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inferential statistics
Intro Stats 6th Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions
Injuries Exercise 33 describes an experiment that studies hamstring injuries. Describe a strategy to randomly assign injured athletes to the two exercise programs. What should be done if one of the athletes prefers the other program?
Insomnia, at last Exercises 24, 36, and 38 describe an experiment investigating the effectiveness of exercise in combating insomnia. Suppose some of the 40 subjects had maintained a healthy weight, but others were quite overweight. Why might researchers choose to block the subjects by weight level
Omega-3, finis Exercises 21, 35, and 37 describe an experiment investigating the effectiveness of omega-3 fats in treating bipolar disorder. Suppose some of the 30 subjects were very active people who walked a lot or got vigorous exercise several times a week, while others tended to be more
Insomnia, again Exercises 24 and 36 describe an experiment investigating the effectiveness of exercise in combating insomnia. Researchers randomly assigned half of the 40 volunteers to an exercise program.a) Why was it important to randomize in deciding who would exercise?b) What would be the
Omega-3, revisited Exercises 21 and 35 describe an experiment investigating a dietary approach to treating bipolar disorder. Researchers randomly assigned 30 subjects to two treatment groups, one group taking a high dose of omega-3 fats and the other a placebo.a) Why was it important to randomize
Insomnia Exercise 24 describes an experiment showing that exercise helped people sleep better. The experiment involved other groups of subjects who didn’t exercise. Why didn’t the experimenters just have everyone exercise and see if their ability to sleep improved?
Omega-3 Exercise 21 describes an experiment that showed that high doses of omega-3 fats might be of benefit to people with bipolar disorder. The experiment involved a control group of subjects who received a placebo. Why didn’t the experimenters just give everyone the omega-3 fats to see if they
Pew Research compared respondents to an ordinary 5-day telephone survey with respondents to a 4-month-long rigorous survey designed to generate the highest possible response rate. They were especially interested in identifying any variables for which those who responded to the ordinary survey were
Athletes who had suffered hamstring injuries were randomly assigned to one of two exercise programs. Those who engaged in static stretching returned to sports activity in a mean of 15.2 days faster than those assigned to a program of agility and trunk stabilization exercises. (Journal of
A dog food company wants to compare a new lower-calorie food with their standard dog food to see if it’s effective in helping inactive dogs maintain a healthy weight. They have found several dog owners willing to participate in the trial.The dogs have been classified as small, medium, or large
Some people claim they can get relief from migraine headache pain by drinking a large glass of ice water. Researchers plan to enlist several people who suffer from migraines in a test. When a participant experiences a migraine headache, they will take a pill that may be a standard pain reliever or
In 2019, a group of researchers examined data on about 2300 2- to 5-year-olds born between 2003 and 2006 in the United States, to study whether children whose mothers had a fever or infection during their pregnancy were more likely to be autistic. The children’s autism status was determined by
Researchers compared the rate of stillbirths at St. George’s University Hospital in London between October 2019 through January 2020 (the pre-pandemic period) and February 2020 through mid-June 2020 (pandemic period), with about 1700 births in each group. Researchers found that the rate of
They found no evidence of benefits associated with the compound.
Scientists at a major pharmaceutical firm investigated the effectiveness of an herbal compound to treat the common cold. They exposed each subject to a cold virus, then gave him or her either the herbal compound or a sugar solution known to have no effect on colds. Several days later, they assessed
The subjects above the age of 38 showed improved vision after the two weeks were over, relative to their vision at the baseline before treatment.
Over a 2-week period, 24 subjects between the ages of 28 and 72 were asked to look into a small red LED light for 3 minutes per day. There were 12 subjects above the age of 38, and 12 subjects at or below the age of
Medical records showed that they had heightened concentrations of dioxin in their blood and that each tenfold increase in dioxin level was associated with a doubling of the risk of breast cancer. (Science News, Aug. 3, 2002)
Researchers have linked an increase in the incidence of breast cancer in Italy to dioxin released by an industrial accident in 1976. The study identified 981 women who lived near the site of the accident and were under age 40 at the time. Fifteen of the women had developed breast cancer at an
After menopause, some women take supplemental estrogen.There is some concern that if these women also drink alcohol, their estrogen levels will rise too high. Twelve volunteers who were receiving supplemental estrogen were randomly divided into two groups, as were 12 other volunteers not on
Is diet or exercise effective in combating insomnia? Some believe that cutting out desserts can help alleviate the problem, while others recommend exercise. Forty volunteers suffering from insomnia agreed to participate in a month-long test. Half were randomly assigned to a special no-desserts
In a test of roughly 200 men and women, those with moderately high blood pressure (averaging 164/89 mm Hg) did worse on tests of memory and reaction time than those with normal blood pressure. (Hypertension 36 [2000]: 1079)
Among a group of women with disabilities aged 65 and older who were tracked for several years, those who had a vitamin B12 deficiency were twice as likely to suffer severe depression as those who did not. (American Journal of Psychiatry 157[2000]: 715)
Over a 4-month period, among 30 people with bipolar disorder, patients who were given a high dose (10 g/day) of omega-3 fats from fish oil improved more than those given a placebo.(Archives of General Psychiatry 56 [1999]: 407)
Honesty Coffee stations in offices often just ask users to leave money in a tray to pay for their coffee, but many people cheat.Researchers at Newcastle University replaced the picture of flowers on the wall behind the coffee station with a picture of staring eyes. They found that the average
Menopause Researchers studied the herb black cohosh as a treatment for hot flashes caused by menopause. They randomly assigned 351 women aged 45 to 55 who reported at least two hot flashes a day to one of five groups: (1) black cohosh, (2) a multiherb supplement with black cohosh, (3) the multiherb
Super Bowl commercials When spending large amounts to purchase advertising time, companies want to know what audience they’ll reach. In January 2011, a poll asked 1008 American adults whether they planned to watch the upcoming Super Bowl.Men and women were asked separately whether they were
MS and vitamin D Multiple sclerosis (MS) is an autoimmune disease that strikes more often the farther people live from the equator. Could vitamin D—which most people get from the sun’s ultraviolet rays—be a factor? Researchers compared vitamin D levels in blood samples from 150 U.S. military
Heart attacks and height Researchers who examined health records of thousands of males found that men who died of myocardial infarction (heart attack) tended to be shorter than men who did not.a) Is this an experiment? If not, what kind of study is it?b) Is it correct to conclude that shorter men
Standardized test scores For his statistics class experiment, researcher J. Gilbert decided to study how parents’ income affects children’s performance on standardized tests like the SAT. He proposed to collect information from a random sample of test takers and examine the relationship between
Tomatoes finis What factors might confound the results of the experiment in Exercise 4?
Confounded tips For the experiment of Exercise 3, name some confounding variables that might influence the experiment’s results.
Blocking tomatoes To obtain enough plants for the tomato experiment of Exercise 4, experimenters have to purchase plants from two different garden centers. They then randomly assign the plants from each garden center to all three fertilizer treatments. Is the experiment blocked? Is that a good idea?
Block that tip The driver of Exercise 3 wants to know about tipping in general. So he recruits several other drivers to participate in the experiment. Each driver randomly decides whether to phone customers before delivery and records the tip percentage. Is this experiment blocked? Is that a good
More tomatoes If the tomato taster doesn’t know how the tomatoes have been treated, is the experiment single- or double-blind? How might the blinding be improved further?
More tips Is the experiment of Exercise 3 blind? Can it be double-blind? Explain.
Tomatoes again For the experiment of Exercise 4, discuss variables that could be controlled or that could not be controlled. Is the experiment randomized and replicated?
Tips again For the experiment of Exercise 3, name some variables the driver did or should have controlled. Was the experiment randomized and replicated?
Tomatoes II For the experiment described in Exercise 4, name the factor and its levels. How might the response be measured?
Tips II For the experiment described in Exercise 3, list the factor, the levels, and the response variable.
Tomatoes You want to compare the tastiness and juiciness of tomatoes grown with three amounts of a new fertilizer: none, half the recommended amount, and the full recommended amount. You allocate 6 tomato plants to receive each amount of fertilizer, assigning them at random. What are the
Tips A pizza delivery driver, always trying to increase tips, runs an experiment on his next 40 deliveries. He flips a coin to decide whether or not to call a customer from his mobile phone when he is five minutes away, hoping this slight bump in customer service will lead to a slight bump in tips.
E-commerce A business student conjectures that the Internet caused companies to become more profitable, since many transactions previously handled “face-to-face” could now be completed online. The student compares earnings from a sample of companies from the 1980s to a sample from the 2000s.
Steroids The 1990s and early 2000s could be considered the steroids era in Major League Baseball, as many players have admitted to using the drug to increase performance on the field.If a sports writer wanted to compare home run totals from the steroids era to an earlier decade, say the 1960s,
More sampling methods Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain.a) We want to know if there is neighborhood support to turn a vacant lot into a playground. We spend a Saturday afternoon going door-to-door in the neighborhood, asking people
Sampling methods Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain.a) We want to know what percentage of local doctors accept Medicaid patients. We call the offices of 50 doctors randomly selected from all Yelp reviews within a 50 mile radius.b) We
Another fish story In recent years, beaches around the world have seen fish washing up on shore in large numbers. One group of scientists thought that leakage from the damaged Fukushima nuclear power plant in Japan might be a cause. They propose to measure the mean amount of radiation in a sample
A fish story Concerned about reports of discolored scales on fish caught downstream from a newly sited chemical plant, scientists set up a field station in a shoreline public park. For one week, they asked fishers there to bring any fish they caught to the field station for a brief inspection. At
Quality control Sammy’s Salsa, a small local company, produces 20 cases of salsa a day. Each case contains 12 jars and is imprinted with a code indicating the date and batch number.To help maintain consistency, at the end of each day, Sammy selects three jars of salsa, weighs the contents, and
Happy workers? A manufacturing company employs 14 project managers, 48 supervisors, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a sample of employees every month.a) Do you see any
Accounting Between quarterly audits, a company likes to check on its accounting procedures to address any problems before they become serious. The accounting staff processes payments on about 120 orders each day. The next day, the supervisor rechecks 10 of the transactions to be sure they were
Fuel economy Occasionally, when I fill my car with gas, I figure out how many miles per gallon my car got. I wrote down those results after six fill-ups in the past few months. Overall, it appears my car gets 28.8 miles per gallon.a) What statistic have I calculated?b) What is the parameter I’m
Arm length How long is your arm compared with your hand size? Put your right thumb at your left shoulder bone, stretch your hand open wide, and extend your hand down your arm. Put your thumb at the place where your little finger is, and extend down the arm again. Repeat this a third time. Now your
Cell phone survey What about drawing a random sample only from cell phone numbers? Discuss the advantages and disadvantages of such a sampling method compared with surveying randomly generated telephone numbers from non–cell phone numbers. Do you think these advantages and disadvantages have
Phone surveys Anytime we conduct a survey, we must take care to avoid undercoverage. Suppose we plan to select 500 names from the city phone book, call their homes between noon and 4 p.m., and interview whoever answers, anticipating contacts with at least 200 people.a) Why is it difficult to use a
More survey questions Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question.a) Do you think high school students should be required to wear uniforms?b) Given humanity’s great tradition of exploration, do you
Survey questions Examine each of the following questions for possible bias. If you think the question is biased, indicate how and propose a better question.a) Should companies that pollute the environment be compelled to pay the costs of cleanup?b) Given that 18-year-olds are old enough to vote and
Banning ephedra An online poll on a website asked:A nationwide ban of the diet supplement ephedra went into effect recently. The herbal stimulant has been linked to 155 deaths and many more heart attacks and strokes. Ephedra manufacturer NVE Pharmaceuticals, claiming that the FDA lacked proof that
Wording the survey Two members of the PTA committee in Exercises 26 and 27 have proposed different questions to ask in seeking parents’ opinions.Question 1: Should elementary school–age children have to pass high-stakes tests in order to remain with their classmates?Question 2: Should schools
Playground, act two The survey described in Exercise 29 asked:Many people believe this playground is too small and in need of repair. Do you think the playground should be repaired and expanded even if that means raising the entrance fee to the park?Describe two ways this question may lead to
Roller coasters An amusement park has opened a new roller coaster. It is so popular that people are waiting for up to 3 hours for a 2-minute ride. Concerned about how patrons (who paid a large amount to enter the park and ride on the rides) feel about this, they survey every 10th person on the line
Playground Some people have been complaining that the children’s playground at a municipal park is too small and is in need of repair. Managers of the park decide to survey city residents to see if they believe the playground should be rebuilt.They hand out questionnaires to parents who bring
Churches For your political science class, you’d like to take a survey from a sample of all the Catholic Church members in your city. A list of churches shows 17 Catholic churches within the city limits. Rather than try to obtain a list of all members of all these churches, you decide to pick 3
Parent opinion, part 2 Let’s revisit the school system described in Exercise 26. Four new sampling strategies have been proposed to help the PTA determine whether parents favor requiring elementary students to pass a test in order to be promoted to the next grade. For each, indicate what kind of
Parent opinion, part 1 In a large city school system with 20 elementary schools, the school board is considering the adoption of a new policy that would require elementary students to pass a test in order to be promoted to the next grade. The PTA wants to find out whether parents agree with this
Another mistaken poll Prior to the mayoral election discussed in Exercise 24, the newspaper also conducted a poll. The paper surveyed a random sample of registered voters stratified by political party, age, sex, and area of residence. This poll predicted that Amabo would win the election with 52%
Mistaken poll A local TV station conducted a “PulsePoll” about the upcoming mayoral election. Evening news viewers were invited to text in their votes, with the results to be announced on the late-night news. Based on the texts, the station predicted that Amabo would win the election with 52%
Milk samples One of our co-authors grew up on a family dairy farm. He notes that to insure the safety of our milk, dairy inspectors visit farms unannounced and take samples of the milk to test for contamination. If the milk is found to contain dirt, antibiotics, or other foreign matter, the milk
Snack foods A company packaging snack foods maintains quality control by randomly selecting 10 cases from each day’s production and weighing the bags sampled from each case. Then they open one bag from each case and inspect the contents.
Roadblock State police set up a roadblock to estimate the percentage of cars with up-to-date registration, insurance, and safety inspection stickers. They usually find problems with about 10% of the cars they stop.
Soil samples The Environmental Protection Agency took soil samples at 16 locations near a former industrial waste dump and checked each for evidence of toxic chemicals. They found no elevated levels of any harmful substances.
Mayoral race Hoping to learn what issues may resonate with voters in the coming election, the campaign director for a mayoral candidate selects one block from each of the city’s election districts. Staff members go there and interview all the adult residents they can find.
Social life A question posted on the gamefaqs.com website asked visitors to the site, “Do you have an active social life outside the Internet?” 22% of the 55,581 respondents said “No” or“Not really, most of my personal contact is online.”
Medical treatments Consumers Union asked all subscribers whether they had used alternative medical treatments and, if so, whether they had benefited from them. For almost all of the treatments, approximately 20% of those responding reported cures or substantial improvement in their condition.
Satisfaction survey A social platform wants to understand how satisfied its users are. On the first week of each month, a random sample of its users will see a banner invitation to rate the platform on a 5-point scale after logging in. Because the users on the platform consist of 20% teenagers
Domoic acid in crabs Domoic acid—a neurotoxin that is lethal in large quantities—can be found in California’s Dungeness crabs. In order to assess the risk level, the state’s health department measures domoic acid concentrations in locally caught crabs in 7 major ports across the state. The
Gallup At its website (www.gallup.com), the Gallup Poll publishes results of a new survey each day. Scroll down to the end, and you’ll find a statement that includes words such as these:Results are based on telephone interviews with 1016 national adults, aged 18 and older, conducted March 7–10,
Drug tests Major League Baseball tests players to see whether they are using performance-enhancing drugs. Officials select a team at random, and a drug-testing crew shows up unannounced to test all 40 players on the team. Each testing day can be considered a study of drug use in Major League
Surveying employees The company of Exercise 2 is considering ways to survey their employees. For each of these proposed designs, identify the problem.a) Leave a stack of surveys out in the employee cafeteria so people can pick them up and return them.b) Stuff a questionnaire in the mailbox of each
Student samples The university administration of Exercise 1 is considering a variety of ways to sample students for a survey.For each of these proposed survey designs, identify the problem.a) Publish an advertisement inviting students to visit a website and answer questions.b) Set up a table in the
Happy employees The company plans to have the head of each corporate division hold a meeting of their employees to ask whether they are happy on their jobs. They will ask people to raise their hands to indicate whether they are happy. What problems do you see with this plan?
Survey students What problems do you see with asking the following question of students? “Are you the first member of your family to seek higher education?”
Satisfactory satisfaction samples For each scenario, determine the sampling method used by the managers from Exercise 2.a) Use the company e-mail directory to contact 150 employees from among those employed for less than 5 years, 150 from among those employed for 5–10 years, and 150 from among
Sampling A&M students For each scenario, identify the kind of sample used by the university administrators from Exercise 1:a) Select several dormitories at random and contact everyone living in the selected dorms.b) Using a computer-based list of registered students, contact 200 freshmen, 200
Sampling satisfaction A company hoping to assess employee satisfaction surveys employees by assigning computer-generated random numbers to each employee on a list of all employees and then contacting all those whose assigned random number is divisible by 7. Is this a simple random sample?
Sampling students A professor teaching a large lecture class of 350 students samples her class by rolling a die. Then, starting with the row number on the die (1 to 6), she passes out a survey to every fourth row of the large lecture hall. She says that this is a Simple Random Sample because
Satisfied respondents The company’s annual report states,“Our survey shows that 87.34% of our employees are ‘very happy’ working here.” Comment on that claim. Use appropriate statistics terminology.
A&M again The president of the university plans a speech to an alumni group. He plans to talk about the proportion of students who responded in the survey that they are the first in their family to attend college, but the first draft of his speech treats that proportion as the actual proportion of
Satisfied workers The managers of a large company wished to know the percentage of employees who feel “extremely satisfied”to work there. The company has roughly 24,000 employees. They contacted a random sample of employees and asked them about their job satisfaction, obtaining 437 completed
Texas A&M Administrators at Texas A&M University were interested in estimating the percentage of students who are the first in their family to go to college. The A&M student body has about 46,000 members. How might the administrators answer their question by applying the three Big Ideas of sampling?
Doctors and life expectancy and TVs Chapter 8 looked at the data on life expectancy in different countries as they related to the (square root of the) number of doctors and to the (square root of the) number of TVs. Here’s a regression using both variables to predict life expectancy,
Penguins again In Chapter 8 we learned about the extraordinary depth and duration of the dives taken by penguins.In that chapter we modeled a re-expression of Heart rate with the Duration (min) of dives. The data also include the depth of each dive. Here is an analysis that incorporates both
Real estate, bedrooms For the real estate data of the previous exercise, consider the value of the number of bedrooms in modeling the price of a home. The correlation between Price and Bedrooms is 0.116. Here is a regression model:a) What is a correct interpretation of the coefficient of
Real estate, bathrooms As a class project, students in a large statistics class collected publicly available information on recent home sales in their hometowns. There are 894 properties.Important predictors of the price of a home are its living area(sq ft) and the number of bathrooms. In fact, the
Companies’ assets and sales How are the assets and sales of major corporations related? The dataset is the same as that for Exercise 2.44. The variable Banks in the dataset is 1 for the banks and 0 for the other companies.As Exercise 2.44 showed, it is best to take the logarithm of most of these
Chips A start-up company has developed an improved electronic chip for use in laboratory equipment. The company needs to project the manufacturing cost, so it develops a spreadsheet model that takes into account the purchase of production equipment, overhead, raw materials, depreciation,
Down the drain Most water tanks have a drain plug so that the tank may be emptied when it’s to be moved or repaired.How long it takes a certain size of tank to drain depends on the size of the plug, as shown in the table. Create a model.
Companies How are a company’s profits related to its sales? Let’s examine data from 71 large U.S. corporations.All amounts are in millions of dollars.a) Histograms of Profits and Sales and histograms of the logarithms of Profits and Sales are seen below. Why are the re-expressed data better for
Vehicle weights The Minnesota Department of Transportation hoped that they could measure the weights of big trucks without actually stopping the vehicles by using a newly developed “weigh-in-motion” scale. After installation of the scale, a study was conducted to find out whether the scale’s
Williams vs. Texas 2020 Here are the average weights of the football team for the University of Texas for various years.a) Fit a straight line to the relationship of Weight by Year for Texas football players.b) According to these models, in what year will the predicted weight of the Williams
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