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inferential statistics
Intro Stats 6th Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions
Cloud seeding In an experiment to determine whether seeding clouds with silver iodide increases rainfall, 52 clouds were randomly assigned to be seeded or not The amount of rain they generated was then measured (in acre-feet).a) Create a 95% confidence interval for the average amount of additional
Insulin and diet A study published in the Journal of the American Medical Association examined people to see if they showed any signs of IRS (insulin resistance syndrome)involving major risk factors for Type 2 diabetes and heart disease. Among 102 subjects who consumed dairy products more than 35
Fisher’s irises In 1936 Sir Ronald Fisher presented data on irises as the example in a famous statistics paper. Ever since,“Fisher’s Iris data” have been a feature of statistics texts.We didn’t want to be an exception. Can measurements of the petal length of flowers be of value when you
Teach for America, part II The study described in Exercise R5.21 also looked at scores in mathematics and language.Here are software outputs for the appropriate tests. Explain what they show.Mathematics T-TEST OF Mu(1) - Mu(2) = 0 Mu(Cert) - Mu(NoCert) = 4.53 t(86) = 2.95 p = 0.002 Language T-TEST
Legionnaires’ disease In 1974, the Bellevue-Stratford Hotel in Philadelphia was the scene of an outbreak of what later became known as Legionnaires’ disease. The cause of the disease was finally discovered to be bacteria that thrived in the air-conditioning units of the hotel. Owners of the Rip
Teach for America Several programs attempt to address the shortage of qualified teachers by placing uncertified instructors in schools with acute needs—often in inner cities.A study compared students taught by certified teachers to others taught by uncertified teachers in the same schools.Reading
Cesareans Some people fear that differences in insurance coverage can affect health care decisions. A survey of several randomly selected hospitals found that 16.6% of 223 recent births in Vermont involved cesarean deliveries, compared to 18.8% of 186 births in New Hampshire. Is this evidence that
Eating disorders A study conducted in the multicultural Spanish city of Ceuta investigated the relationship between religion and the prevalence of eating disorders. Students aged 12–20 were selected from three public schools. In the tudy, suppose there were 150 Muslim students and 46 were
Smoking In the depression and heart attack research described in Exercise R5.17, 32% of the diseased group were smokers, compared with only 23.7% of those free of heart disease.a) Create a 95% confidence interval for the difference in the proportions of smokers in the two groups.b) Is this evidence
Age In a study of how depression may affect one’s ability to survive a heart attack, the researchers reported the ages of the two groups they examined. The mean age of 2397 patients without cardiac disease was 69.8 years (SD = 8.7 years), while for the 450 patients with cardiac disease, the mean
Seat belts 2015 The National Highway Traffic Safety Administration reported seat belt use and fatalities in car accidents. (Reference: Seat belt use in 2015—use rates in the states and territories. Report no. DOT HS-812-274) Is the rate of seat belt use different in New England compared to the
Feeding fish In the midwestern United States, a large aquaculture industry raises largemouth bass. Researchers wanted to know whether the fish would grow better if fed a natural diet of fathead minnows or an artificial diet of food pellets.They stocked six ponds with bass fingerlings weighing about
Grant writing Does race matter when applying for National Institutes of Health grants? A study found that of 58,148 applications submitted by white researchers, 15,700 were accepted and funded by the NIH. Additionally, 198 of the 1164 applications submitted by black researchers were funded.
Pottery Archaeologists can use the chemical composition of clay found in pottery artifacts to determine whether different sites were populated by the same ancient people.They collected five samples of Romano-British pottery from each of two sites in Great Britain—the Ashley Rails site and the New
Mazes and smells Can pleasant smells improve learning?Researchers timed 21 subjects as they tried to complete paper-and-pencil mazes. Each subject attempted a maze both with and without the presence of a floral aroma. Subjects were randomized with respect to whether they did the scented trial first
Crawling A study found that babies born at different times of the year may develop the ability to crawl at different ages.The authors 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, “Season of birth and
Preemies Among 242 Cleveland-area children born prematurely at low birthweights between 1977 and 1979, only 74% graduated from high school. Among a comparison group of 233 children of normal birthweight, 83% were high school graduates. (“Outcomes in Young Adulthood for Very-Low-Birth-Weight
More errors A corporation with a fleet of vehicles wanted to test the cost-effectiveness of using Motor Silk oil additive.For the study, 6100 delivery and passenger vehicles were tested for the same 3-month period in one year and then again in the subsequent year. In the initial year, the fleet was
Perfect pitch A recent study of perfect pitch tested 2700 students in American music conservatories. It found that 7% of non-Asian and 32% of Asian students have perfect pitch. A test of the difference in proportions resulted in a P-value of 60.0001.a) What are the researchers’ null and
Eclampsia deaths Refer again to the research summarized in Exercise R5.6. Is there any evidence that when eclampsia does occur, the magnesium sulfide treatment may help prevent the woman’s death?a) Write an appropriate hypothesis.b) Check the assumptions and conditions.c) Find the P-value of the
Eclampsia It’s estimated that 50,000 pregnant women worldwide die each year of eclampsia, a condition involving elevated blood pressure and seizures. A research team from 175 hospitals in 33 countries investigated the effectiveness of magnesium sulfate in preventing the occurrence of eclampsia in
Twins There is some indication in medical literature that doctors may have become more aggressive in inducing labor or doing preterm cesarean sections when a woman is carrying twins. Records at a large hospital show that, of the 43 sets of twins born in 2000, 20 were delivered before the 37th week
Free throws 2017 At the middle of the 2016–2017 NBA season, James Hardin led the league by making 468 of 544 free throws, for a success rate of 86%. But Russell Westbook was close behind with 425 of 517 (82.2%).a) Find a 95% confidence interval for the difference in their free throw
Surgery and germs Joseph Lister (for whom Listerine is named!) was a British physician who was interested in the role of bacteria in human infections. He suspected that germs were involved in transmitting infection, so he tried using carbolic acid as an operating room disinfectant.In 75
Birth days During a 2-month period, 72 babies were born at the Tompkins Community Hospital in upstate New York.The table shows how many babies were born on each day of the week.
Herbal cancer A report in the New England Journal of Medicine notes growing evidence that the herb Aristolochia fangchi can cause urinary tract cancer in those who take it.Suppose you are asked to design a study of this claim.Imagine that you have data on urinary tract cancers in subjects who have
Cost of higher education Are there fundamental differences between liberal arts colleges and universities? In this case, we have information on the top 25 liberal arts colleges and the top 25 universities in the United States. We will consider the type of school as our response variable and use the
Embrace or protect? In January 2017, Dalia Research(daliaresearch.com/why-trump-and-clinton-supportersperceiveimmigrants-so-differently/) asked people which statement they indentified more with:1) Our lives are threatened by terrorists, criminals, and immigrants and our priority should be to
Property assessments The following software output provides information about the Size (in square feet) of 18 homes in Ithaca, New York, and the city’s assessed Value of those homes.
Education and mortality The following software output is based on the mortality rate (deaths per 100,000 people) and the education level (average number of years in school) for 58 U.S.cities.
Midterms? The professor teaching the introductory statistics class discussed in Exercise 57 wonders whether performance on homework can accurately predict midterm scores.a) To investigate it, she fits a regression of the sum of the two midterms scores on homework scores. Fit the regression model.b)
Midterms The dataset provides midterm and homework scores from an introductory statistics course.a) Use your technology of choice to fit a model predicting the second midterm score from the first.b) Comment on the model you found, including a discussion of the assumptions and conditions for
Crawling Researchers at the University of Denver Infant Study Center wondered whether temperature might influence the age at which babies learn to crawl. Perhaps the extra clothing that babies wear in cold weather would restrict movement and delay the age at which they started crawling. Data were
Tablet computers 2020 Cnet.com tests tablet computers and continuously updates its list. As of October 2020, the list included the battery life (in hours) and luminous intensity (i.e., screen brightness, in cd>m2). We want to know if Battery life is related to the maximum Screen Brightness.
More sales and profits Consider again the relationship between the sales and profits of Fortune 500 companies that you analyzed in Exercise 52.a) Find a 95% confidence interval for the slope of the regression line. Interpret your interval in context.b) Use the Regression Bootstrap tool
Ozone, again Consider again the relationship between the population and ozone level of U.S. cities that you analyzed in Exercise 51.a) Give a 90% confidence interval for the slope of the relationship between ozone level and population.b) For the cities studied, the mean population was 1.7 million
Sales and profits A business analyst was interested in the relationship between a company’s sales and its profits. She collected data (in millions of dollars) from a random sample of Fortune 500 companies and created the regression analysis and summary statistics shown. The assumptions for
Ozone and population The Environmental Protection Agency is examining the relationship between the ozone level (in parts per million) and the population (in millions) of U.S. cities. Part of the regression analysis is shown.Dependent variable is Ozone R-squared = 84.4%s = 5.454 with 16 - 2 = 14 df
See ice? A skeptic suggests that reduced sea ice isn’t due to global climate change at all. He offers the following model, including Year since 1979 as another predictor as an alternative to the model in Exercise 23: (Data in Sea ice 2020):Response variable is: Extent R squared = 78.4%s = 0.5323
City climate The output shows an attempt to model the association between average January Temperature (in degrees Fahrenheit) and Latitude (in degrees north of the equator) for 59 U.S. cities. Which of the assumptions for inference do you think are violated? Explain.
Cereals, part 2 Further analysis of the data for the breakfast cereals in Exercise 46 looked for an association between Fiber content and Calories by attempting to construct a linear model.Here are three graphs. Which of the assumptions for inference are violated? Explain.
Brain size Does your IQ depend on the size of your brain? A group of female college students took a test that measured their verbal IQs and also underwent an MRI scan to measure the size of their brains (in 1000s of pixels). The scatterplot and regression analysis are shown, and the assumptions for
Cereals A healthy cereal should be low in both calories and sodium. Data for 77 cereals were examined and judged acceptable for inference. The 77 cereals had between 50 and 160 calories per serving and between 0 and 320 mg of sodium per serving. Here’s the regression analysis:Dependent variable
Climate change again Consider once again the CO2 and global temperature data of Exercise 41. The mean CO2 level for these data is 355.429 ppm.a) Find a 90% confidence interval for the mean global temperature anomaly if the CO2 level reaches 450 ppm.b) Find a 90% prediction interval for the mean
Fuel economy, part III Consider again the data in Exercise 40 about the gas mileage and weights of cars.a) Create a 95% confidence interval for the average fuel efficiency among cars weighing 2500 pounds, and explain what your interval means.b) Create a 95% prediction interval for the gas mileage
Climate change, part II Consider the CO2 and global temperature data of Exercise 41.a) Find a 90% confidence interval for the slope of the true line describing the association between Temp and CO2.b) Explain in this context what your confidence interval means.*c) use the Regression Bootstrap tool
Fuel economy, part II Consider again the data in Exercise 40 about the gas mileage and weights of cars.a) Create a 95% confidence interval for the slope of the regression line.b) Explain in this context what your confidence interval means.
Climate change 2019 Data collected from around the globe(including the sea ice data of Exercise 23) show that the earth is getting warmer. The generally accepted explanation relates climate change to an increase in atmospheric levels of carbon dioxide (CO2) because CO2 is a greenhouse gas that
Fuel economy A consumer organization has reported test data for 50 car models. We will examine the association between the weight of the car (in thousands of pounds) and the fuel efficiency (in miles per gallon). Here are the scatterplot, summary statistics, and regression analysis:
Streams again Here is a regression model in which the variable Alkali has been included in the model from Exercise 37:Response variable is: BCI R squared = 37.8%s = 130.1 with 163 - 3 = 160 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Intercept 1641.48 271.1 6.06 60.0001 pH
Civics again The price of a car depends on its age as well as on its mileage. Here is a regression in which the age of the cars(in years) is included in the regression model from Exercise 34:Response variable is: Price R squared = 89.6%s = 1284 with 55 - 3 = 52 degrees of freedom Variable
Streams Biologists studying the effects of acid rain on wildlife collected data from 172 streams in the Adirondack Mountains. They recorded the pH (acidity) of the water and the BCI, a measure of biological diversity. Here’s a scatterplot of BCI against pH for the 163 streams for which we have
Used Civics 2020 againa) Based on the analysis of used car prices in Exercise 34, create a 95% confidence interval for the slope of the regression line and explain what your interval means in context.*b) use the Regression Bootstrap tool (astools.datadesk.com) to find a 95% confidence interval. How
Marriage age 2019 again Based on the analysis of marriage ages given in Exercise 33, find a 95% confidence interval for the rate at which the age gap is closing. Explain what your confidence interval means.
Used Civics 2020 On October 3, 2020, autolist.com listed 55 used Honda Civics for sale by owner. Here’s a scatterplot of the asking price vs. the number of miles on the odometer (in thousands):a) Do you think a linear model is appropriate? Explain.Here is the regression model:Response variable
Marriage age 2019 Chapter 8, Exercises 42, 44, and 49, looked at the how the age at first marriage has changed over time for men and women. One trend was that people have been waiting until they are older to get married
Cholesterol, finisa) Based on the regression output seen in Exercise 28, create a 95% confidence interval for the slope of the regression line and interpret it in context.*b) use the Regression Bootstrap tool (astools.datadesk.com) to find a 95% confidence interval. How does your result compare to
Last doga) Based on the regression output seen in Exercise 27, create a 95% confidence interval for the slope of the regression line and interpret your interval in context.*b) use the Regression Bootstrap tool (astools.datadesk.com) to find a 95% confidence interval. How does your result compare to
More cholesterol Look again at Exercise 28’s regression output for age and cholesterol level. (Data in Framingham)a) The output reports s = 46.16. Explain what that means in this context.b) What’s the value of the standard error of the slope of the regression line?c) Explain what that means in
Second frank Look again at Exercise 27’s regression output for the calorie and sodium content of hot dogs.a) The output reports s = 59.66. Explain what that means in this context.b) What’s the value of the standard error of the slope of the regression line?c) Explain what that means in this
Cholesterol Does a person’s 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 association between age and
Hot dogs 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.
Second home Exercise 24 shows computer output examining the association between the sizes of houses and their sale prices.a) Check the assumptions and conditions for inference.b) Find a 95% confidence interval for the slope and interpret it in context.*c) Use the Regression Bootstrap tool
More sea ice 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.
Saratoga house prices 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:a) Explain in context what the regression
Sea ice 2020 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. Here is an analysis relating
Drug use 2013 The 2013 World Drug Report investigated0 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.
Tracking hurricanes 2018 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 vs. the year in
Shoot to score, shootout 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?
Earnings, planning 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?
Shoot to score, predictions The coach we’ve been following wants to predict how many goals each of his players will score this season. Explain why a model like the ones we’ve made won’t be very successful at doing that.
Earnings, predictions Naturally, you would like to know what you are going to earn in the next few years. Explain why a regression model such as the ones we have found won’t do a very good job of such a prediction. (Sorry.)
Shoot to score, double overtime Continuing from Exercise 14, the coach responds to the players by claiming that shooting accuracy is more important than time on the ice. He adds Shoot%(% of shots on goal) to the model.Response variable is: Goals R squared = 95.7%s = 0.8850 with 65 - 4 = 61 degrees
Why the change?b) Find a 95% confidence interval for the coefficient of SAT.How does it compare with the one you found in Exercise 13?c) The t-ratio associated with the SAT coefficient is now much smaller and the corresponding P-value much larger. Explain why this has happened
Earnings and more A second predictor in Exercise 13 improved the regression model of Exercise 1, so let’s try a third. Here’s a model with average ACT score of the entering class included:Response variable is: Earn R squared = 36.5%s = 5372 with 687 - 4 = 683 degrees of freedom Variable
Shoot to score, time on ice The players on the team in Exercise 2 point out to the coach that they can’t shoot if they are not on the ice. They add the variable TimeOnIce/Game (TOI/G)(in minutes per game) to the regression:
Earnings and need Continuing with the data from Exercise 1, here’s a regression with the percent of students who receive merit-based financial aid included in the model:Response variable is: Earn R squared = 35.5%s = 5409 with 687 - 3 = 684 degrees of freedom Variable Coefficient SE(Coeff)t-ratio
Shoot to score, overtime The coach in Exercise 2 found a 95% confidence interval for the slope of his regression line.Recall that he is trying to understand how the number of goals scored is related to shots taken. Interpret with a sentence the meaning of the interval 0.099267 { 2 * 0.0125
Earnings VI Construct a 95% confidence interval for the slope of the regression line in Exercise 1. Interpret the meaning of the interval. Be sure to state it in the context of the data and the question about the data.
Shoot to score, number five What can the hockey coach in Exercise 2 conclude about shooting and scoring goals from the fact that the P-value 6 0.0001 for the slope of the regression line? Write a sentence in context.
Earnings, part V Use the information in Exercise 1 to test the hypotheses H0:b1 = 0 vs. HA:b1 ≠ 0. What do you conclude about the relationship between earnings and SAT scores?
Shoot to score, hat trick Returning to the results of Exercise 2, write a sentence to explain the meaning of the standard error of the slope of the regression line, SE(b1) = 0.0125, and the corresponding P-value.
Earnings, part IV Continuing with the regression of Exercise 1, write a sentence that explains the meaning of the standard error of the slope of the regression line, SE(b1) = 1.545, and the corresponding P-value.
Shoot to score, another one Using the regression output from Exercise 2, identify the residual standard deviation and explain its meaning with a sentence in context.
Earnings, part III Using the regression output in Exercise 1, identify the residual standard deviation and explain what it means in the context of the problem.
Shoot to score II Discuss the assumptions and conditions necessary for proceeding with the regression analysis in Exercise 2.Do you think the conditions are satisfied?
Earnings II Discuss the assumptions and conditions necessary for proceeding with the regression analysis in Exercise 1. Do you think the conditions are satisfied?
Shoot to score 2016 A college hockey coach collected data from the 2016–2017 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 65
Graduate earnings Does attending college pay back the investment? What factors predict higher earnings for graduates?Money magazine surveyed graduates, asking about their point of view of the colleges they had attended (Money’s Best Colleges). One good predictor of early career earnings
Education by age Use the survey results in the table to investigate differences in education level attained among different age groups in the United States.
Pregnancies 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
Survival on the 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’s a table with the relevant data. Do you think that survival was independent of whether the person
Racial steering 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
Full moon, next phase In Exercise 44, you found that the expected cell counts failed to satisfy the conditions for inference.a) 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.
Grades, again 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
Full moon 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
Grades 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
Working parents Gallup published results of 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
Montana revisited 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)
Fish diet 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)a) Is this a survey, a retrospective study, a
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