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inferential statistics
Intro Stats 6th Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions
Streams In Chapter 6, Exercise 25, we looked at collected samples of water from streams in the Adirondack Mountains to investigate the effects of acid rain. Researchers measured the pH (acidity) of the water and classified the streams with respect to the kind of substrate (type of rock over which
Reading 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
Egyptians 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
Cereal sugar 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
New construction The 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, dƒ = 197.8.) Here are the summaries and boxplots of the
View of the water 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 boxplots of the two groups of prices:Construct and interpret a 95% confidence interval for
Pulse rates 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 boxplots and summarized below.a) What do the boxplots suggest about differences between male and female pulse rates?b) Is it
Commuting 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
CPMP and word problems 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?
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?
Stereograms In Exercises 49 and 50, Chapter 4, we looked at data from an experiment to determine whether visual information about an image helped people “see” the image in 3D.2-Sample t-Interval for m1 - m2 Conf level= 90% df = 70 m(NV) - m(VV) interval: (0.55, 5.47)a) Interpret your interval
Learning math 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
Still riding In Exercise 54 we saw a 90% confidence interval of(-$2.12, -$0.87) for the difference in mean taxi trip payments, mweekend - mweekday. Explain why each of the following statements is true or false:a) 90% of weekend taxi rides are between $0.87 and $2.12 more expensive than weekday
Hot dogs, last one In Exercise 53, we saw a 90% confidence interval of ( -6.5, -1.4) grams for mMeat - mBeef , 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,
Another ride Another variable in the Chicago taxi data reports the total paid for the ride. A 90% confidence interval for the difference mweekend - mweekday is -$2.12 to -$0.87.a) The endpoints of this confidence interval are negative numbers. What does that indicate?b) What does the fact that the
Hot dogs, second helping 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 mMeat - mBeef is ( -6.5, -1.4).a) The endpoints of this confidence interval are negative numbers.
Chicago taxi Chicago’s Department of Business Affairs and Consumer Protection provides monthly reports of all taxi trips in Chicago, tagged with trip distances, trip durations, fare amounts, and tip amounts. The dataset Chicago taxi holds data on 13,082 taxi trips for which the duration exceeded
Hot dogs 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 beef hot dogs. A
Fast food 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
Food preference 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
Carbs 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.
Sensitive men 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
Stay-at-home dads A 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
Convention bounce 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 2020 political conventions, Joe Biden’s net favorability (% favorable - % unfavorable)
Gender gap 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
Pain 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, then administered the pain killers.Of the 112 people in the group who received
Mammograms redux A 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. (The New York Times, Dec. 9, 2001)a) Do these results support
Mammograms 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
Politics and sex 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
Birthweight 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
Depression 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
Teen smoking 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
Anorexia again 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. (Answer these questions without actually doing the test.)a) What hypotheses would you test?b) State a
Another ear infection 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. (Answer these questions without actually doing the test.)a) What hypotheses would you test?b)
Anorexia 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
Ear infections 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
COVID and blood type In Chapter 3 we saw evidence that a person’s blood type (A, B, AB, O) may predict their susceptibility to the Corona virus that causes COVID-19. Researchers found that the proportion of blood group O in patients with COVID-19 was 25.80% (458 patients) among 1775 patients as
Prostate cancer 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
Carpal tunnel The painful wrist condition called carpal tunnel syndrome can be treated with surgery or, less invasively, with 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
Pets 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
Graduation 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 they had
Arthritis 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 535 of 1062 women suffered from some form of arthritis.a) Are the assumptions and conditions necessary for inference satisfied? Explain.b)
Buy it again? 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
Gender gap 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
Regulating access When a random sample of 935 parents were asked about rules in their homes, 77% said they had rules about the kinds of TV shows their children could watch. Among the 790 of those parents whose teenage children had Internet access, 85% had rules about the kinds of Internet sites
Revealing information Eight hundred eighty-six randomly sampled teens were asked which of several personal items of information they thought it ok to share with someone they had just met. Forty-four percent said it was ok to share their e-mail addresses, but only 29% said they would give out their
Conspiracy theory In the same study as cited in Exercise 21, Pew found that 16% of respondents who get their news primarily from network TV had heard about the (false) conspiracy theory that powerful people intentionally planned the coronavirus outbreak. By contrast, 26% of those who get their news
Social media In a study in 2020, the Pew Research Center on Journalism & Media surveyed 9220 U.S. adults and found that 18%, or about 1660 respondents, said that their most common way to get political and election news was social media. They were compared to the 16%–about 1475—respondents who
Athletes, extra innings Looking back at Exercise 12, instead of comparing the ages of players in Major League Baseball to play
Cost of shopping, once more 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 t-test be a
Athlete ages, overtime 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?
Cost of shopping, yet again 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?
Athlete ages, ninth inning The researchers in Exercise 12 decide to test the hypothesis. The degrees of freedom formula gives 51.83 df. Test the null hypothesis at a = 0.05. Is the alternative one- or two-sided?
Cost of shopping, once more 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 a = 0.05.
Athlete ages, again Using the summary statistics provided in Exercise 12, the sports reporter calculated the following 95%confidence interval for the mean difference between major league baseball players and professional football players. The 95% interval for mMLB - mNFL was ( -0.41, 3.09).
Cost of shopping, again Using the summary statistics provided in Exercise 11, researchers calculated a 95% confidence interval for the mean difference between Walmart and Target purchase amounts. The interval was ( - +14.15, - +1.85).Explain in context what this interval means.
Athlete ages 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. Using data from sports.yahoo.com, one player was selected
Cost of shopping 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
Non-profits test Complete the analysis begun in Exercise 2.a) What is the difference in the proportions of the two types of companies?b) What is the value of the z-statistic?c) What do you conclude at a = 0.05?
Canada, test The researchers from Exercise 1 want to test if the proportions of foreign born are the same in the United States and Canada. What is the appropriate standard error to use for the hypothesis test?a) What is the difference in the proportions of foreign born residents in both
Non-profits, again 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.
Canada, encore If the information in Exercise 1 is to be used to make inferences about the proportion all Canadians and all U.S. citizens born in other countries, what conditions must be met before proceeding? Are they met? Explain.
Non-profits, part 3 For the interval given in Exercise 4, explain what “95% confidence” means.
Canada, trois For the interval given in Exercise 3, explain what “95% confidence” means.
Non-profits, part 2 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
Canada, deux The information in Exercise 1 was used to create a 95% two-proportion confidence interval for the difference between Canadians and U.S. citizens who were born in foreign countries. Interpret this interval with a sentence in context.95% confidence interval for pCanadians - pAmericans is
Non-profits 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
Canada 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 U.S. citizens reported being foreign-born. Find the standard error of the difference in sample proportions.
Exam time The professor of a large math class estimates that at the intended level of difficulty, his undergraduate midterm exams require on average 10 minutes for graduate students in his department to complete. If the average is longer than 10 minutes, then the exam is likely too hard and needs
Redesigned packaging A company that sells cookies decided to redesign their packaging with brighter colors with the hope of improving sales. They chose a random sample of 50 stores to pilot the new packaging, which holds the same amount of product at the same price point as before.Over the period
Door prize You are among 100 people attending a charity fundraiser at which a large-screen TV will be given away as a door prize. To determine who wins, 99 white balls and 1 red ball have been placed in a box and thoroughly mixed.The guests will line up and, one at a time, pick a ball from the box.
Recalls In a car rental company’s fleet, 70% of the cars are American brands, 20% are Japanese, and the rest are German.The company notes that manufacturers’ recalls seem to affect 2% of the American cars, but only 1% of the others.a) What’s the probability that a randomly chosen car is
Batteries We work for the “Watchdog for the Consumer”consumer advocacy group. We’ve been asked to look at a battery company that claims its batteries last an average of 100 hours under normal use. There have been several complaints that the batteries don’t last that long, so we decide to
And it means? Every statement about a confidence interval contains two parts—the level of confidence and the interval.Suppose that an insurance agent estimating the mean loss claimed by clients after home burglaries created the 95%confidence interval ($1644, $2391).a) What’s the margin of error
Fritos® As a project for an Introductory Statistics course, students checked 6 bags of Fritos marked with a net weight of 35.4 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 35.5, 35.3, 35.1, 36.4, 35.4, 35.5. Is there evidence that the mean
Bread Clarksburg Bakery is trying to predict how many loaves to bake. In the past 100 days, the bakery has sold between 95 and 140 loaves per day. Here are a histogram and the summary statistics for the number of loaves sold for the past 100 days.a) Can you use these data to estimate the number of
Skin cancer In February 2012, MedPage Today reported that researchers used vemurafenib to treat metastatic melanoma (skin cancer). Out of 152 patients, 53% had a partial or complete response to vemurafenib.a) Write a 95% confidence interval for the proportion helped by the treatment, and interpret
Streams Researchers in the Adirondack Mountains collect data on a random sample of streams each year. One of the variables recorded is the substrate of the stream—the type of soil and rock over which they flow. The researchers found that 69 of the 172 sampled streams had a substrate of shale.
Occupy Wall Street In 2011, the Occupy Wall Street movement protested the concentration of wealth and power in the United States. A 2012 University of Delaware survey asked a random sample of 901 American adults whether they agreed or disagreed with the following statement:The Occupy Wall Street
Meals A college student is on a “meal program.” His budget allows him to spend an average of $10 per day for the semester. He keeps track of his daily food expenses for 2 weeks; the data are given in the table below. Is there strong evidence that he will overspend his food allowance?Explain.
Petitions To get a voter initiative on a state ballot, petitions that contain at least 250,000 valid voter signatures must be filed with the Elections Commission. The board then has 60 days to certify the petitions. A group wanting to create a statewide system of universal health insurance has just
Speeding A newspaper report in August 2002 raised the issue of racial bias in the issuance of speeding tickets. The following facts were noted:◆◆ Sixteen percent of drivers registered in New Jersey are black.◆◆ Of the 324 speeding tickets issued in one month on a 65-mph section of the New
Women The U.S. Census Bureau reports that 36% of all U.S. businesses are owned by women (www.entrepreneur.com/article/252048). A Colorado consulting firm surveys a random sample of 410 businesses in the Denver area and finds that 164 of them have women owners. Should the firm conclude that its area
Dropouts One study comparing various treatments for the eating disorder anorexia nervosa initially enlisted 198 subjects, but found overall that 105 failed to complete their assigned treatment programs. Construct and interpret an appropriate confidence interval. Discuss any reservations you have
Name recognition, part II The advertising company described in Exercise R4.39 is thinking about signing a WNBA star to an endorsement deal. In its poll, 27% of the respondents could identify her.a) Fans who never took statistics can’t understand why the company did not offer this WNBA player an
Name recognition An advertising agency won’t sign an athlete to do product endorsements unless it is sure the person is known to more than 25% of its target audience. The agency always conducts a poll of 500 people to investigate the athlete’s name recognition before offering a contract.Then it
Grade inflation In 1996, 20% of all students at a major university had an overall grade point average of 3.5 or higher (on a scale of 4.0). In 2012, a random sample of 1100 student records found that 25% had a GPA of 3.5 or higher. Is this evidence of grade inflation?
Approval 2016 President Obama was very popular at the end of his eight years in office. A CNN/ORC poll of 1000 U.S. adults conducted in the week before the end of his term found that 63% of Americans said they held a favorable view of the President
Power We are replicating an experiment. How will each of the following changes affect the power of our test?Indicate whether it will increase, decrease, or remain the same, assuming that all other aspects of the situation remain unchanged.a) We increase the number of subjects from 40 to 100.b) We
Fried PCs A computer company recently experienced a disastrous fire that ruined some of its inventory. Unfortunately, during the panic of the fire, some of the damaged computers were sent to another warehouse, where they were mixed with undamaged computers. The engineer responsible for quality
Safety Observers in Texas watched children at play in eight communities. Of the 814 children seen biking, roller skating, or skateboarding, only 14% wore a helmet.a) Create and interpret an appropriate 95% confidence interval.b) What concerns do you have about this study that might make your
Pregnant? Suppose that 70% of the women who suspect they may be pregnant and purchase an in-home pregnancy test are actually pregnant. Further suppose that the test is 98% accurate. What’s the probability that a woman whose test indicates that she is pregnant actually is?
Errors An auto parts company advertises that its special oil additive will make the engine “run smoother, cleaner, longer, with fewer repairs.” An independent laboratory decides to test part of this claim. It arranges to have a taxicab company’s fleet of cars use the additive, and follows
Alcohol abuse Growing concern about binge drinking among college students has prompted one large state university to conduct a survey to assess the size of the problem on its campus. The university plans to randomly select students and ask how many have been drunk during the past week. If the
Dogs A census by the county dog control officer found that 18% of homes kept one dog as a pet, 4% had two dogs, and 1% had three or more. If a salesman visits two homes selected at random, what’s the probability he encountersa) no dogs?b) some dogs?c) dogs in each home?d) more than one dog in
Teen smoking 2015 The Centers for Disease Control and Prevention reports that 9.3% of surveyed high school students reported in 2015 that they had smoked cigarettes in the past 30 days. A college has 522 students in its freshman class.How likely is it that more than 10% of them are smokers?
Religion 2014 The 2014 U.S. Religious Landscape Study interviewed more than 35,000 Americans from all 50 states about their beliefs and the role of religion in their lives. The fastest-growing group is the 22.8% who are “Nones”—those who are not affiliated with any organized religion or have
Language Neurological research has shown that in about 80% of people language abilities reside in the brain’s left side. Another 10% display right-brain language centers, and the remaining 10% have two-sided language control.(The latter two groups are mainly left-handers.) (Science News, 161, no.
Cheating A Rutgers University study found that many high school students cheat on tests. The researchers surveyed a random sample of 4500 high school students nationwide;74% of them said they had cheated at least once.a) Create a 90% confidence interval for the level of cheating among high school
Largemouth bass Organizers of a fishing tournament believe that the lake holds a sizable population of largemouth bass. They assume that the weights of these fish have a model that is skewed to the right with a mean of 3.5 pounds and a standard deviation of 2.2 pounds.a) Explain why a skewed model
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