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mathematics
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Stats Data And Models 4th Edition Richard D. De Veaux, Paul D. Velleman, David E. Bock - Solutions
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 to list all the
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
The researchers from Exercise 1 want to test if the proportions of foreign born are the same in the United States as in Canada. In Exercise 1 Suppose an advocacy organization surveys 960 Canadians and 192 of them reported being born in another country (www.unitednorthamerica.org/simdiff .htm).
Which of the following scenarios should be analyzed as paired data? a) Students take a MCAT prep course. Their before and after scores are compared b) 20 male and 20 female’s students in class take a midterm. We compare their scores. c) A group of college freshmen are asked about the quality of
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 crossword
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 remember the
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 to analyze
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
Simpson, Alsen, and Eden (Technimetrics 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 study the
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 are
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?
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
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):In Exercise 17 a) Which of the summaries would help you decide whether the
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 subjects sleep
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 qualify, but how can we
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.In Exercise 17In Exercise 19
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.In Exercise 18In Exercise 20
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 the others, set it
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 Superstore Sandy.). Assuming that performances in the Big Apple resemble performances elsewhere, we can think of these data as a
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 assigned to gym
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 placed in
(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 workers'
(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 consider these
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!
We have data on the city and highway fuel efficiency of 316 cars and 316 trucks.a) Would it be appropriate to use paired t methods to compare the cars and the trucks? b) Would it be appropriate to use paired t methods to compare the city and highway fuel efficiencies of these vehicles? c) A
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, decided by
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 for the mean
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.a) Write a 95% confidence interval for the mean dry pavement stopping distance. Be sure to check the appropriate
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 interval
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 items, one with
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 Leaguers
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 introductory health course.
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
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 start-up years of new events are
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
Weighing trucks One kind of scale for weighing trucks can measure their weight as they drive across a plate. 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.
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 other?
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.In Exercise 3
Find a 98% confidence interval of the weight differences in Exercise 4. Interpret this interval in context.In Exercise 4
Thinking about the data on fuel efficiency in Exercise 3, why is the blocking accomplished by a matched pair€™s analysis particularly important for a sample that has both cars and trucks?In Exercise 3
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 number of eggs
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, 32 in
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 the expected values?b)
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, Gold, or
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 examines a random
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?FaceCount111273941551266a) If the die is
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 bought
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 of
Census data for New York City indie 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% Asian. Do the
In its study When Murder Women: An Analysis of 2009 Homicide Data, 2011, the Violence Policy Center (www.vpc.org) repo that'l818 women were murdered by men in 2009. Of these victims, a weapon could be identified for 1 of them. Of those for whom a weapon could be identified, 861 were killed by guns,
Offspring of certain fruit flies may have yellow or ebony bodies and normal wings or short win Genetic theory predicts that these traits will appear in ratio 9:3:3:1 (9 yellow, normal: 3 yellow, short: 3 ebon; normal: 1 ebony, short). A researcher checks 100 such flies and finds the distribution of
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 Platinum. Is there
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
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 number of large
The fairness of the South African lottery was recently challenged by one of the country's political parties. The lottery publishes historical statis¬tics 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 "Powerball"
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 conducted at Sydney
A survey of articles from the New England Journal of Medicine (NEJM) classified those according to the principal statistics methods used. The articles recorded were all no editorial articles appearing during the indicated years. Let's just look at whether these articles used statistics at all.Has
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.In Exercise 23a) How many degrees of freedom are there? b) The smallest expected
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.In Exercise 24a) How many degrees of freedom are there? b) The smallest expected count will be in the 1989/No cell. What is it? c) Check the
In Exercises 23 and 25, we've beg" to examine the possible impact of epidurals on success 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 conclusionIn Exercise 23
In Exercises 24 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.In Exercise 24
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 residuals.a) Show how the residual for the epidural/no breastfeeding cell was calculated. b) What can you conclude from the standardized residuals?
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) What does that
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.a) Show how the residual for the 1989/No cell was calculated. b) What can you conclude from the patterns in the standardized
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 third-class staterooms:a) If we draw an individual at random, what's the probability that we will draw a member of the
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?a) What's the probability that a person selected at random from the NYPD is a
Its 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 drank cranberry juice
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 homogeneity?b) Write
A poll conducted by the University of Montana classified respondents by whether they were male or female and political party, as shown in the table. We wonder if there is evidence of an association between being male or female and party affiliation.a) Is this a test of homogeneity or
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 large in
Medical researchers followed 6272 Swedish men for 30 years to see if there was any association between the amount of fish in their diet and prostate cancer. (Source: "Fatty Fish Consumption and Risk of Prostate Cancer," Lancet, June 2001)a) Is this a survey, a retrospective study, a prospective
The poll described in Exercise 39 also investigated the respondents' party affiliations based on what area of the state they lived in. Test an appropriate hypothesis about this table and state your conclusions.
In April 2009, Gallup published results from data collected from a large sample of adults in the 27 European Union member states. One of the questions asked was, "Which is the most practicable and realistic option for child care, taking into account the need to earn a living?" The counts below are
Two different professors teach an introductory Statistics course. The table shows the distribution of final grades they reported. We wonder whether one of these professors is an "easier" grader.a) Will you test goodness-of-fit, homogeneity, or independence?b) Write appropriate hypotheses.c) Find
Some people believe that a full moon elicits unusual behavior in people. The table shows the number of arrests made in a small town during weeks of six full moons and six other randomly selected weeks in the same year. We wonder if there is evidence of a difference in the types of illegal activity
In some situations where the expected cell counts are too small, as in the case of the grades given by Professors Alpha and Beta in Exercise 43, we can complete an analysis anyway. We can often proceed after combining cells in some way that makes sense and also produces a table in which the
In Exercise 44, you found that the expected cell counts failed to satisfy the conditions for inference.In Exercise 44a) Find a sensible way to combine some cells that will make the expected counts acceptable.b) Test a hypothesis about the full moon and state your conclusion.
A subtle form of racial discrimination in housing is "racial steering." Racial steering occurs when real estate agents show prospective buyers only homes in neighborhoods already dominated by that family's race. This violates the Fair Housing Act of 1968. According to an article in Chance magazine
Newspaper headlines at the time, and traditional wisdom in the succeeding decades, have held that women and children escaped the Titanic in greater proportions than men. Here's a table with the relevant data. Do you think that survival was independent of whether the person was male or female?
You could have checked the data in Exercise 47 for evidence of racial steering using two-proportion z procedures.In Exercise 47a) Find the z-value for this approach, and show that when you square your z-value, you get the value of x2 you calculated in Exercise 47. b) Show that the resulting
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.a) What is the
In Exercise 48, you could have checked for a difference in the chances of survival for men and women using two-proportion Z procedures.In Exercise 48a) Find the z-value for this approach. b) Show that the square of your calculated value of z is the value of x2 you calculated in Exercise 48. c) Show
Most pregnancies are full term, but some are preterm (less than 37 weeks). Of those that are preterm, the Centers for Disease Control and Prevention classifies them as early (less than 34 weeks) and late (34 to 36 weeks). A December 2010 National Vital Statistics Report examined those outcomes in
Education by age Use the survey results in the table investigate differences in education level attained different age groups in the United States.
A market researcher working for the bank in Exercise 2 wants to know if the distribution of applications by card is the same for the past three mailings. She takes a random sample of 200 from each mailing and counts the number applying for Silver, Gold, and Platinum. The data follow:a) What is the
For the data in Exercise 1, In Exercise 1 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, 32 in summer, and 28 in fall. a) Compute the standardized residual for each season. b) Are any of these particularly
For the data in Exercise 2, In Exercise 2 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
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 followa) Under the null hypothesis, what
A prestigious college is interested in factors that might be associated with better graduation rates. The administrators wonder whether there is a relationship between acceptance rates and graduation rates. Before proceeding with their regression inference, what conditions and assumptions must be
Would it be wise for the administrators at the college described in Exercise 1 to conclude that lowering their admission rate (i.e., making it harder to get in) would help to increase their graduation rates? Why or why not?
The coach from Exercise 2 called a team meeting to summarize the results from his study. Would it be a good strategy to tell the players that all they need to do is to shoot more and the goals will follow?
We looked at data from the National Oceanic and Atmospheric Administration about their success in predicting hurricane tracks. On the following page is a scatter plot of the error (in nautical miles) for predicting hurricane locations 24 hours in the future vs. the year in which the prediction (and
A college hockey coach collected data I from the 2010-2011 National Hockey League season. He hopes to convince his players that the number of shots taken has an effect on the number of goals scored. The coach performed a preliminary analysis, using the scoring statistics from 293 offensive players
The 2013 World Drug Report investigated the prevalence of drug use as a percentage of the population aged 15 to 64. Data from 32 European countries are shown in the following scatter plot and regression analysis. (Source: World Drug Report, 2013. www.unodc
How does the cost of a movie depend on its length? Data on the cost (millions of dollars) and the running time (minutes) for major release films of 2005 are summarized in these plots and computer outputDependent variable is Budget ($millions) R-squared = 27.3% s = 32.95 with 120 - 2 = 118 degrees
How does the price of a house depend on its size? Data from Saratoga, New York, on 1064 randomly selected houses that had been sold include data on price ($ 1000s) and size ($ 1000s ft2), producing the following graphs and computer output:Dependent variable is Price R-squared = 59.5% s = 53.79 with
Exercise 21 shows computer output examining the association between the length of a movie and its cost.In Exercise 21a) Check the assumptions and conditions for inference. b) Find a 95% confidence interval for the slope and interpret it in context.
Exercise 22 shows computer output examining the association between the sizes of houses and their sale prices.In Exercise 22a) Check the assumptions and conditions for inference. b) Find a 95% confidence interval for the slope and interpret it in context.
Healthy eating probably doesn't include hot dogs, but if you are going to have one, you'd probably hope it's low in both calories and sodium. Recently, Consumer Reports listed the number of calories and sodium content (in milligrams) for 13 brands of all-beef hot dogs it tested. Examine the
Does a person's cholesterol level tend to change with age? Data collected from 1406 adults aged 45 to 62 produced the regression analysis shown. Assuming that the data satisfy the conditions for inference, examine the association between age and cholesterol level.Dependent variable is Chols =
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