Question: Here some additional information about the Ontario
Here 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 crossings, the boxplots look like this:
Although not designated as an outlier, the slowest female time belongs to Vikki Keith, who crossed the lake swimming only butterfly stroke. Omitting that extraordinary swim gives the following summary statistics:
1. Do women or men appear to be faster at swimming across the lake? Support your answer by interpreting a confidence interval. (Use 37 df.)
2. Some might argue that the men are being unfairly slowed down by two extraordinarily slow swims. Here are the summaries without those two swims. Repeat part a based on these data. Does your conclusion change? (Use 47 df.)
3. Vikki Keith was responsible for two of the more remarkable crossings, but she also swam Lake Ontario two other times. In fact, of the 50 crossings in this analysis, 7 were repeat crossings by a swimmer who crossed the lake before. How does this fact affect your thoughts about the confidence interval?
> 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 Braz
> As noted in an earlier chapter, Mars Inc. says that until very recently yellow candies made up 20% of its milk chocolate M&M 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
> Here are some summary statistics to go with the histogram of the ZIP codes of 500 customers from the Holes-R-Us Internet Jewelry Salon that we saw in Exercise 81: What can these statistics tell you about the company sales?
> After getting trounced by your little brother in a children 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 fairness? 1.
> 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: 1. Is the quality of a car affected by what day it was 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: 1. A brokerage firm wants to see whether the type of acc
> 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 experim
> 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
> 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 deviatio
> Marathon start-up years 2016 When we considered the Boston Marathon in Exercise 37 , we were unable to check the Nearly Normal Condition. Here a histogram of the differences: The three largest differences are in the first three years of wheelchair compet
> The Boston Marathon has had a wheelchair division since 1977. Who do you think is typically faster, the men marathon winner on foot or the women wheelchair marathon winner? Because the conditions differ from year to year, and speeds have improved over th
> In Exercise 12, you thought about how to design a study to see if it 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 sectio
> 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 te
> Holes-R-Us, an Internet company that sells piercing jewelry, keeps transaction records on its sales. At a recent sales meeting, one of the staff presented a histogram of the ZIP codes of the last 500 customers, so that the staff might understand where sa
> In Exercise 11, you considered the question of whether sexual images in ads affected people 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 ea
> 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 Fal
> 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 rea
> 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. 1.
> 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 ei
> 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 condi
> When you first read about the summer school issue in Chapter 20, 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
> 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 satisfaction. Scores for 10 randomly selected workers before and after the implementation of the exerc
> 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 gro
> 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
> After receiving many complaints about his final-grade histogram from students currently taking a statistics course, the professor from Exercise 79 distributed the following revised histogram: 1. Comment on this display. 2. Describe the distribution of gr
> A different regression from the one in Exercise 7 , now using all of the available data (years 1959 to 2016), looks like this: Response variable is: Avg Global temp R squared =90.0% R squared (adjusted)=89.6% s=0.0882 with 583=55 degrees of freedom 1. D
> The table below shows the winning times (in minutes) for men and women in the New York City Marathon between 1978 and 2016. (www.nycmarathon.org) (The race was not run in 2012 because of Superstorm Sandy.) Assuming that performances in the Big Apple rese
> 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. 1. a) Check the assumptions and conditions. If you find a
> 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.
> 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 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 s
> 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 quotes and for the difference (Local Online): 1. Which of the summaries would help you decid
> To select the site for an electricity-generating 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
> 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
> 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
> 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 Fri
> A professor (of something other than statistics!) distributed the following histogram to show the distribution of grades on his 200-point final exam. Comment on the display.
> Alsen, and Eden (Techno metrics 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
> 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 ch
> Many people believe that students gain weight as freshmen. Suppose we plan to conduct a study to see if this is true. 1. Describe a study design that would require a matched-pairs t-procedure to analyze the results. 2. Describe a study design that would
> Ads for many products use sexual images to try to attract attention to the product. But do these ads bring people 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
> 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 t
> 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? 1. Test an appropriate hypothesis and state your conclusion. 2. If you concluded
> 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
> 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.
> 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
> In Exercise 81 , we looked at the times in two different heats for the 400-m women 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 heat
> In 2015 the Council of Europe published a report entitled The European School Survey Project on Alcohol and Other Drugs. (www.espad.org) Among other issues, the survey investigated the percentages of 16-year-olds who had used marijuana. Shown here are th
> 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 run in the 2012 Olympics i
> As we saw in Chapter 8, Exercise 46, between 1954 and 2016, swimmers have crossed Lake Ontario 62 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 nort
> 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
> Researchers investigated how the size of a bowl affects how much ice cream people tend to scoop when serving themselves.12 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
> 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 descr
> 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
> 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, expl
> 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 exercis
> 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
> Two researchers measured the pH (a scale on which a value of 7 is neutral and values below 7 are acidic) of water collected from rain and snow over a 6-month period in Allegheny County, Pennsylvania: 4.57 5.62 4.12 5.29 4.64 4.31 4.30 4.39 4.45 5.67 4.39
> 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 an
> 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 bef
> Are men or women at higher risk for having high cholesterol? The answer may surprise you. Use the data in Framingham. 1. Make boxplots comparing the cholesterol levels of men and women. 2. Does it seem convincing from the boxplots that one gender has hig
> In Chapter 6, Exercise 25, we looked at collected samples of water from streams in the Adirondack Mountains to investigate the effects of acid rain. Researchers measured the pH (acidity) of the water and classified the streams with respect to the kind of
> 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 trad
> 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 E
> The data below show the sugar content (as a percentage of weight) of several national brands of children and adults cereals. Create and interpret a 95% confidence interval for the difference in mean sugar content. Be sure to check the necessary assumptio
> The 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 sum
> 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 9
> 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 below. 1. What do the boxplots suggest about differences between male and f
> Students were given the assignment to make a histogram of the data on bird counts reported in Exercise 48. One student submitted the following display: 1. Comment on this graph. 2. Create your own histogram of the data.
> 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 deter
> 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?
> 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 differe
> In Exercises 49 and 50, Chapter 4, we looked at data from an experiment to determine whether visual information about an image helped people see the image in 3D. 2-Sample t-Interval  for  μ1 μ2Conf level=90%   df=70μ(NV)−μ(VV) interval:(0.5
> 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 pe
> In Exercise 54, we saw a 98% confidence interval of (40, 22) minutes for μTop μFront 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:
> In Exercise 53 , we saw a 90% confidence interval of (6.5, 1.4) grams for μMeat−μBeef 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: 1. If I eat a meat hot d
> 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 machin
> 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 μMeat μBeef is (6.5, 1.4). 1. The endpoints of this confidence interval are ne
> 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-loadi
> Students were asked to make a histogram of the number of home runs Alex Rodriguez hit from 1994 to 2016 (see Exercise 73). One student submitted the following display: 1. Comment on this graph. 2. Create your own histogram of the data.
> 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
> The global survey we learned about in Exercise 49 also asked respondents how they felt about the statement 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 somew
> 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
> 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.
> In the same article from Exercise 46 , Time magazine, reporting on a survey of men 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 9
> A Time magazine article about a survey of men 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?
> Political pundits talk about the bounce that a presidential candidate gets after his party convention. In the past 40 years, it has averaged about 6 percentage points. Just before the 2004 Democratic convention, Rasmussen Reports polled 1500 likely voter
> 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
> 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
> 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, co
> The following data give the numbers of hurricanes classified as major hurricanes in the Atlantic Ocean each year from 1944 through 2013 (www.nhc.noaa.gov/data/): 3, 3, 1, 2, 4, 3, 8, 5, 3, 4, 2, 6, 2, 2, 5, 2, 2, 7, 1, 2, 6, 1, 3, 1, 0, 5, 2, 1, 0, 1, 2,
> It 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 n
> One month before the election, a poll of 630 randomly selected voters showed 54% planning to vote for a certain candidate. A week later, it became known that he had had an extramarital affair, and a new poll showed only 51% of 1010 voters supporting him.
> The Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the 9/11 attack on New York World Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who
> A study published in the Archives of General Psychiatry examined the impact of depression on a patient ability to survive cardiac disease. Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4
> A Vermont study published by the American Academy of Pediatrics examined parental influence on teenagers decisions to smoke. A group of students who had never smoked were questioned about their parents attitudes toward smoking. These students were questi
> In Exercise 34 , you used a confidence interval to examine the effectiveness of Prozac in treating anorexia nervosa. Suppose that instead you had conducted a hypothesis test. (Answer these questions without actually doing the test.) 1. What hypotheses wo
> In Exercise 33 , you used a confidence interval to examine the effectiveness of a vaccine against ear infections in babies. Suppose that instead you had conducted a hypothesis test. (Answer these questions without actually doing the test.) 1. What hypoth
> The Journal of the American Medical Association reported on an experiment intended to see if the drug Prozac could be used as a treatment for the eating disorder anorexia nervosa. The subjects, women being treated for anorexia, were randomly divided into
> A new vaccine was recently tested to see if it could prevent the painful and recurrent ear infections that many infants suffer from. The Lancet, a medical journal, reported a study in which babies about a year old were randomly divided into two groups. O
