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inferential statistics
Stats Modeling The World AP Edition Grades 9-12 3rd Edition David E. Bock, Paul F. Velleman, Richard D. De Veaux - Solutions
Crawling. A study published in 1993 found that babies born at different times of the year may develop the ability to crawl at different ages! The author of the study suggested that these differences may be related to the temperature at the time the infant is 6 months old. (Benson and Janette,
Seasonal spending II. As we saw in Exercise 37, financial analysts know that January credit card charges will generally be much lower than the month before.What about the difference between January and February? Does the trend continue into the next month? A simple random sample of 99 cardholders
Seasonal spending. The success of the Christmas spending season (in the United States, roughly from Thanksgiving to Christmas) drives much of retail sales for the year. Financial analysts for credit card companies know that January credit card charges will generally be much lower than the month
Seasonal spending II. As we saw in Exercise 37, financial analysts know that January credit card charges will generally be much lower than the month before.What about the difference between January and February? Does the trend continue into the next month? A simple random sample of 99 cardholders
Seasonal spending. The success of the Christmas spending season (in the United States, roughly from Thanksgiving to Christmas) drives much of retail sales for the year. Financial analysts for credit card companies know that January credit card charges will generally be much lower than the month
Uninsured. During the economic recession of 2000 2001, unemployment increased and job benefits were scaled back. The table shows the percentage of people in each state who lacked health insurance during the 99 00 and 00 01 fiscal years, as reported by the U.S.Census Bureau. Is there any evidence
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
Freshman 15, revisited. In Exercise 4 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
Sex sells, part II. In Exercise 3 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,
Tuition 2006. How much more do public colleges and universities charge out-of-state students for tuition per semester? A random sample of 19 public colleges and universities listed at www.collegeboard.com yielded the following data. Tuition figures per semester are rounded to the nearest hundred
Braking, test 2. For another test of the tires in Exercise 29, the company tried them on 10 different cars, recording the stopping distance for each car on both wet and dry pavement. Results are shown in the table.
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
Braking. In a test of braking performance, a tire manufacturer measured the stopping distance for one of its tire models. On a test track, a car made repeated stops from 60 miles per hour. The test was run on both dry and wet
Caffeine. A student experiment investigating the potential impact of caffeine on studying for a test involved 30 subjects randomly divided into two groups. Each group took a memory test. The subjects then each drank two cups of regular (caffeinated) cola or caffeine-free cola.Thirty minutes later
Yogurt. Do these data suggest that there is a significant difference in calories between servings of strawberry and vanilla yogurt? Test an appropriate hypothesis and state your conclusion. Don t forget to check assumptions and conditions!
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,
Sleep. W.S. Gosset (Student) refers to data recording the number of hours of additional sleep gained by 10 patients from the use of laevohyoscyamine hydrobromide. We want to see if there is strong evidence that the herb can help people get more sleep.a) State the null and alternative hypotheses
Summer school. (When you first read about the summer school issue in Chapter 24 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. If we consider
Job satisfaction. (When you first read about this exercise break plan in Chapter 24, 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
Exercise. An August 2001 article in the journal Medicine and Science in Sports and Exercise compared how long it would take men and women to burn 200 calories during light or heavy workouts on various kinds of exercise equipment. The results summarized in the table are the average times for a group
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
Marathons 2006. Shown are the winning times (in minutes) for men and women in the New York City Marathon between 1978 and 2006. Assuming that performances in the Big Apple resemble performances elsewhere, we can think of these data as a sample of performance in marathon competitions. Create a
Temperatures. The table below gives the average high temperatures in January and July for several European cities. Write a 90% confidence interval for the mean temperature difference between summer and winter in Europe. Be sure to check conditions for inference, and clearly explain what your
BST II. In the experiment about hormone injections in cows described in Exercise 17, 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
Boston startup years 2007. When we considered the Boston Marathon in Exercise 15, we were unable to check the Nearly Normal Condition. Here s a histogram of the differences:
Wheelchair marathon 2007. 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
Windy, part III. Exercises 10 and 12 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 3. Exercises 9 and 11 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.
Windy, part II. In Exercise 10, 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,
Online insurance II. In Exercise 9, 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):
Windy, 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 higher
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
Friday the 13th, II: The researchers in Exercise 7 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, I. In 1993 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
Rain. 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 study the
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
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 twosample t procedure to
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
MTV. Some students do homework with the TV on.(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 puzzles. During some of
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
Cuckoos. Cuckoos lay their eggs in the nests of other(host) birds. The eggs are then adopted and hatched by the host birds. But the potential host birds lay eggs of different sizes. Does the cuckoo change the size of her eggs for different foster species? The numbers in the table are lengths (in
Rap. Using the results of the experiment described in Exercise 42, 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
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
Statistics journals. When a professional statistician has information to share with colleagues, he or she will submit an article to one of several Statistics journals for publication. This can be a lengthy process; typically, the article must be circulated for peer review and perhaps edited before
Golf again. Given the test results on golf tees described in Exercise 39, 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 the
Swimming heats. In Exercise 37 we looked at the times in two different heats for the 400-m women s run from the 2004 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 times (in
Is there any evidence that the mean time to finish is different for randomized heats? Explain. Be sure to include a discussion of assumptions and conditions for your analysis.
Running heats. 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 2004 Olympics in Athens for
Still swimming. Here s some additional information about the Ontario crossing times presented in Exercise 35.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
Crossing Ontario. Between 1954 and 2003, swimmers have crossed Lake Ontario 43 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 minutes):
The Internet. The NAEP report described in Exercise 33 compared science scores for students who had home Internet access to the scores of those who did not, as shown in the graph. They report that the differences are statistically significant.a) Explain what statistically significant means in this
Lower scores? Newspaper headlines recently announced a decline in science scores among high school seniors. In 2000, a total of 15,109 seniors tested by The National Assessment in Education Program (NAEP)scored a mean of 147 points. Four years earlier, 7537 seniors had averaged 150 points. The
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 ( ) into their glass. Did the shape glass make a difference in how much liquid they poured?11 Here are the summaries:
Hungry? Researchers investigated how the size of a bowl affects how much ice cream people tend to scoop when serving themselves.10 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 invited
Ad recall. In Exercises 27 and 29, we see the number of advertised brand names people recalled immediately after watching TV shows and 24 hours later. Strangely enough, it appears that they remembered more about the ads the next day. Should we conclude this is true in general about people s memory
Sex and violence II. In the study described in Exercise 27, the researchers also contacted the subjects again, 24 hours later, and asked them to recall the brands advertised. Results are summarized below.Program Type Violent Sexual Neutral No. of subjects 101 106 103 Brands recalled Mean 3.02 2.72
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 19, then use a
Sex and violence. In June 2002, 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
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, do these results provide evidence
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. 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
Double header 2006. Do the data in Exercise 21 suggest that the American League s designated hitter rule may lead to more runs?a) Using a 95% confidence interval, estimate the difference between the mean number of runs scored in American and National League games.b) Interpret your interval.c) Does
Handy. A factory hiring people to work on an assembly line gives job applicants a test of manual agility. This test counts how many strangely shaped pegs the applicant can fit into matching holes in a one-minute period. The table below summarizes the data by sex of the job applicant. Assume that
Baseball 2006. 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 on the next page some computer output from a
Hurricanes 2006. The data below show the number of hurricanes 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.
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 13 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. Here are the summaries and boxplots of the Sale Prices:
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:
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 on the next page and summarized below.
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 7 also tested students abilities to solve word problems.This table shows how the CPMP and traditional groups performed. What do you conclude?2 Performance on Algebraic Symbolic Manipulation Without Use
CPMP, again. During the study described in Exercise 7, 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?a) Write an appropriate
Stereograms. Stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can fuse into a three-dimensional(3D) image by staring at the dots while defocusing the eyes. An experiment was performed to determine whether knowledge of the form of the
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
Second load of wash. In Exercise 4, we saw a 98% confidence interval of minutes for , the difference in time it takes top-loading and frontloading 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 are 22 to 40 minutes
Dogs and fat, second helping. In Exercise 3, we saw a 90% confidence interval of grams for, 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, there s a 90%
Washers. In the June 2007 issue, Consumer Reports examined the relative merits of top-loading and frontloading washing machines, testing samples of several different brands of each type. One of the variables the article reported was cycle time , the number of minutes it took each machine to wash a
Dogs and fat. The Consumer Reports article described in Exercise 1 also listed the fat content (in grams) for samples of beef and meat hot dogs. The resulting 90% confidence interval for is .a) The endpoints of this confidence interval are negative numbers. What does that indicate?b) What does the
Dogs and sodium. The Consumer Reports article described in Exercise 1 also listed the sodium content (in mg) for the various hot dogs tested. A test of the null hypothesis that beef hot dogs and meat hot dogs don t differ in the mean amounts of sodium yields a P-value of 0.11.Would a 95% confidence
Dogs and calories. 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
Wind power. Should you generate electricity with your own personal wind turbine? That depends on whether you have enough wind on your site. To produce enough energy, your site should have an annual average wind speed of at least 8 miles per hour, according to the Wind Energy Association. One
Driving distance. How far do professional golfers drive a ball? (For non-golfers, the drive is the shot hit from a tee at the start of a hole and is typically the longest shot.) A histogram of the average driving distances of thea) Find a 95% confidence interval for the mean drive distance.b)
Should the company adopt the new tread pattern? Test an appropriate hypothesis and state your conclusion. Explain how you dealt with the outlier and why you made the recommendation you did.
Braking. A tire manufacturer is considering a newly designed tread pattern for its all-weather tires. Tests have indicated that these tires will provide better gas mileage and longer tread life. The last remaining test is for braking effectiveness. The company hopes the tire will allow a car
Maze. Psychology experiments sometimes involve testing the ability of rats to navigate mazes. The mazes are classified according to difficulty, as measured by the mean length of time it takes rats to find the food at the end. One researcher needs a maze that will take rats an average of about one
Yogurt. Consumer Reports tested 14 brands of vanilla yogurt and found the following numbers of calories per serving:160 200 220 230 120 180 140 130 170 190 80 120 100 170a) Check the assumptions and conditions for inference.b) Create a 95% confidence interval for the average calorie content of
Chips Ahoy. In 1998, as an advertising campaign, the Nabisco Company announced a 1000 Chips Challenge, claiming that every 18-ounce bag of their Chips Ahoy cookies contained at least 1000 chocolate chips. Dedicated Statistics students at the Air Force Academy (no kidding)purchased some randomly
Portable phones. A manufacturer claims that a new design for a portable phone has increased the range to 150 feet, allowing many customers to use the phone throughout their homes and yards. An independent testing laboratory found that a random sample of 44 of these phones worked over an average
Cars. One of the important factors in auto safety is the weight of the vehicle. Insurance companies are interested in knowing the average weight of cars currently licensed in the United States; they believe it is 3000 pounds. To see if that estimate is correct, they checked a random sample of 91
Ski wax. Bjork Larsen was trying to decide whether to use a new racing wax for cross-country skis. He decided that the wax would be worth the price if he could average less than 55 seconds on a course he knew well, so he planned to test the wax by racing on the course 8 times.a) Suppose that he
Popcorn. Yvon Hopps ran an experiment to test optimum power and time settings for microwave popcorn.His goal was to find a combination of power and time that would deliver high-quality popcorn with only 10%of the kernels left unpopped, on average. After experimenting with several bags, he
Doritos. Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5.a) Do these data satisfy the assumptions for inference?Explain.b) Find the mean
Ruffles. Students investigating the packaging of potato chips purchased 6 bags of Lay s Ruffles marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.3, 28.2, 29.1, 28.7, 28.9, 28.5.a) Do these data satisfy the
Fuel economy. A company with a large fleet of cars hopes to keep gasoline costs down and sets a goal of attaining a fleet average of at least 26 miles per gallon. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random, finding a mean of 25.02 mpg and a
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