention, Rasmussen Reports polled 1500 likely voters at random and found that 47% favored
Time magazine article about a survey of men's attitudes reported that 11 of 161 black respondents and 20 of 358 Latino respondents responded "Yes" to the question "Are you a stay-at-home dad?" How big is the difference in proportions in the two populations? a) Construct and interpret an appropriate
In the same article from Exercise 46, Time magazine, reporting on a survey of men's attitudes, noted that "Young men are more comfortable than older men talking about their problems." The survey reported that 80 of 129 surveyed 18- to 24-year-old men and 98 of 184 25- to 34-year-old men said they
Recently, the Gallup Poll asked 1005 U.S. adults if they actively try to avoid carbohydrates in their diet. That number increased to 27% from 20% in a similar 2002 poll. Is this a statistically significant increase? Explain.
GfK Roper Consulting gathers information on consumer preferences around the world to help companies monitor attitudes about health, food, and healthcare products. They asked people in many different cultures how they felt about the following statement: I have a strong preference for regional or
The global survey we learned about in Exercise 49 also asked respondents how they felt about the statement "I try to avoid eating fast foods." The random sample of 800 included 411 people 35 years old or younger, and of those, 197 agreed (completely or somewhat) with the statement. Of the 389
In the July 2007 issue, Consumer Reports examined the calorie content of two kinds of hot dogs: meat (usually a mixture of pork, turkey, and chicken) and all beef. The researchers purchased samples of several different brands. The meat hot dogs averaged 111.7 calories, compared to 135.4 for the
In the June 2007 issue, Consumer Reports also examined the relative merits of top-loading and front-loading washing machines, testing samples of several different brands of each type. Suppose the study tested the null hypothesis that top- and front-loading machines don't differ in their mean costs,
The Consumer Reports article described in Exercise 51 also listed the fat content (in grams) for samples of beef and meat hot dogs. The resulting 90% confidence interval for µMeat - µBeef is (-6.5, -1.4). a) The endpoints of this confidence interval are negative numbers. What does that
The Consumer Reports article described in Exercise 52 continued their investigation of washing machines. One of the variables the article reported was "cycle time," the number of minutes it took each machine to wash a load of clothes. Among the machines rated good to excellent, the 98% confidence
In Exercise 53, we saw a 90% confidence interval of (-6.5, -1.4) grams for (Meat - (Beef the difference in mean fat content for meat vs. all-beef hot dogs. Explain why you think each of the following statements is true or false: a) If I eat a meat hot dog instead of a beef dog, there's a 90% chance
In Exercise 54, we saw a 98% confidence interval of (-40, -22) minutes for (top - (Front the difference in time it takes top-loading and front-loading washers to do a load of clothes. Explain why you think each of the following statements is true or false: a) 98% of top loaders are 22 to 40 minutes
The Core plus Mathematics Project (CPMP) is an innovative approach to teaching Mathematics that engages students in group investigations and mathematical modeling. After field tests in 36 high schools over a three-year period, researchers compared the performances of CPMP students with those taught
In Exercise 50, Chapter 4, we looked at data from an experiment to determine whether visual information about an image helped "see" the image in 3D. 2-Sample t-interval for (1 - (2 Conf level = 90% df = 70 ((NV) - ((VV) interval: (0.55, 5.47) a) Interpret your interval in context. b) Does it appear
CPMP, again During the study described in Exercise 57, students in both CPMP and traditional classes took another algebra test that did not allow them to use calculators. The table below shows the results. Are the mean scores of the two groups significantly different?Performance on Algebraic
The researchers from Exercise 2 created a 95% two-proportion confidence interval for the difference in those who are "highly satisfied" when comparing people who work at non-profits to people who work at for-profit companies. Interpret the interval with a sentence in context. 95% confidence
The study of the new CPMP Mathematics methodology described in Exercise 57 also tested students' abilities to solve word problems. This table shows how the CPMP and traditional groups performed. (The df are 590.049.) What do you conclude?
A man who moves to a new city sees that there are two routes he could take to work. A neighbor who has lived there a long time tells him Route A will average 5 minutes faster than Route B. The man decides to experiment. Each day, he flips a coin to determine which way to go, driving each route 20
A researcher wanted to see whether there is a significant difference in resting pulse rates for men and women. The data she collected are displayed in the box-plots and summarized in the next column.a) What do the boxplots suggest about differences between male and female pulse rates? b) Is it
How much extra is having a waterfront property worth? A student took a random sample of 170 recently sold properties in Upstate New York to examine the question. Here are her summaries and box plots of the two groups of prices:Construct and interpret a 95% confidence interval for the mean
The sample of 100 house sales we looked at in Exercise 63 also listed whether the home was new construction or not. Find and interpret a 95% confidence interval for how much more an agent can expect to sell a new home for. (From technology, df = 197.8.) Here are the summaries and box plots of the
The data below show the sugar content (as a percentage of weight) of several national brands of children's and adults' cereals Create and interpret a 95% confidence interval for the difference in mean sugar content. Be sure to check the necessary assumptions and conditions. Children's cereals:
Some archaeologists theorize that ancient Egyptians interbred with several different immigrant populations over thousands of years. To see if there is any indication of changes in body structure that might have resulted, they measured 30 skulls of male Egyptians dated from 4000 B.C.E. and 30 others
An educator believes that new reading activities for elementary school children will improve reading comprehension scores. She randomly assigns third graders to an eight-week program in which some will use these activities and others will experience traditional teaching methods. At the end of the
Researchers collected samples of water from streams in the Adirondack Mountains to investigate the effects of acid rain. They measured the pH (acidity) of the water and classified the streams with respect to the kind of substrate (type of rock over which they flow). A lower pH means the water is
The data below show the number of hurricanes (category 3 or higher) recorded annually before and after 1970. Create an appropriate visual display, and determine whether these data are appropriate for testing whether there has been a change in the frequency of hurricanes. 1944-1969 1970-2013 3,
Memory Does ginkgo biloba enhance memory? In an experiment to find out subjects were assigned randomly to take ginkgo biloba supplements or a placebo. Their memory was tested to see whether it improved. Here are boxplots comparing the two groups and in the next column is some computer output from a
American League baseball teams play their games with the designated hitter rule, meaning that pitchers do not bat. The league believes that replacing the pitcher, traditionally a weak hitter, with another player in the batting order produces more runs and generates more interest among fans. Below
Derby In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, ppm) in the drinking
A company institutes an exercise break for its workers to see if this will improve job satisfaction, as measured by a questionnaire that assesses workers' satisfaction. Scores for 10 randomly selected workers before and after implementation of the exercise program are shown. The company wants to
Having done poorly on their math final exams in June, six students repeat the course in summer school, and then take another exam in August. If we consider these students representative of all students who might attend this summer school in other years, explain why you can't use the methods
The Journal of Applied Psychology reported on a study that examined whether the content of TV shows influenced the ability of viewers to recall brand names of items featured in the commercials. The researchers randomly assigned volunteers to watch one of three programs, each containing the same
You are a consultant to the marketing department of a business preparing to launch an ad campaign for a new product. The company can afford to run ads during one TV show, and has decided not to sponsor a show with sexual content. You read the study described in Exercise 75, and then use a computer
Researchers investigated how the size of a bowl affects how much ice cream people tend to scoop when serving themselves. At an "ice cream social," people were randomly given either a 17 oz or a 34 oz bowl (both large enough that they would not be filled to capacity). They were then invited to scoop
Researcher€™s randomly assigned participants either a tall, thin "highball" glass or a short, wide "tumbler," each of which held 355 ml. Participants were asked to pour a shot (1.5 oz = 44.3 ml) into their glass. Did the shape glass make a difference in how much liquid they poured? Here
As we saw in chapter 8, Exercise 40, between 1954 and 2013, swimmers have crossed Lake Ontario 58 times. Both women and men have made the crossing. Here are some plots (we've omitted a crossing by Vikki Keith, who swam a round trip€”North to South to North€”in 3390
Here's some additional information about the Ontario crossing times presented in Exercise 79. It is generally thought to be harder to swim across the lake from north to south. Indeed, this has been done only 5 times. Every one of those crossings was by a woman. If we omit those 5 crossings, the box
In Olympic running events, preliminary heats are determined by random draw, so we should expect that the abilities of runners in the various heats to be about the same, on average. Here are the times (in seconds) for the 400-m women's run in the 2012 Olympics in Lon-don for preliminary heats 2 and
In Exercise 81, we looked at the times in two different heats for the 400-m women's. Is there evidence that balls hit off the Stinger tees would have a higher initial velocity?
Does it matter what kind of tee a golfer places the ball on? The company that manufactures "Stinger" tees claims that the thinner shaft and smaller head will lessen resistance and drag, reducing spin and allowing the ball to travel farther. In August 2003, Golf Laboratories, Inc., compared the
Given the test results on golf tees described in Exercise 83, is there evidence that balls hit off Stinger tees would travel farther? Again, assume that 6 balls were hit off each tee and that the data were suitable for inference.

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