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intro stats
Stats Data And Models 4th Global Edition Richard D. De Veaux, Paul Velleman, David E. Bock - Solutions
Grant writing Does race matter when applying for National Institutes of Health grants? A new 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
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
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 author of the study suggested that these differences may be related to the temperature at the time the infant is 6 months old. (Source: Benson and Janette, Infant Behavior
Preemies Among 242 Cleveland-area children born prematurely at low birth weights between 1977 and 1979, only 74% graduated from high school. Among a comparison group of 233 children of normal birth weight, 83% were high school graduates. (Source: “Outcomes in Young Adulthood for
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 2007 and then again in 2008. In 2007, the fleet was driven without Motor Silk.
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 6 0.0001.a) What are the researchers’ null and
Eclampsia deaths Refer again to the research summarized in Exercise 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 2011 During the 2010–2011 NBA season, Stephen Curry led the league by making 212 of 227 free throws, for a success rate of 93.39%. But Chauncey Billups was close behind, with 384 of 419 (91.65%).a) Find a 95% confidence interval for the difference in their free throw percentages.b)
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.a) If births are uniformly distributed across all days of the week, how many would you expect on each day?b) Test the
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 an experiment to study this claim. Imagine that you have data on urinary tract cancers in
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 Unites States.We will consider the type of school as our response variable and will use
Right-to-work laws Are so-called “right-to-work”laws related to the percent of public sector employees in unions and the percent of private sector employees in unions? This data set looks at these percentages for the states in the United States in 1982. The dependent variable is whether the
Property assessments The following software outputs provide information about the Size (in square feet) of 18 homes in Ithaca, New York, and the city’s assessed Value of those homes.a) Explain why inference for linear regression is appropriate with these data.b) Is there a significant association
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.a) Comment on the assumptions for inference.b) Is there evidence of a strong association between the level
All the efficiency money can buy 2011 A sample of 84 model-2011 cars from an online information service was examined to see how fuel efficiency(as highway mpg) relates to the cost (Manufacturer’s Suggested Retail Price in dollars) of cars. Here are displays and computer output:a) State what you
Strike two Remember the Little League instructional video discussed in Chapter 23? Ads claimed it would improve the performances of Little League pitchers. To test this claim, 20 Little Leaguers threw 50 pitches each, and we recorded the number of strikes. After the players participated in the
Grades? The professor teaching the Introductory Statistics class discussed in Exercise 55 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)
Grades The data set below shows midterm scores from an Introductory Statistics course.a) 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 regression.Is the coefficient for the slope
Body fat, again Use the data from Exercise 53 to examine the association between Weight and %Body Fat.a) Find a 90% confidence interval for the slope of the regression line of %Body Fat on Weight.b) Interpret your interval in context.c) Give a 95% prediction interval for the %Body Fat of an
Body fat Do the data shown in the table below indicate an association between Waist size and %Body Fat?a) Test an appropriate hypothesis and state your conclusion.b) Give a 95% confidence interval for the mean %Body Fat found in people with a 40-inch Waist. Waist Weight Body Fat Waist Weight (in.)
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 2014 cnet.com tests tablet computers and continuously updates its list. As of January 2014, the list included the battery life (in hours) and luminous intensity (i.e., screen brightness, in cd>m2). We want to know if brighter screens are 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 48.a) Find a 95% confidence interval for the slope of the regression line. Interpret your interval in context.b) Last year, the drug manufacturer Eli Lilly,
Ozone, again Consider again the relationship between the population and ozone level of U.S. cities that you analyzed in Exercise 47.a) Give a 90% confidence interval for the approximate increase in ozone level associated with each additional million city inhabitants.b) For the cities studied, the
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
Climate change 2013 Data collected from around the globe show that the earth is getting warmer. The most common theory relates climate change to an increase in atmospheric levels of carbon dioxide (CO2), a greenhouse gas. The mean annual CO2 concentration in the atmosphere (parts per million) is
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
Winter 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. 60 Mean Jan. Temp (F) 47 30- 15+ 30
Cereals, part 2 Further analysis of the data for the breakfast cereals in Exercise 41 looked for an association between Fiber content and Calories by attempting to construct a linear model. Here are several graphs. Which of the assumptions for inference are violated? Explain. 12 Fiber (g) 6 8 3 50
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
SATs, again Consider the high school SAT scores data from Exercise 36 once more.a) Find a 90% confidence interval for the mean SAT-Math score for all students with an SAT-Verbal score of 500.b) Find a 90% prediction interval for the Math score of the senior class president if you know she scored
Fuel economy, part III Consider again the data in Exercise 35 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
SATs, part II Consider the high school SAT scores data from Exercise 36.a) Find a 90% confidence interval for the slope of the true line describing the association between Math and Verbal scores.b) Explain in this context what your confidence interval means.
Fuel economy, part II Consider again the data in Exercise 35 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.
SAT scores How strong was the association between student scores on the Math and Verbal sections of the old SAT? Scores on each ranged from 200 to 800 and were widely used by college admissions offices. Here are summaries and plots of the scores for a graduating class at Ithaca High School:a) Is
Fuel economy A consumer organization has reported T 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:a) Is there
Used cars 2010, again Based on the analysis of used car prices you did for Exercise 32, create a 95% confidence interval for the slope of the regression line and explain what your interval means in context.
Marriage age 2011, again Based on the analysis of marriage ages since 1975 given in Exercise 31, find a 95% confidence interval for the rate at which the age gap is closing. Explain what your confidence interval means.
Used cars 2010 Vehix.com offered several used Toyota Corollas for sale. Listed below are the ages of the cars and the advertised prices.a) Make a scatterplot for these data.b) Do you think a linear model is appropriate? Explain.c) Find the equation of the regression line.d) Check the residuals to
Marriage age 2011 The scatterplot suggests a decrease in the difference in ages at first marriage for men and women since 1975. We want to examine the regression to see if this decrease is significant.a) Write appropriate hypotheses.b) Here is the residuals plot and a histogram of the residuals.Do
Cholesterol, finis Based on the regression output seen in Exercise 26, create a 95% confidence interval for the slope of the regression line and interpret it in context.
Last dog Based on the regression output seen in Exercise 25, create a 95% confidence interval for the slope of the regression line and interpret your interval in context.
More cholesterol Look again at Exercise 26’s regression output for age and cholesterol level.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 this context.
Second frank Look again at Exercise 25’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 produced the regression analysis shown.Assuming that the data satisfy the conditions for inference, examine the association between age and cholesterol level.a) State the
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 22 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.
Movie budgets, the sequel Exercise 21 shows computer output examining the association between the length of a movie and its cost.a) Check the assumptions and conditions for inference.b) 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 1064 randomly selected houses that had been sold include data on price ($1000s) and size ($1000s ft2 ), producing the following graphs and computer output:Dependent variable is Price R-squared =
Movie budgets13 How does the cost of a movie depend on its length? Data on the cost (millions of dollars) and the running time (minutes) for major release films of 2005 are summarized in these plots and computer output:a) Explain in context what the regression says.b) The intercept is negative.
Drug use 2013 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. (Source: World Drug Report, 2013.
Tracking hurricanes 2012 In Chapter 6, we looked at data from the National Oceanic and Atmospheric Administration about their success in predicting hurricane tracks. On the following page is a scatterplot of the error (in nautical miles) for predicting hurricane locations 24 hours in the future vs.
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?
Graduation 2013 party Would it be wise for the administrators at the college described in Exercise 1 to conclude that lowering their admission rate (i.e., making it harder to get in) would help to increase their graduation rates? Why or why not?
Shoot to score, again The coach, still working with his superstar from Exercise 12, went on to suggest the player shoot more. Hopeful for 150 shots for the season, he calculated a 95% prediction interval for the number of goals this player might score. If the prediction interval for goals scored
Graduation 2013, part VIII The administrators from Exercise 1 also determined a 95% prediction interval for the graduation rate of a school admitting 33% of applicants to be (82.96,, 93.28,). Carefully explain what the 95% indicates for this interval.
Shoot to score, triple overtime As in Exercise 12, one of the coach’s best players has been in a slump, and the coach is trying to convince him to take more shots. Last year, the player took 104 shots. The coach calculated a 95% confidence interval for the mean number of goals a player would
Graduation 2013, part VII As in Exercise 11, the college described in Exercise 1 admits about 33% of applicants each year. Using their regression model, the administrators calculated a 95% confidence interval for the mean 6-Year Graduation Rate for all top colleges who admit 33% of students. The
Shoot to score, double overtime One of the coach’s best players has been in a slump, and the coach is trying to convince him to take more shots. Last year, the player took 104 shots. Would the standard error of the predicted number of goals he shot be larger or smaller than the standard error of
Graduation 2013, part VI The college described in Exercise 1 admits about 33% of applicants each year.Which will be larger, the standard error of the predicted 6-Year Graduation Rate of this college, or the standard error of the mean 6-Year Graduation Rate of all colleges admitting 33% of their
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 predict total goals scored based on shots taken. Interpret with a sentence the meaning of the interval 0.12 { 0.01.
Graduation 2013, part V The college administrators in Exercise 1 constructed a 95% confidence interval for the slope of their regression line. Interpret the meaning of their interval ( -0.332, -0.238) within the context of the problem.
Shoot to score, number four 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.
Graduation 2013, part IV The college administrators in Exercise 1 tested the hypotheses H0: b1 = 0 vs. HA:b1 0 and rejected the null hypothesis because the P-value was less than 0.0001. What can they conclude about the relationship between admission rates and graduation rates?
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) = 0.0053.
Graduation rates 2013, part III 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) = 0.0240.
Shoot to score another one Using the regression output from Exercise 2, identify the error standard deviation and explain its meaning with a sentence in context.
Graduation rates 2013, part II Using the regression output in Exercise 1, identify the error standard deviation and explain what it means in the context of the problem.
Shoot to score A college hockey coach collected data from the 2010–2011 National Hockey League season.He hopes to convince his players that the number of shots taken has an affect on the number of goals scored. The coach performed a preliminary analysis, using the scoring statistics from 293
Graduation rates 2013 A prestigious college is interested in factors that might be associated with better graduation rates. The administrators wonder whether there is a relationship between acceptance rates and graduation rates.Before proceeding with their regression inference, what conditions and
Look at the moon with binoculars or a telescope, and you’ll see craters formed by thousands of impacts. The earth, being larger, has been hit even more often. Meteor Crater in Arizona was the first recognized impact crater and was identified as such only in the 1920s. With the help of satellite
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. Education Level 25-34 35-44 Age Group 45-54 55-64 65 Not HS Grad 27 50 52 71 101 HS 82 19 88 83 59 1-3 Years College 43 56 26 20 4 Years
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, one more time In Exercise 48, you could have checked for a difference in the chances of survival for men and women using two-proportion z procedures.a) Find the z-value for this approach.b) Show that the square of your calculated value of z is the value of x2 you calculated
Steering, revisited You could have checked the data T in Exercise 47 for evidence of racial steering using two-proportion z procedures.a) Find the z-value for this approach, and show that when you square your z-value, you get the value of x2 you calculated in Exercise 47.b) Show that the resulting
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 In April 2009, Gallup published results from data collected from a large sample of adults in the 27 European Union member states. One of the questions asked was, “Which is the most practicable and realistic option for child care, taking into account the need to earn a living?”
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. Democrat Republican Independent West 39 17 12 Northeast 15 30 12
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.(Source: “Fatty Fish Consumption and Risk of Prostate Cancer,” Lancet, June 2001)a) Is this a survey, a retrospective study, a
Montana A poll conducted by the University of Montana classified respondents by whether they were male or female and political party, as shown in the table.We wonder if there is evidence of an association between being male or female and party affiliation.a) Is this a test of homogeneity or
Car origins A random survey of autos parked in the student lot and the staff lot at a large university classified the brands by country of origin, as seen in the table. Are there differences in the national origins of cars driven by students and staff?a) Is this a test of independence or
Cranberry juice It’s common folk wisdom that drinking cranberry juice can help prevent urinary tract infections in women. In 2001, the British Medical Journal reported the results of a Finnish study in which three groups of 50 women were monitored for these infections over 6 months. One group
NYPD again Examine and comment on this table of the standardized residuals for the chi-square test you looked at in Exercise 34. Male Female Officer -2.34 5.57 Detective -1.18 2.80 Sergeant 3.84 -9.14 Lieutenant 3.58 -8.52 Captain 2.46 -5.86 Higher Ranks 1.74 -4.14
Titanic, again Examine and comment on this table of the standardized residuals for the chi-square test you looked at in Exercise 33. Crew First Second Third Alive -4.35 9.49 2.72 -3.30 Dead 3.00 -6.55 -1.88 2.27
NYPD and sex discrimination The table below shows the rank attained by male and female officers in the New York City Police Department (NYPD). Do these data indicate that men and women are equitably represented at all levels of the department?a) What’s the probability that a person selected at
Titanic Here is a table we first saw in Chapter 2 showing who survived the sinking of the Titanic based on whether they were crew members, or passengers booked in first-, second-, or third-class staterooms:a) If we draw an individual at random, what’s the probability that we will draw a member of
Does your doctor know? (part 5) 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-square test on
Childbirth, part 5 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 alcohol, whether this was a
Does your doctor know? (part 4) In Exercises 24, 26, and 28, we’ve tested a hypothesis about whether the use of statistics in NEJM medical articles has changed over time. The table shows the test’s residuals.a) Show how the residual for the 1989/No cell was calculated.b) What can you conclude
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