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inferential statistics

Intro Stats 6th Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions

Montana A poll conducted by the University of Montana classified respondents by whether they identified as male or female and which political party they identified with, as shown in the table. We wonder if there is evidence of an association between gender and party affiliation.a) Is this a test of
Car origins A random survey of autos parked in the student lot and the staff lot at a large university classified the brands by country of origin, as seen in the table. Are there differences in the national origins of cars driven by students and staff?a) Is this a test of independence or
Cranberry juice It’s common folk wisdom that drinking cranberry juice can help prevent urinary tract infections in women. In 2001, the British Medical Journal reported the results of a Finnish study in which three groups of 50 women were monitored for these infections over 6 months. One group
NYPD again Examine and comment on this table of the standardized residuals for the chi-square test you looked at in Exercise 34.
Titanic, again Examine and comment on this table of the standardized residuals for the chi-square test you looked at in Exercise 33.
NYPD The table below shows the rank attained by male and female officers in the New York City Police Department (NYPD).Do these data indicate that men and women are equitably represented at all levels of the department?) What’s the probability that a person selected at random from the NYPD is a
Titanic Here is a table we first saw in Chapter 2 showing who survived the sinking of the Titanic based on whether they were crew members, or passengers booked in first-, second-, or thirdclass staterooms: (Data in Titanic 2020)a) If we draw an individual at random, what’s the probability that we
Does your doctor know? (part 5) In Exercises 24, 26, 28, and 30, we considered data on articles in the NEJM. The original study listed 23 different statistics methods. (The list read: ttests, contingency tables, linear regression, . . . .) Why would it not be appropriate to use a chi-square test on
Childbirth, part 5 In Exercises 23, 25, 27, and 29, we’ve looked at a study examining epidurals as one factor that might inhibit successful breastfeeding of newborn babies. Suppose a broader study included several additional issues, including whether the mother drank alcohol, whether this was a
Does your doctor know? (part 4) In Exercises 24, 26, and 28, we’ve tested a hypothesis about whether the use of statistics in NEJM medical articles has changed over time. The table shows the test’s residuals.
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 epidural/no 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 survey8 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. The International Breastfeeding Journal published results of a study conducted at
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 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 yellow or ebony bodies and normal wings or short wings. Genetic theory predicts that these traits will appear in the ratio 9:3:3:1 (9 yellow, normal: 3 yellow, short: 3 ebony, normal: 1 ebony, short).A researcher checks 100 such flies and finds
Violence against women 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 be
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 122 miles on Mondays, 203 miles on Tuesdays, 176 miles on Wednesdays, 181 miles on
Nuts A company says its premium mixture of nuts contains 10% Brazil nuts, 20% cashews, 20% almonds, and 10% 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 112 grams of Brazil nuts, 183 grams of cashews, 207 grams
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 60 times, recording the number of times each face appears. Do these results cast doubt on the die’s fairness?
Which test, again? For each of the following situations, state whether you’d use a chi-square goodness-of-fit test, a chisquare 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,
Iliad weapons The Iliad also reports the cause of many injuries.Here is a table summarizing those reports for the 152 injuries for which the Iliad provides that information. Is there an association?
Iliad injuries 800 BCE Homer’s Iliad is an epic poem, compiled around 800 BCE, that describes several weeks of the last year of the 10-year siege of Troy (Ilion) by the Achaeans. The story centers on the rage of the great warrior Achilles. But it includes many details of injuries and outcomes,
Bank cards, last time For the data in Exercise 2,a) Compute the standardized residual for each type of card.b) Are any of these particularly large? (Compared to what?)c) What does the answer to part b say about this new group of customers?
Human births, last time For the data in Exercise 1,a) Compute the standardized residual for each season.b) Are any of these particularly large? (Compared to what?)c) Why should you have anticipated the answer to part b?
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)
Bank cards At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are 60%, 30%, and 10%, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for
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
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
BST Many dairy cows now receive injections of BST, a hormone intended to spur greater milk production. After the first injection, a test herd of 60 Ayrshire cows increased their mean daily production from 47 pounds to 61 pounds of milk. The standard deviation of the increases was 5.2 pounds. We
Marathon start-up years 2020 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:a) Comment on the assumptions and conditions.b) Assuming that these times are representative of such races, construct and
Wheelchair marathon 2020 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
White House staff salaries In Chapter 17 we examined whether the mean White House staff salary was higher in 2020 than in 2016. Consider the following sample of 14 job positions, and the annual salary for each.
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 2020 How much more do public colleges and universities charge out-of-state students for tuition per year? A random sample of 20 public colleges and universities listed at www.collegeboard.com yielded the following data for students entering as Freshmen in Fall 2020.
Stopping distance 60 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
Stopping distance 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
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!
Summer school (When you first read about the summer school issue in Chapter 17, 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. Here are the
Job satisfaction (When you first read about this exercise break plan in Chapter 17, 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
Brain waves An experiment was performed to see whether sensory deprivation over an extended period of time has any effect on the alpha-wave patterns produced by the brain. To determine this, 20 subjects, inmates in a Canadian prison, were randomly split into two groups. Members of one group were
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 a random sample of seniors and 7th graders are given below, create a 90% confidence interval for how
NY Marathon 2020 The table below shows the winning times(in minutes) for men and women in the New York City Marathon between 1978 and 2020. (www.nycmarathon.org) (The race was not run in 2012 because of Superstorm Sandy and not in 2020 because of the pandemic.) Assuming that performances in the Big
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
Wind speed, part III Exercises 18 and 20 give summaries and displays for two potential sites for a wind turbine. Test an appropriate hypothesis to see if there is evidence that either of these sites has a higher average wind speed.
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.
Wind speed, part II In Exercise 18, we saw summary statistics for wind speeds at two sites near each other, both being considered as locations for an electricity-generating wind turbine. The data, recorded every 6 hours for a year, showed each of the sites had a mean wind speed high enough to
Online insurance II In Exercise 17, we saw summary statistics for 10 drivers’ car insurance premiums quoted by a local agent and an online company. Here are displays for each company’s quotes and for the difference (Local - Online)::
Wind speed, part I To select the site for an electricitygenerating wind turbine, wind speeds were recorded at several potential sites every 6 hours for a year. Two sites not far from each other looked good. Each had a mean wind speed high enough to qualify, but we should choose the site with a
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).
Friday the 13th, traffic The British Medical Journal (1993;307:1584) 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.
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 selected
Freshman 15? Many people believe that students gain weight as freshmen. Suppose we plan to conduct a study to see if this is true.a) Describe a study design that would require a matched-pairs t procedure to analyze the results.b) Describe a study design that would require a two-sample t procedure
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
Music Some students do homework with music playing in their headphones. (Anyone come to mind?) Some researchers want to see if people can work as effectively with as without distraction. The researchers will time some volunteers to see how long it takes them to complete some relatively easy
More eggs? Can a food additive increase egg production?Agricultural researchers want to design an experiment to find out. They have 100 hens available. They have two kinds of feed: the regular feed and the new feed with the additive. They plan to run their experiment for a month, recording the
Vehicle weights IV Consider the weights from Exercise 4. The side-by-side boxplots below show little difference between the two groups. Should this be sufficient to draw a conclusion about the accuracy of the weigh-in-motion scale?
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?
Vehicle weights III 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.
Vehicle weights II The calibration test for a new weight-inmotion method of weighing trucks was introduced in Chapter 6, exercise 52. Is this method consistent with the traditional method of static weighing? Are the conditions for matched pairs inference satisfied? Weights are in 1000s of pounds.
Cars and trucks We have data on the city and highway fuel efficiency of 633 cars and trucks.a) Would it be appropriate to use paired t methods to compare the city fuel efficiency of the cars and the trucks?b) Would it be appropriate to use paired t methods to compare the city and highway fuel
Which method II? Which of the following scenarios should be analyzed as paired data?a) Spouses are asked about the number of hours of sleep they get each night. We want to see if husbands get more sleep than wives.b) 50 insomnia patients are given a placebo and 50 are given a mild sedative. Which
Which method? Which of the following scenarios should be analyzed as paired data?a) Students take an MCAT prep course. Their before and after scores are compared.b) 20 male and 20 female students in class take a midterm. We compare their scores.c) A group of college freshmen are asked about the
Memory II Does ginkgo biloba enhance memory? Repeat the analysis in Exercise 70, this time using a randomization test to see if the difference in mean number of items recalled is statistically significant. Be sure to include a P-value.
Cholesterol and gender II Using the data in Framingham, repeat the analysis in Exercise 69, this time using a randomization test to see if the difference in mean cholesterol levels is statistically significant. Be sure to include a P-value.
Hard water revisited In Exercise 72, we saw that the towns in the region south of Derby seemed to have fewer deaths than the towns in the north. To see whether that difference is statistically significant, look at this histogram of 1000 differences in mean Mortality by Region. What does it say
Attendance 2019 revisited We have seen data on ballpark attendance in Chapters 6, 7, and 9. Now we find that National League teams drew in, on average, nearly 60,000 more fans per season than American League teams. That translates to over $1,000,000 a year. To see whether that difference is
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 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 lessen resistance and drag, reducing spin and allowing the ball to travel farther. In August 2003, Golf Laboratories, Inc., compared the
Swimming heats 2016 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 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
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 boxplots look like this:a) Do women or men appear to be faster at swimming across the lake?
Still swimming Here’s some additional information about the Ontario crossing times presented in Exercise
Swim the lake 2019 revisited As we saw in Chapter 8, Exercise 46, between 1954 and 2019, swimmers have crossed Lake Ontario 65 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 of the glass make a difference in how much liquid they
Hungry? Researchers investigated how the size of a bowl affects how much ice cream people tend to scoop when serving themselves.15 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 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
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 by region Recall from Chapter 7, Exercise 75, that 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
Home runs 2019 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. The numbers reported are the number of items recalled before and after taking a supplement.Here
Cholesterol and gender Are men or women at higher risk for having high cholesterol? The answer may surprise you. Use the data in Framingham.a) Make boxplots comparing the cholesterol levels of men and women.b) Does is seem convincing from the boxplots that one gender has higher average levels of

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