Questions and Answers of Intro Stats

The Boston Marathon has had a wheelchair division since 1977. Who do you think is typically faster, the men’s marathon winner on foot or the women’s wheelchair marathon winner? Because the
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.Data From
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
Large herds of wild horses can become a problem on some federal lands in the West. Researchers hoping to improve the management of these herds collected data to see if they could predict the number
In Exercise 69, we saw the relationship between CO2 measured at Mauna Loa and average global temperature anomaly from 1959 to 2016. Here is a plot of average global temperatures plotted against
Here is a regression model in which the variable Alkali has been included in the model from Exercise 37:a) State the null and alternative hypotheses about the coefficient of pH in this regression.b)
In Chapter 6, Exercise 41 we examined the relationship between the fuel economy (Combined MPG) and Displacement (in liters) for 1211 models of cars. (Data in Fuel Economy 2016) Further analysis
In Exercise 15, the regression model Potassium = 38 + 27 Fiber relates fiber (in grams) and potassium content (in milligrams) in servings of breakfast cereals. Explain what the slope means.Data From
In Exercise 16, the regression model Combined MPG = 33.46 - 3.23 Displacement relates cars’ engine size to their fuel economy (Combined mpg). Explain what the slope means.Data From Exercise 16In
A student resampled the Maze times from Exercise 55 1000 times. The histogram shows the distributions of the means, and a summary of the quantiles is shown below it.a) Find a 99% bootstrap confidence
The College Board reported that 60.3% of all students who took the 2016 AP Statistics exam earned scores of 3 or higher. One teacher wondered if the performance of her school was better. She believed
Yahoo surveyed 2400 U.S. men. 1224 of the men identified themselves as the primary grocery shopper in their household.a) Estimate the percentage of all American males who identify themselves as the
Exercise 53 of Chapter 15 asked for a Student’s t-based test of the hypothesis that every bag of Chips Ahoy! cookies had at least 1000 chips. Here is a histogram of 10,000 bootstrapped means based
The information in Exercise 1 was used to create a 95% two-proportion confidence interval for the difference between Canadians and U.S. citizens who were born in foreign countries. Interpret this
In January 2016, at the end of his time in office, President Obama’s approval rating stood at 57% in Gallup’s daily tracking poll of 1500 randomly surveyed U.S. adults.
In Chapter 14 we saw data from samples of farmed salmon and examined the mirex content. The EPA sets a limit of 0.08 ppm as a maximum safe value. We performed a bootstrap on these data, drawing
In 2015, the U.S. Census Bureau reported that 62.2% of American families owned their homes—the lowest rate in 20 years. Census data reveal that the ownership rate in one small city is much lower.
According to the website Righting Injustice.com, about 77% of all underground storage tanks, or USTs, have “confirmed releases” or leaks. Researchers in California want to know if the percentage
Does ginkgo biloba enhance memory? Repeat the analysis in Exercise 70, this time using a randomization test to see if the difference in mean number of items recalled is statistically significant. Be
Using the data in Framingham, repeat the analysis in Exercise 69, this time using a randomization test to see if the difference in mean cholesterol levels is statistically significant. Be sure to
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
a) Make histograms of the cloud seeding data for both unseeded and seeded clouds. Do you think either of the inference methods used in Exercise R5.26 is appropriate? b) Find a re-expression that
The mean price of pizza in Baltimore was $2.85, $0.23 higher than the mean price of $2.62 in Dallas. To see if that difference was real, or due to chance, we took the 156 prices from Baltimore and
Horsepower is another measure commonly used to describe auto engines. Here are the summary statistics and histogram displaying horse powers of the same group of 38 cars discussed in Exercise R1.38.a)
Exercise 15 describes a regression model that estimates a cereal’s potassium content from the amount of fiber it contains. In this context, what does it mean to say that a cereal has a negative
Exercise 16 describes a regression model that uses a car’s engine displacement to estimate its fuel economy. In this context, what does it mean to say that a certain car has a positive
For Exercise 16’s regression model predicting fuel economy (in mpg) from the car’s engine size, se = 3.522. Explain in this context what that means.Data From Exercise 16In Chapter 6, Exercise 41
Avoiding an accident when driving can depend on reaction time. That time, measured from the moment the driver first sees the danger until he or she steps on the brake pedal, is thought to follow a
In Chapter 6, Exercise 45 looked at the relationship between the number of runs scored by American League baseball teams and the average attendance at their home games for the 2016 season. Here are
For Exercise 15’s regression model predicting potassium content (in milligrams) from the amount of fiber (in grams) in breakfast cereals, se = 30.77. Explain in this context what that means.Data
Numbeo.com lists the cost of living (COL) for 576 cities around the world. It reports the typical cost of a number of staples. Here are a scatterplot and regression relating the cost of a cappuccino
The National Interagency Fire Center (www .nifc.gov) reports statistics about wildfires. Here’s an analysis of the number of wildfires between 1985 and 2015.a) Is a linear model appropriate for
Burger King introduced a meat-free burger in 2002. The nutrition label for the 2014 BK Veggie burger (no mayo) is shown here:a) Use the regression model created in this chapter, Protein, to predict
Exercise 30 examined the association between the Duration of a roller coaster ride and the height of its initial Drop, reporting that R2 = 29.4,. Write a sentence in context, of course)
We saw in this chapter that in Tompkins County, New York, older bridges were in worse condition than newer ones. Tompkins is a rural area. Is this relationship true in New York City as well? Here are
The earth’s climate is getting warmer. The most common theory attributes the increase to an increase in atmospheric levels of carbon dioxide (CO2), a greenhouse gas. Here is a scatterplot showing
Exercise 41 of Chapter 6 looked at a sample of 35 vehicles to examine the relationship between gas mileage and engine displacement. The full data set holds data on 1211 cars. How well did our sample
data file Receivers 2015 holds information about the 488 NFL players who caught at least one pass during the 2015 football season. A typical 53-man roster has about 13 players who would be expected
Recall the data about the Burger King menu items in Chapter 7. Here are boxplots of protein content comparing items that contain meat with those that do not. The plot on the right graphs
We discussed the women’s 2016 Olympic heptathlon in Chapter 5. Here are the results from the high jump, 800-meter run, and long jump for the 27 women who successfully completed all three events in
Exercise 18 revisited the relationship between life expectancy and TVs per capita and saw that re-expression to the square root of TVs per capita made the plot more nearly straight. But was that the
The Centers for Disease Control and Prevention track cigarette smoking in the United States (www.cdc.gov/ nchs). How has the percentage of people who smoke changed since the danger became clear
The United Nations Development Programme (UNDP) uses the Human Development Index (HDI) in an attempt to summarize in one number the progress in health, education, and economics of a country
Exercise 17 looked at the distribution of protein in the Burger King menu items, comparing meat and non-meat items. That exercise offered the logarithm as a re-expression of Protein. Here are two
In Exercise 41, you investigated the federal rate on 3-month Treasury bills between 1950 and 1980. The scatterplot below shows that the trend changed dramatically after 1980, so we computed a new
We saw the data for the women’s 2016 Olympic heptathlon in Exercise 73. Are the two jumping events associated? Perform a regression of the long-jump results on the high-jump results.a) What is the
Marine biologists warn that the growing number of powerboats registered in Florida threatens the existence of manatees. The data in the table come from the Florida Fish and Wildlife Conservation
Continue your analysis of the manatee situation from Exercise R2.8.a) Create a linear model of the association between Manatee Deaths and Powerboat Registrations.b) Interpret the slope of your
Recall the example of life expectancy vs. TVs per person in the chapter. In that example, we use the square root of TVs per person. Here are the original data and the re-expressed version. Which of
Exercise R2.9 fit a regression model to the relationship between BCI and pH in streams sampled in the Adirondack Mountains. More variables are available. For example, scientists also recorded the
Exercise R2.7 examined the correlation between BCI and pH in streams sampled in the Adirondack Mountains. Here is the corresponding regression model:a) Write the regression model.b) What is the
Several exercises in Chapter 7 showed that attendance at American League baseball games increased with the number of runs scored. But fans may respond more to winning teams than to high-scoring
Can we predict the Horsepower of the engine that manufacturers will put in a car by knowing the Weight of the car? Here are the regression analysis and residuals plot:a) Write the equation of the
Several exercises in Chapter 7 showed that attendance at American League baseball games increased with the number of runs scored. But fans may respond more to winning teams than to high-scoring
There is evidence that eruptions of Old Faithful can best be predicted by knowing the duration of the previous eruption.a) Describe what you see in the scatterplot of Intervals between eruptions vs.
The Child Trends Data Bank monitors issues related to children. The table shows a 50-state average of the percent of expectant mothers who smoked cigarettes during their pregnancies.a) Create a
Researchers studied the dexterity of children using a timed test called the Functional Dexterity Test (FDT). Of course, they needed to allow for differences in dexterity between their subjects’
Look again at the correlation table for cars in the previous exercise.a) Which two variables in the table exhibit the strongest association?b) Is that strong association necessarily cause-and-effect?
The downward trend in smoking you saw in the last exercise is good news for the health of babies, but will it ever stop?a) Explain why you can’t use the linear model you created in Exercise R2.26
The data set Grades shows the five scores from an Introductory statistics course. Find a model for final exam score by trying all possible models with two predictor variables. Which model would you
Data from 50 large U.S. cities show the mean January Temperature and the Latitude. Describe what you see in the scatterplot. Avg. Jan. Temp (°F) 60 45 30 + + 15+ 30 35 40 Latitude (°N) 45
The data on candy bars per serving from Exercise 16 also has information on whether the candy bar has nuts. The variable Nuts is coded 0 for candy bars without nuts and 1 for those with nuts.
The Scottish hill races considered in Exercises 14 and 29 are run by both men and women. We can combine the data to fit a single model for both. Here is one such model. The variable Climb*Sex is the
The study of U.S. cities in Exercise R2.29 found the mean January Temperature (degrees Fahrenheit), Altitude (feet above sea level), and Latitude (degrees north of the equator) for 55 cities.
Scottish hill races considered in Exercise 14 are run by both men and women. We can combine the data to fit a single model for both. Here is one such model. The variable Dist*Sex is the product of
How are Olympic performances in various events related? The plot shows winning long-jump and high-jump distances, in meters, for the Summer Olympics from 1912 through 2016:a) Describe the
Twins are often born at less than 9 months gestation. The graph from the Journal of the American Medical Association (JAMA) shows the rate of preterm twin births in the United States over the past 20
The September 1998 issue of the American T Psychologist published an article by Kraut et al. that reported on an experiment examining “the social and psychological impact of the Internet on 169
It’s commonly believed that people use tips to reward good service. A researcher for the hospitality industry examined tips and ratings of service quality from 2645 dining parties at 21 different
Here are the average weights of the football team for the University of Texas for various years in the 20th century.a) Fit a straight line to the relationship of Weight by Year for Texas football
How are a company’s profits related to its sales? Let’s examine data from 71 large U.S. corporations. All amounts are in millions of dollars.a) Histograms of Profits and Sales and histograms of
Here are the summary statistics for the Olympic jumps displayed in the previous exercise.a) Write the equation of the line of regression for estimating High Jump from Long Jump.b) Interpret the
How are the assets and sales of major corporations related? The data set is the same as that for Exercise 2.44. The variable Banks in the data set is 1 for the banks and 0 for the other companies. As
Does how long toddlers sit at the lunch table help predict how much they eat? The table and graph show the number of minutes the kids stayed at the table and the number of calories they consumed.
As a class project, students in a large statistics class collected publicly available information on recent home sales in their hometowns. There are 894 properties. Among the variables available is
As a class project, students in a large statistics class collected publicly available information on recent home sales in their hometowns. There are 894 properties. Important predictors of the price
For the real estate data of the previous exercise, consider the value of the number of bedrooms in modeling the price of a home. The correlation between Price and Bedrooms is 0.116. Here is a
In Chapter 8 we learned about the extraordinary depth and duration of the dives taken by penguins. In that chapter we modeled a re-expression of Heart rate with the Duration (min) of dives. The data
Readers’ Digest (April 2002) reported results of several surveys that asked graduate students to examine photographs of men and women and try to guess their ages. Researchers compared these guesses
To obtain enough plants for the tomato experiment of Exercise 4, experimenters have to purchase plants from two different garden centers. They then randomly assign the plants from each garden center
What fraction of cars made in Japan? The computer output below summarizes the results of a random sample of 50 autos. z-Interval for proportion With 90.00% confidence, 0.29938661 P(japan) < 0.46984416
Exercise 21 describes an experiment that showed that high doses of omega-3 fats might be of benefit to people with bipolar disorder. The experiment involved a control group of subjects who received a
An automatic character recognition device can successfully read about 85% of handwritten credit card applications. To estimate what might happen when this device reads a stack of applications, the
Exercise 24 describes an experiment showing that exercise helped people sleep better. The experiment involved other groups of subjects who didn’t exercise. Why didn’t the experimenters just have
Exercises 21, 35, and 37 describe an experiment investigating the effectiveness of omega-3 fats in treating bipolar disorder. Suppose some of the 30 subjects were very active people who walked a lot
A 2015 study conducted by the National Center for Health Statistics (www.cdc.gov/nchs/data/ nhis/earlyrelease/wireless201512.pdf) found that 51% of U.S. households had no landline service. This
The weather reporter on TV makes predictions such as a 25% chance of rain. What do you think is the meaning of such a phrase?
For high school students graduating in 2015, college admissions to the nation’s most selective schools were the most competitive in memory. Harvard accepted about 5.3% of its applicants, Dartmouth
In Exercise 37 we saw that in 2015 Harvard accepted about 5.3% of its applicants, Dartmouth 10%, and Penn 9.9%. Jorge has applied to all three. He figures that his chances of getting into at least
The 95% confidence interval for the number of teens in Exercise 5 who reported that they went online several times daily is from 53% to 59%.a) Interpret the interval in this context.b) Explain the
Consider the poll of Exercise 15.a) Are the assumptions and conditions met?b) Would the margin of error be larger or smaller for 95% confidence? Data From Exercise 15An Ipsos/Reuters poll
In 2013 the environmental group Oceana (usa.oceana.org) analyzed 1215 samples of seafood purchased across the United States and genetically compared the pieces to standard gene fragments that can
In Chapter 4, Exercise 38, we saw an ogive of the distribution of cholesterol levels (in mg/dL) of a random sample of 1406 participants (taken in 1948 from Framingham, MA). To find a bootstrap
A Consumer Reports study similar to the one described in Exercise 31 found that 12 of the 22 “red snapper” packages tested were a different kind of fish.a) Are the conditions for creating a
The Pew Research poll described in Exercise 5 found that 56% of a sample of 1060 teens go online several times a day. (Treat this as a simple random sample.)a) Find the margin of error for this poll
Chapter 2, Exercise 16 showed the histogram of the European shoe sizes from a sample of 269 college students. Looking at the men only, a 95% confidence interval for the mean shoe size shows: 95
The Professional Golfers Association reported the average distance that 199 professional golfers drove the ball (in yd) during a week in 2015. Here is a histogram of those drives. Assume this is a
In 2016, the Centers for Disease Control and Prevention reported that 36.5% of adults in the United States are obese. A county health service planning a new awareness campaign polls a random sample
For the confidence interval you found in Exercise 11, interpret this interval and explain what 95% confidence means in this context.Data From Exercise 11The housing market recovered slowly from the
In the latest National Health and Nutrition Examination Survey (NHANES 2013/2014 – wwwn.cdc.gov/nchs/nhanes), pulse rate (30 sec rate multiplied by 2) of 2536 U.S. adults averaged 71.6 beats/min

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