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 almonds, 71 grams of hazelnuts, and 446 grams of peanuts. You wonder whether your mix is significantly different from what the company advertises. 1. Explain why the chi-square goodness-of-fit test is not an appropriate way to find out. 2. What might you do instead of weighing the nuts in order to use a χ2 test?
> Does a person cholesterol level tend to change with age? Data collected from 1406 adults aged 45 to 62 as part of the Framingham study produced the regression analysis shown. Assuming that the data satisfy the conditions for inference, examine the associ
> Healthy eating probably doesn’t include hot dogs, but if you are going to have one, you’d probably hope it low in both calories and sodium. Recently, Consumer Reports listed the number of calories and sodium content (i
> Exercise 24 shows computer output examining the association between the sizes of houses and their sale prices. 1. Check the assumptions and conditions for inference. 2. Find a 95% confidence interval for the slope and interpret it in context.
> Exercise 23 shows computer output examining the association between Arctic sea ice extent and global mean temperature. Find a 95% confidence interval for the slope and interpret it in context.
> How does the price of a house depend on its size? Data from Saratoga, New York, on 1063 randomly selected houses that had been sold include data on price ($1000s) and size (1000 ft2), producing the following graphs and computer output: Dependent variable
> Climate scientists have been observing the extent of sea ice in the northern Arctic using satellite observations. Many have expressed concern because in recent decades the extent of sea ice has declined precipitously possibly due to global climate change
> 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 scatterplot and regression analysis. (World Drug Report, 2013. www.unodc.org/un
> The dataset Student survey contains 299 responses to a student survey from a statistics project. The questions asked included: How would you rate yourself politically? (1=Far left, 9 = Far right) What is your gender? Do you believe in God? Pick a random
> In Chapter 6, we looked at data from the National Oceanic and Atmospheric Administration about their success in predicting hurricane tracks. Here is a scatterplot of the error (in nautical miles) for predicting hurricane locations 24 hours in the future
> 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?
> An SAT preparation course wants to advertise based on the analyses we’ve seen that raising your SAT scores will increase your eventual earnings. Is that conclusion supported by these analyses?
> Use the survey results in the table to investigate differences in education level attained among different age groups in the United States.
> 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 S
> Titanic 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 a table with the relevant data. Do you think that survival was independ
> 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 race. This violates the Fair Housing Act of 1968. Ac
> In Exercise 44, you found that the expected cell counts failed to satisfy the conditions for inference. 1. Find a sensible way to combine some cells that will make the expected counts acceptable. 2. Test a hypothesis about the full moon and state your co
> 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 a
> 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
> The following data show the percentage change in population for the 50 states and the District of Columbia from the 2000 census to the 2010 census. Using appropriate graphical displays and summary statistics, write a report on the percentage change in po
> 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. 1. Will you test goodness-of-fit, homogeneity, or independenc
> 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 n
> 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. (Data in Montana revisited)
> 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. (Fatty Fish Consumption and Risk of Prostate Cancer, Lancet, June 2001) 1. Is this a survey, a re
> 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. 1. I
> 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? 1. Is this a
> It 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 ove
> Examine and comment on this table of the standardized residuals for the chi-square test you looked at in Exercise 34.
> Examine and comment on this table of the standardized residuals for the chi-square test you looked at in Exercise 33.
> 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? 1. What the probability that a person
> In 2015, the website NewGeography.com listed its ranking of the best cities for job growth in the United States. The magazine top 20 large cities, along with their weighted job rating indices, are given in the table. The full dataset contains 70 cities.
> 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: 1. If we draw an individual at random, what the probabi
> 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: t-tests, contingency tables, linear regression, . . . .) Why would it not be appropriate to use a chi-
> 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 alcoh
> 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 residuals. 1. Show how the residual for the 1989/No cell was calculated.
> 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 residuals. 1. Show how the residual for the epidural/no breastfeeding cell was calculat
> In Exercises 24 and 26, we’ve begun to examine whether the use of statistics in NEJM medical articles has changed over time. 1. Calculate the component of chi-square for the 1989/No cell. 2. For this test, χ2=25.28. What the P-value? 3. State your concl
> In Exercises 23 and 25, we’ve begun to examine the possible impact of epidurals on successful breastfeeding. 1. Calculate the component of chi-square for the epidural/no breastfeeding cell. 2. For this test, χ2=14.87. What the P-value? 3. State your con
> The table in Exercise 24 shows whether NEJM medical articles during various time periods included statistics or not. Were planning to do a chi-square test. 1. How many degrees of freedom are there? 2. The smallest expected count will be in the 1989/No ce
> In Exercise 23, the table shows results of a study investigating whether aftereffects of epidurals administered during childbirth might interfere with successful breastfeeding. Were planning to do a chi-square test. 1. How many degrees of freedom are the
> A survey6 of articles from the New England Journal of Medicine (NEJM) classified them according to the principal statistics methods used. The articles recorded were all non-editorial articles appearing during the indicated years. Let just look at whether
> The National Center for Education Statistics reports average mathematics achievement scores for eighth graders in all 50 states (nces.ed.gov/nationsreportcard/): 1. Using technology and the provided data file, find the median, IQR, mean, and standard dev
> There is some concern that if a woman has an epidural to reduce pain during childbirth, the drug can get into the baby bloodstream, making the baby sleepier and less willing to breastfeed. The International Breastfeeding Journal published results of a st
> The fairness of the South African lottery was recently challenged by one of the country 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
> 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 been some concer
> Many people know the mathematical constant is approximately 3.14. But that 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
> 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 researche
> 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 who
> 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%
> 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 mile
> 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
> 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
> 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
