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intro stats
Stats Data And Models 4th Global Edition Richard D. De Veaux, Paul Velleman, David E. Bock - Solutions
Childbirth, part 4 In Exercises 23, 25, and 27, we’ve tested a hypothesis about the impact of epidurals on successful breastfeeding. The following table shows the test’s residualsa) Show how the residual for the epiduralo breastfeeding cell was calculated.b) What can you conclude from the
Does your doctor know? (part 3) In Exercises 24 and 26, we’ve begun to examine whether the use of statistics in NEJM medical articles has changed over time.a) Calculate the component of chi-square for the 1989/No cell.b) For this test, x2 = 25.28. What’s the P-value?c) State your conclusion.
Childbirth, part 3 In Exercises 23 and 25, we’ve begun to examine the possible impact of epidurals on successful breastfeeding.a) Calculate the component of chi-square for the epidural/no breastfeeding cell.b) For this test, x2 = 14.87. What’s the P-value?c) State your conclusion.
Does your doctor know? (part 2) The table in Exercise 24 shows whether NEJM medical articles during various time periods included statistics or not.We’re planning to do a chi-square test.a) How many degrees of freedom are there?b) The smallest expected count will be in the 1989/No cell. What is
Childbirth, part 2 In Exercise 23, the table shows results of a study investigating whether aftereffects of epidurals administered during childbirth might interfere with successful breastfeeding. We’re planning to do a chi-square test.a) How many degrees of freedom are there?b) The smallest
Does your doctor know? A survey7 of articles from the New England Journal of Medicine (NEJM) classified them according to the principal statistics methods used. The articles recorded were all noneditorial articles appearing during the indicated years. Let’s just look at whether these articles
Childbirth, part 1 There is some concern that if a woman has an epidural to reduce pain during childbirth, the drug can get into the baby’s bloodstream, making the baby sleepier and less willing to breastfeed. In December 2006, the International Breastfeeding Journal published results of a study
Lottery numbers The fairness of the South African lottery was recently challenged by one of the country’s political parties. The lottery publishes historical statistics at its website (www.nationallottery.co.za). Here is a table of the number of times each number appeared in the lottery and as
Hurricane frequencies The National Hurricane Center provides data that list the numbers of large (category 3, 4, or 5) hurricanes that have struck the United States, by decade since 1851 (www.nhc.noaa.gov/dcmi.shtml).The data are given below.Recently, there’s been some concern that perhaps the
Pi Many people know the mathematical constant p is approximately 3.14. But that’s not exact.To be more precise, here are 20 decimal places:3.14159265358979323846. Still not exact, though.In fact, the actual value is irrational, a decimal that goes on forever without any repeating pattern. But
Fruit flies Offspring of certain fruit flies may have ebony or yellow bodies and normal wings or short wings.Genetic theory predicts that these traits will appear in the ratio 9:3:3:1 (9 ebony, normal: 3 ebony, short: 3 yellow, normal: 1 yellow, short). A researcher checks 100 such flies and finds
Violence against women 2009 In its study When Men Murder Women: An Analysis of 2009 Homicide Data, 2011, the Violence Policy Center (www.vpc.org) reported that 1818 women were murdered by men in 2009.Of these victims, a weapon could be identified for 1654 of them. Of those for whom a weapon could
NYPD and race Census data for New York City indicate that 29.2% of the under-18 population is white, 28.2%black, 31.5% Latino, 9.1% Asian, and 2% other ethnicities.The New York Civil Liberties Union points out that, of 26,181 police officers, 64.8% are white, 14.5% black, 19.1% Latino, and 1.4%
Mileage A salesman who is on the road visiting clients thinks that, on average, he drives the same distance each day of the week. He keeps track of his mileage for several weeks and discovers that he averages 132 miles on Mondays, 213 miles on Tuesdays, 168 miles on Wednesdays, 180 miles on
Nuts A company says its premium mixture of nuts contains 8% Brazil nuts, 18% cashews, 20% almonds,and 9% hazelnuts, and the rest are peanuts. You buy a large can and separate the various kinds of nuts. On weighing them, you find there are 108 grams of Brazil nuts, 188 grams of cashews, 213 grams of
M&M’s As noted in an earlier chapter, Mars Inc. says that until very recently yellow candies made up 20% of its milk chocolate M&M’s, red another 20%, and orange, blue, and green 10% each. The rest are brown. On his way home from work the day he was writing these exercises, one of the authors
Dice After getting trounced by your little brother in a children’s game, you suspect the die he gave you to roll may be unfair. To check, you roll it 96 times, recording the number of times each face appears. Do these results cast doubt on the die’s fairness?a) If the die is fair, how many
Which test, again? For each of the following situations, state whether you’d use a chi-square goodness-of-fit test, a chi-square test of homogeneity, a chi-square test of independence, or some other statistical test:a) Is the quality of a car affected by what day it was built? A car manufacturer
Which test? For each of the following situations, state whether you’d use a chi-square goodness-of-fit test, a chi-square test of homogeneity, a chi-square test of independence, or some other statistical test:a) A brokerage firm wants to see whether the type of account a customer has (Silver,
Internet use poll, II The same poll as in Exercise 9 also asked the questions“Did you use the Internet yesterday?”and “What is your educational level?” Is the response to the question about the internet independent of educational level? The data follow:a) Under the null hypothesis, what are
Internet use poll A Pew Research poll in April 2009 from a random sample of U.S. adults asked the questions“Did you use the Internet yesterday?” and “Are you White, Black, or Hispanic/Other?” Is the response to the question about the Internet independent of race?The data follow:a) Under the
Customer ages An analyst at a local bank wonders if the age distribution of customers coming for service at his branch in town is the same as at the branch located near the mall. He selects 100 transactions at random from each branch and researches the age information for the associated customer.
Bank cards, again For the customers in Exercise 2,a) If the customers apply for the three cards according to the historical proportions, about how big, on average, would you expect the x2 statistic to be (what is the mean of the x2 distribution)?b) Does the statistic you computed in Exercise 2 seem
Human births, again For the births in Exercise 1,a) If there is no seasonal effect, about how big, on average, would you expect the x2 statistic to be(what is the mean of the x2 distribution)?b) Does the statistic you computed in Exercise 1 seem large in comparison to this mean? Explain briefly.c)
Human births If there is no seasonal effect on human births, we would expect equal numbers of children to be born in each season (winter, spring, summer, and fall).A student takes a census of her statistics class and finds that of the 120 students in the class, 25 were born in winter, 35 in spring,
Birth month may not be related to success as a CEO, but what about on the ball field? It has been proposed by some researchers that children who are the older ones in their class at school naturally perform better in sports and that these children then get more coaching and encouragement. Could
BST II In the experiment about hormone injections in cows described in Exercise 39, a group of 52 Jersey cows increased average milk production from 43 pounds to 52 pounds per day, with a standard deviation of 4.8 pounds. Is this evidence that the hormone may be more effective in one breed than the
Marathon start-up years 2013 When we considered the Boston Marathon in Exercise 37, we were unable to check the Nearly Normal Condition. Here’s a histogram of the differences:The three largest differences are the first three years of wheelchair competition: 1977, 1978, and 1979. Often the
Wheelchair marathon 2013 The Boston Marathon has had a wheelchair division since 1977. Who do you think is typically faster, the men’s marathon winner on foot or the women’s wheelchair marathon winner? Because the conditions differ from year to year, and speeds have improved over the years, it
Freshman 15, revisited In Exercise 12, you thought about how to design a study to see if it’s true that students tend to gain weight during their first year in college.Well, Cornell Professor of Nutrition David Levitsky did just that. He recruited students from two large sections of an
Strikes Advertisements for an instructional video claim that the techniques will improve the ability of Little League pitchers to throw strikes and that, after undergoing the training, players will be able to throw strikes on at least 60% of their pitches. To test this claim, we have 20 Little
Sex sells, part II In Exercise 11, you considered the question of whether sexual images in ads affected people’s abilities to remember the item being advertised. To investigate, a group of Statistics students cut ads out of magazines. They were careful to find two ads for each of 10 similar
Tuition 2013 How much more do public colleges and universities charge out-of-state students for tuition per year?A random sample of 19 public colleges and universities listed at www.collegeboard.com yielded the following data for students entering as Freshmen in Fall 2013.a) Create a 90% confidence
Braking test 2 For another test of the tires in Exercise 31, a car made repeated stops from 60 miles per hour. The test was run on both dry and wet pavement, with results as shown in the table. (Note that actual braking distance, which takes into account the driver’s reaction time, is much
Braking test A tire manufacturer tested the braking performance of one of its tire models on a test track.The company tried the tires on 10 different cars, recording the stopping distance for each car on both wet and dry pavement. Results are shown in the table.a) Write a 95% confidence interval
Gasoline Many drivers of cars that can run on regular gas actually buy premium in the belief that they will get better gas mileage. To test that belief, we use 10 cars from a company fleet in which all the cars run on regular gas. Each car is filled first with either regular or premium gasoline,
Yogurt Is there a significant difference in calories between servings of strawberry and vanilla yogurt?Based on the data shown in the table, test an appropriate hypothesis and state your conclusion. Don’t forget to check assumptions and conditions! Calories per Serving Brand Strawberry Vanilla
Summer school (When you first read about the summer school issue in Chapter 22, you did not have an inference method that would work. Try again now.) Having done poorly on their Math final exams in June, six students repeat the course in summer school and take another exam in August.a) If we
Job satisfaction (When you first read about this exercise break plan in Chapter 22, you did not have an inference method that would work. Try again now.) A company institutes an exercise break for its workers to see if it will improve job satisfaction, as measured by a questionnaire that assesses
Push-ups Every year, the students at Gossett High School take a physical fitness test during their gym classes. One component of the test asks them to do as many push-ups as they can. Results for one class are shown below, separately for boys and girls. Assuming that students at Gossett are
NY Marathon 2013 The table below shows the winning times (in minutes) for men and women in the New York City Marathon between 1978 and 2013. (The race was not run in 2012 because of Superstorm Sandy.). Assuming that performances in the Big Apple resemble performances elsewhere, we can think of
City Temperatures The following table gives the average daily high temperatures in January and July for several cities.Find a 95% confidence interval for the mean temperature difference between summer and winter.a) Check the assumptions and conditions. If you find a city that doesn’t belong with
Online insurance III Exercises 17 and 19 give summaries and displays for car insurance premiums quoted by a local agent and an online company. Test an appropriate hypothesis to see if there is evidence that drivers might save money by switching to the online company.
Online insurance I After seeing countless commercials claiming one can get cheaper car insurance from an online company, a local insurance agent was concerned that he might lose some customers. To investigate, he randomly selected profiles (type of car, coverage, driving record, etc.) for 10 of his
Friday the 13th, accidents The researchers in Exercise 15 also examined the number of people admitted to emergency rooms for vehicular accidents on 12 Friday evenings (6 each on the 6th and 13th).Based on these data, is there evidence that more people are admitted, on average, on Friday the 13th?
Friday the 13th, traffic The British Medical Journal published an article titled, “Is Friday the 13th Bad for Your Health?” Researchers in Britain examined how Friday the 13th affects human behavior. One question was whether people tend to stay at home more on Friday the 13th. The data below
Cloud seeding Simpson, Alsen, and Eden (Technometrics 1975) report the results of trials in which clouds were seeded and the amount of rainfall recorded. The authors report on 26 seeded and 26 unseeded clouds in order of the amount of rainfall, largest amount first. Here are two possible tests to
Women Values for the labor force participation rate of women (LFPR) are published by the U.S. Bureau of Labor Statistics. We are interested in whether there was a difference between female participation in 1968 and 1972, a time of rapid change for women. We check LFPR values for 19 randomly
Sex sells? Ads for many products use sexual images to try to attract attention to the product. But do these ads bring people’s attention to the item that was being advertised? We want to design an experiment to see if the presence of sexual images in an advertisement affects people’s ability to
Blocking cars and trucks Thinking about the data on fuel efficiency in Exercise 3, why is the blocking accomplished by a matched pairs analysis particularly important for a sample that has both cars and trucks?
Weighing trucks II Find a 98% confidence interval of the weight differences in Exercise 4. Interpret this interval in context.
Cars and trucks again In Exercise 3, after deleting an outlying value of -27, the mean difference in fuel efficiencies for the 632 vehicles was 7.37 mpg with a standard deviation of 2.52 mpg. Find a 95% confidence interval for this difference and interpret it in context.
Field workers for a health department compared driving mileage on a five-day work schedule with mileage on a new four-day schedule. To see if the new schedule changed the amount of driving they did, we’ll look at paired differences in mileages before and after.Question: Is it okay to use these
Do flexible schedules reduce the demand for resources? The Lake County, Illinois, Health Department experimented with a flexible four-day workweek. For a year, the department recorded the mileage driven by 11 field workers on an ordinary five-day workweek. Then it changed to a flexible four-day
Rap Using the results of the experiment described in Exercise 85, does it matter whether one listens to rap music while studying, or is it better to study without music at all?a) Test an appropriate hypothesis and state your conclusion.b) If you concluded there is a difference, estimate the size of
Music and memory Is it a good idea to listen to music when studying for a big test? In a study conducted by some Statistics students, 62 people were randomly assigned to listen to rap music, music by Mozart, or no music while attempting to memorize objects pictured on a page. They were then asked
Golf again 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.
Tees 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
Swimming heats London In Exercise 81, we looked at the times in two different heats for the 400-m women’s run from the 2012 Olympics. Unlike track events, swimming heats are not determined at random. Instead, swimmers are seeded so that better swimmers are placed in later heats. Here are the
Running heats London 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 London for
Still swimming 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
Swim the Lake 2013 revisited 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
Thirsty? Researchers 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?15
Hungry? Researchers investigated how the size of a bowl affects how much ice cream people tend to scoop when serving themselves.14 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
Ad campaign You are a consultant to the marketing T 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, then use a
Sex and violence 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
Summer school Having done poorly on their math final exams in June, six students repeat the course in summer school, 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
Job satisfaction 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
Hard water 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
Home runs 2013 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
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
Hurricanes to 2013 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
Streams 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
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 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
New construction 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
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 in the next column.a) What do the boxplots suggest about differences between male and female pulse rates?b)
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? Math Program Mean SD CPMP 320 57.4
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
Stereograms test 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 m1 - m2 Conf level = 90% df = 70 m(NV) - m(VV) interval: (0.55, 5.47)a) Interpret your interval in
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 with
Third load of wash In Exercise 54, we saw a 98%confidence interval of ( -40, -22) minutes for mTop - mFront, 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
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,
Second load of wash 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
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.
Washers 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
Hot dogs 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
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 2004 Democratic convention, Rasmussen Reports polled 1500 likely voters at random and
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 116 people in the group who received
Mammograms redux 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
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
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