Questions and Answers of Intro Stats

Referring to the study of Exercise 1:a) Is the alternative to the null hypothesis more naturally one sided or two-sided?b) The P-value from a clinical trial testing the hypothesis is 0.0028. What do
After the political ad campaign described in Exercise 15, part a, pollsters check the governor’s negatives. They test the hypothesis that the ads produced no change against the alternative that the
During the first 15 weeks of the 2016 season, the home team won 137 of the 238 regular-season National Football League games. Is this strong evidence of a home field advantage in professional
For the interval given in Exercise 3, explain what “95% confidence” means.Data From Exercise 3The information in Exercise 1 was used to create a 95% two-proportion confidence interval for
A study of the effects of acid rain on trees in the Hopkins Forest shows that 25 of 100 trees sampled exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted
For the interval given in Exercise 4, explain what “95% confidence” means.Data From Exercise 4The researchers from Exercise 2 created a 95% two-proportion confidence interval for the
The researchers from Exercise 1 want to test if the proportions of foreign born are the same in the United States and Canada. What is the appropriate standard error to use for the hypothesis test?a)
How large are hamster litters? Among 47 golden hamster litters recorded, there were an average of 7.72 baby hamsters, with a standard deviation of 2.5 hamsters per litter.a) Create and interpret a
Complete the analysis begun in Exercise 2.a) What is the difference in the proportions of the two types of companies?b) What is the value of the z-statistic?c) What do you conclude at α = 0.05?Data
A group of 5 women became pregnant while undergoing fertility treatments with the drug Clomid, discussed in Exercise 4. What’s the probability thata) None will have twins?b) Exactly 1 will have
Using the summary statistics provided in Exercise 11, researchers calculated a 95% confidence interval for the mean difference between Walmart and Target purchase amounts. The interval was (–14.15,
We have seen data on ballpark attendance in Chapters 6, 7, and 9. Now we find that National League teams drew in, on average, nearly 60,000 more fans per season than American League teams. That
In Exercise 72, we saw that the towns in the region south of Derby seemed to have fewer deaths than the towns in the north. To see whether that difference is statistically significant, look at this
Using the summary statistics provided in Exercise 12, the sports reporter calculated the following 95% confidence interval for the mean difference between major league baseball players and
We have data on the city and highway fuel efficiency of 633 cars and trucks.a) Would it be appropriate to use paired t methods to compare the city fuel efficiency of the cars and the trucks?b) Would
Consider the weights from Exercise 4. The side-by-side boxplots below show little difference between the two groups. Should this be sufficient to draw a conclusion about the accuracy of the
In a survey of 1002 U.S. adults in December 2016 by Pew Research (www.journalism.org/2016/12/15/many-americans-believe-fake-news-is- owing-confusion/), 64% of adult respondents say they think that
Examine and comment on this table of the standardized residuals for the chi-square test you looked at in Exercise 33.Data From Exercise 33Here is a table we first saw in Chapter 2 showing who
In March 2016, Pew Research asked a random sample of 2254 U.S. adults, “Do you strongly favor, favor, oppose, or strongly oppose allowing gays and lesbians to marry legally?”
Data collected in 2015 by the Behavioral Risk Factor Surveillance System revealed that in the state of New Jersey, 27.3% of whites and 47.2% of blacks were cigarette smokers. Suppose these
Data From Exercise 1Does 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
Examine and comment on this table of the standardized residuals for the chi-square test you looked at in Exercise 34.Data From Exercise 34The table below shows the rank attained by male and
For the data in Exercise 2,a) Compute the standardized residual for each type of card.b) Are any of these particularly large? (Compared to what?)c) What does the answer to part b say about this new
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.
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,
Discuss the assumptions and conditions necessary for proceeding with the regression analysis in Exercise 2. Do you think the conditions are satisfied?Data From Exercise 2A college hockey coach
Discuss the assumptions and conditions necessary for proceeding with the regression analysis in Exercise 1. Do you think the conditions are satisfied?Data From Exercise 1Does attending college pay
Using the regression output in Exercise 1, identify the residual standard deviation and explain what it means in the context of the problem.Data From Exercise 1Does attending college pay back the
Consider the relationship between the life expectancy (in years) and the illiteracy rate (per hundred people) in the 50 U.S. states plus Washington, DC. A linear model is run and the output is
Use the information in Exercise 1 to test the hypotheses H0: β1 = 0 vs. HA: β1 ≠ 0. What do you conclude about the relationship between earnings and SAT scores?Data From Exercise 1Does
Since 2000, Cornell University has used lake source cooling plant that circulates water from Cayuga Lake through a heat transfer system to chill water for use on campus in refrigeration and air
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.Data
A Harvard psychologist recruited 75 female hotel maids to participate in a study. She randomly selected 41 and informed them (truthfully) that the work they do satisfies the Surgeon General’s
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
A Harvard psychologist recruited 75 female hotel maids to participate in a study. She randomly selected 41 and informed them (truthfully) that the work they do satisfies the Surgeon General’s
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:a) Write the regression model.b) What is the
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:a) The coefficient of SAT
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.
The Belmont Stakes is the last and longest of the three horse races that make up the Triple Crown. Curiously, some of the Belmont races have been run clockwise around the track, and others have been
But maybe the BMIs of all the participants changed during the four-week period. We can calculate the change in BMI for each participant in the study, and then compare the mean change for the 41 maids
Which type of study is this?a) A prospective observational study because it followed the maids for four weeks.b) A retrospective observational study because at the end of four weeks, the researcher
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 Time OnIce/Game (TOI/G) (in minutes per game) to the
The Paralyzed Veterans of America (PVA) is a Congressionally chartered veterans’ service organization that represents the interests of paralyzed veterans. The agency provides a range of services to
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
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:a) What is the
On January 22, 2017, www.autotrader.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
Are twin births becomming more common? Part II Review Exercise R2.5 looked at the number of twin births by year from 1980 to 2014. Now we can include some inference:a) State and test the standard
A regression of the calories in breakfast cereals on their carbohydrate content (g) looks like this:A second regression with fiber content included gives this model: A second regression with fiber
Exercise R5.41 looked at regressions to model calories in breakfast cereals based on their carbohydrates and fiber content. Here is a scatterplot of carbohydrates vs. fiber content for these
The study described in Exercise R5.21 also looked at scores in mathematics and language. Here are software outputs for the appropriate tests. Data From Exercise R5.21Several programs attempt to
The Pew Research Center conducted a representative telephone survey in October of 2016. Among the reported results was the following table concerning the preferred political party affiliation of
At a barbershop music singing competition, choruses are judged on three scales: Music (quality of the arrangement, etc.), Performance, and Singing. The scales are supposed to be independent of each
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
We saw in Part II Review Exercise R2.21 that Old Faithful eruptions do not occur at constant intervals and the intervals may vary greatly. In that exercise, we fit a regression model, which we can
Consider once again the CO2 and global temperature data of Exercise 41. The mean CO2 level for these data is 352.566 ppm.a) Find a 90% confidence interval for the mean global temperature
Peninsula Creameries sells both cottage cheese and ice cream. The CEO recently noticed that in months when the company sells more cottage cheese, it seems to sell more ice cream as well. Two of his
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
Fitting someone for a hearing aid requires assessing the patient’s hearing ability. In one method of assessment, the patient listens to a tape of 50 English words. The tape is played at low volume,
Who reads the newspaper more, men or women? Eurostat, an agency of the European Union (EU), conducts surveys on several aspects of daily life in EU countries. Recently, the agency asked samples of
For each of the following descriptions, select the letter of the inference method you would use a) Ithaca garbage bags In Ithaca, New York, every garbage bag must be tagged and not exceed 20 lb
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.a) The
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
Has the trend of decreasing difference in age at first marriage seen in Exercise 42 gotten stronger recently? The scatterplot and residual plot for the data from 1980 through 2015, along with a
People swam across Lake Ontario from Niagara on the Lake to Toronto (52 km, or about 32.3 mi) 62 times between 1954 and 2016. We might be interested in whether the swimmers are getting any faster or
In Chapter 7, we found a relationship between the age of a bridge in Tompkins County, New York, and its condition as found by inspection. (Data in Tompkins County Bridges 2016) But we considered only
In Exercise 46, we saw in the Swim the Lake 2016 data that Vicki Keith’s round-trip swim of Lake Ontario was an obvious outlier among the other one-way times.Here is the new regression after this
Look again at the graph of the age at first marriage for women in Exercise 42. Here is a regression model for the data on women, along with a residuals plot:a) Based on this model, what would you
The World Bank reports many demographic statistics about countries of the world. The data file holds the Fertility rate (births per woman) and the female Life expectancy at birth (in years) for 200
The Consumer Price Index (CPI) tracks the prices of consumer goods in the United States, as shown in the following table. The CPI is reported monthly, but we can look at selected values. The table
In Exercise 29, we considered whether a linear model would be appropriate to describe the trend in the number of passengers departing from the Oakland (CA) airport each month since the start of 1997.
Look once more at the data from Tour de France 2016. In Exercise 52, we looked at the whole history of the race, but now let’s consider just the modern era from 1967 on.a) Make a scatterplot and
Here is a table of the 9 sun-orbiting objects formerly known as planets.a) Plot the Length of the year against the Distance from the sun. Describe the shape of your plot.b) Re-express one or both
Consider again the post-1950 trend in U.S. GDP we examined in Exercise 61. Here are regression output and a residual plot when we use the log of GDP in the model. Is this a better model for GDP?
The scatterplot shows the gross domestic product (GDP) of the United States in trillions of 2009 dollars plotted against years since 1950.A linear model fit to the relationship looks like this:a)
Every year, US News and World Report publishes a special issue on many U.S. colleges and universities. The scatterplots have Student/Faculty Ratio (number of students per faculty member) for the
Listed below are the world record men’s weightlifting performances as of 2016.a) Create a linear model for the Weight Lifted in each Weight Class, leaving out the 105+ unlimited class.b) Check the
In January 2012, the New York Times published a story called Twin Births in the U.S., Like Never Before, in which they reported a 76 percent increase in the rate of twin births from 1980 to 2009.
In July 2005, astronomers Mike Brown, Chad Trujillo, and David Rabinowitz announced the discovery of a sun-orbiting object, since named Eris,8 that is 5% larger than Pluto. Eris orbits the sun once
The Dow Jones stock index measures the performance of the stocks of America’s largest companies (finance.yahoo.com). A regression of the Dow prices on years 1972–2015 looks like this:a) What is
Insurance companies and other organizations use actuarial tables to estimate the remaining lifespans of their customers. The data file gives life expectancy and estimated additional years of life for
Biologists studying the effects of acid rain on wildlife collected data from 163 streams in the Adirondack Mountains. They recorded the pH (acidity) of the water and the BCI, a measure of biological
The 3-month Treasury bill interest rate is watched by investors and economists. Here’s the scatterplot of the 3-month Treasury bill rate since 1934 that we saw in Exercise 43:Clearly, the
In Chapters 4 and 6 we’ve seen data from the Hopkins Forest. Here’s a regression that models the maximum daily wind speed in terms of the average temperature and precipitation: a) Write the
You pick a card from a standard deck and record its denomination (7, say) and its suit (maybe spades).a) Is the variable suit categorical or quantitative?b) Name a game you might be playing for which
Results of a 1996 American Medical Association report about the infant mortality rate for twins carried for the full term of a normal pregnancy are shown on the next page, broken down by the level of
The times from the first race of the women’s 2 x 500-m speed skating timesare listed in the table below.a) The mean finishing time was 40.72 seconds, with a standard deviation of 9.82 seconds. If
A study by the Pew Internet & American Life Project found that 78% of U.S. residents over 16 years old read a book in the past 12 months. They also found that 21% had read an e-book using a
In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water
The data set from England and Wales also notes for each town whether it was south or north of Derby. Here are some summary statistics and a comparative boxplot for the two regions.a) What is the
Average daily temperatures in January and July for 60 large U.S. cities are graphed in the histograms below.a) What aspect of these histograms makes it difficult to compare the distributions?b) What
Progressive Insurance asked customers who had been involved in auto accidents how far they were from home when the accident happened. The data are summarized in the table.a) Create an appropriate
It is a common belief that Yellowstone’s most famous geyser erupts once an hour at very predictable intervals. The histogram below shows the time gaps (in minutes) between 222 successive eruptions.
Is the Statue of Liberty’s nose too long? Her nose measures 4'6", but she is a large statue, after all. Her arm is 42 feet long. That means her arm is 42/4.5 = 9.3 times as long as her nose. Is
The histogram shows the distribution of mean ACT composite scores for all Wisconsin public schools in 2015. 80.1% of the data points fall between one standard deviation below the mean and one
A study in South Africa focusing on the impact of health insurance identified 1590 children at birth and then sought to conduct follow-up health studies 5 years later. Only 416 of the original group
Does the duration of an eruption have an effect on the length of time that elapses before the next eruption?a) The histogram below shows the duration (in minutes) of those 222 eruptions. Describe
Here are the number of pieces of mail received at a school office for 36 days.a) Plot these data.b) Find appropriate summary statistics.c) Write a brief description of the school’s mail
The National Highway Traffic Safety Administration reported that there were 3206 fatal accidents involving drivers between the ages of 15 and 19 years old the previous year, of which 65.5% involved
One measure of the size of an automobile engine is its “displacement,” the total volume (in liters or cubic inches) of its cylinders. Summary statistics for several models of new cars are shown.
Is your birth order related to your choice of major? A statistics professor at a large university polled his students to find out what their majors were and what position they held in the family

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