Questions and Answers of Practice of Statistics

Of the 98 teachers who responded, 23.5% said that they had one or more tattoos.a. Construct and interpret a 95% confidence interval for the true proportion of all teachers at the AP® institute who
What percent of U.S. adults have one or more tattoos? The Harris Poll conducted an online survey of 2302 adults and found 29% of respondents had at least 1 tattoo. According to the published report,
Marcella takes a shower every morning when she gets up. Her time in the shower varies according to a Normal distribution with mean 4.5 minutes and standard deviation 0.9 minute.a. Find the
A scatterplot of y versus x shows a positive, nonlinear association. Two different transformations are attempted to try to linearize the association: using the logarithm of the y -values and using
Students in Mr. Handford’s class dropped a kickball beneath a motion detector. The detector recorded the height of the ball (in feet) as it bounced up and down several times. Here is computer
Some high school physics students dropped a ball and measured the distance fallen (in centimeters) at various times (in seconds) after its release. If you have studied physics, you probably know that
Suppose that the relationship between a response variable y and an explanatory variable x is modeled by y = 2.7(0.316)x.Which of these scatterplots would approximately follow a straight line?a. A
Companies work hard to have their website listed at the top of an Internet search. Is there a relationship between a website’s position in the results of an Internet search (1 = top position,2=2nd
Here are some data on the hearts of various mammals:a. Make an appropriate scatterplot for predicting heart weight from length. Describe what you see.b. Use transformations to linearize the
How well do professional golfers putt from various distances to the hole? The scatterplot shows various distances to the hole (in feet) and the percent of putts made at each distance for a sample of
Ecologists look at data to learn about nature’s patterns. One pattern they have identified relates the size of a carnivore (body mass in kilograms) to how many of those carnivores exist in an area.
Many populations grow exponentially. Here are the data for the estimated population of North America (in millions) from 1700 to 2012. The dates are recorded as years since 1700 so that x = 312 is the
Many populations grow exponentially. Here are the data for the estimated population of Europe (in millions) from 1700 to 2012. The dates are recorded as years since 1700 so that x = 312 is the year
Some college students collected data on the intensity of light at various depths in a lake. Here is a scatterplot of their data:a. At top right is a scatterplot of the natural logarithm of light
Expose marine bacteria to X-rays for time periods from 1 to 15 minutes. Here is a scatterplot showing the number of surviving bacteria (in hundreds) on a culture plate after each exposure time:a.
How is the braking distance for a car related to the amount of tread left on the tires? Here are the braking distances (measured in car lengths) for a car making a panic stop in standing water, along
How is the braking distance for a motorcycle related to the speed at which the motorcycle was traveling when the brake was applied? Statistics teacher Aaron Waggoner gathered data to answer this
It is easy to measure the diameter at breast height (in centimeters) of a tree. It’s hard to measure the total aboveground biomass (in kilograms) of a tree, because to do this, you must cut and
How is the weight of an animal’s brain related to the weight of its body? Researchers collected data on the brain weight (in grams) and body weight (in kilograms) for 96 species of mammals. The
Refer to Exercise 33. We took the logarithm (base 10) of the values for both length and period. Here is some computer output from a linear regression analysis of the transformed data.a. Based on the
Refer to Exercise 34. We took the logarithm (base 10) of the values for both volume and pressure. Here is some computer output from a linear regression analysis of the transformed data.a. Based on
Refer to Exercise 34. Here is a graph of 1Pressure versus volume, along with output from a linear regression analysis using these variables:a. Give the equation of the least-squares regression line.
Refer to Exercise 33. Here is a graph of period2 versus length, along with output from a linear regression analysis using these variables.a. Give the equation of the least-squares regression line.
If you have taken a chemistry or physics class, then you are probably familiar with Boyle’s law: for gas in a confined space kept at a constant temperature, pressure times volume is a constant (in
Mrs. Hanrahan’s precalculus class collected data on the length (in centimeters) of a pendulum and the time (in seconds) the pendulum took to complete one back-andforth swing (called its period).
In the game of Yahtzee, 5 six-sided dice are rolled simultaneously. To get a Yahtzee, the player must get the same number on all 5 dice.a. Luis says that the probability of getting a Yahtzee in one
Can we use a student’s word task time to predict his or her color task time?a. Make an appropriate scatterplot to help answer this question. Describe what you see.b. Use technology to find the
Now let’s analyze the data.a. Calculate the difference (Colors-Words) for each subject and summarize the distribution of differences with a boxplot. Does the graph provide evidence of a difference
Let’s review the design of the study.a. Explain why this was an experiment and not an observational study.b. Did Mr. Starnes use a completely randomized design or randomized block design? Why do
Which of the following would have resulted in a violation of the conditions for inference?a. If the entire sample was selected from one classroomb. If the sample size was 15 instead of 25c. If the
Which of the following is a 95% confidence interval for the population slope β1?a. 3.0867 ± 0.4117b. 3.0867 ± 0.8518c. 3.0867 ± 0.8069d. 3.0867 ± 0.8497e. 3.0867 ± 0.8481To see if students with
Which of the following is the best interpretation of the value 0.4117 in the computer output?a. For each increase of 1 cm in foot length, the average height increases by about 0.4117 cm.b. When using
Is there convincing evidence that height increases as foot length increases? To answer this question, test the hypothesesa. H0:β1 = 0 versus Ha:β1 > 0.b. H0:β1 = 0 versus Ha: β1 < 0.c.
The slope β1 of the population regression line describesa. The exact increase in height (cm) for students at this high school when foot length increases by 1 cm.b. The average increase in foot
Which of the following is the equation of the least-squares regression line for predicting height from foot length?a.b.c.d.e.To see if students with longer feet tend to be taller, a random sample of
Exercise 75 in Chapter 10 (page 686) compared two methods for estimating tire wear. The first method used the amount of weight lost by a tire. The second method used the amount of wear in the grooves
A random sample of 21 AP® Statistics teachers was asked to report the age (in years) and mileage of their primary vehicles. Here is a scatterplot of the data:Here is some computer output from a
Is there a relationship between a student’s GPA and the number of pencils in his or her backpack? Jordynn and Angie decided to find out by selecting a random sample of students from their high
Nicole and Elena wanted to know if listening to music at a louder volume negatively impacts test performance. To investigate, they recruited 30 volunteers and randomly assigned 10 volunteers to
Here are data on the time (in minutes) Professor Moore takes to swim 2000 yards and his pulse rate (beats per minute) after swimming on a random sample of 23 days:Is there convincing evidence of a
A researcher from the University of California, San Diego, collected data on average per capita wine consumption and heart disease death rate in a random sample of 19 countries for which data were
Does how long young children remain at the lunch table help predict how much they eat? Here are data on a random sample of 20 toddlers observed over several months. “Time” is the average number
Lamb’s quarters is a common weed that interferes with the growth of corn. An agriculture researcher planted corn at the same rate in 16 small plots of ground and then weeded the plots by hand to
The students in Mr. Shenk’s class measured the arm spans and heights (in inches) of a random sample of 18 students from their large high school. Here is computer output from a leastsquares
Do beavers benefit beetles? Researchers laid out 23 circular plots, each 4 meters in diameter, at random in an area where beavers were cutting down cottonwood trees. In each plot, they counted the
When Mentos are dropped into a newly opened bottle of Diet Coke, carbon dioxide is released from the Diet Coke very rapidly, causing the Diet Coke to be expelled from the bottle. To see if using more
Kerry and Danielle wanted to investigate if tapping on a can of soda would reduce the amount of soda expelled after the can has been shaken. For their experiment, they vigorously shook 40 cans of
Refer to Exercises 6 and 8.a. Find the critical value for a 90% confidence interval for the slope of the true regression line. Then calculate the confidence interval.b. Interpret the interval from
Refer to Exercises 5 and 7.a. Find the critical value for a 99% confidence interval for the slope of the true regression line. Then calculate the confidence interval.b. Interpret the interval from
Refer to Exercise 6. Here is computer output from the least-squares regression analysis of the perch data.a. What is the estimate for β0? Interpret this value.b. What is the estimate for β1?
Refer to Exercise 5. Here is computer output from the least-squares regression analysis of the beer and blood alcohol data.a. What is the estimate for β0? Interpret this value.b. What is the
Here is one way in which nature regulates the size of animal populations: high population density attracts predators, which remove a higher proportion of the population than when the density of the
Conduct a follow-up analysis for the test in Exercise 50.Exercise 50.A study of first-year college students asked separate random samples of students from private and public universities the
One of the first decisions the class had to make was what kind of sampling method to use.a. They knew that a simple random sample was the “preferred” method. With 1100 teachers in 40 different
How well does the number of beers a person drinks predict his or her blood alcohol content (BAC)? Sixteen volunteers aged 21 or older with an initial BAC of 0 took part in a study to find out. Each
Is there a relationship between the percent of high school graduates in each state who took the SAT and the state’s mean SAT Math score? Here is a residual plot from a linear regression analysis
Researchers examined data on the depth of small defects in the Trans-Alaska Oil Pipeline. The researchers compared the results of measurements on 100 defects made in the field with measurements of
Using the daily high and low temperature readings at Chicago’s O’Hare International Airport for an entire year, a meteorologist made a scatterplot relating y = high temperature to x = low
Using the health records of every student at a high school, the school nurse created a scatterplot relating y = height (in centimeters) to x=age (in years). After verifying that the conditions for
In this project, your team will formulate a statistical question, design a study to answer the question, conduct the study, collect the data, analyze the data, and use statistical inference to answer
In each of the following settings, state which inference procedure from Chapter 8, 9, 10, or 11 you would use. Be specific. For example, you might answer, “Two-sample z test for the difference
Cocaine addicts need cocaine to feel any pleasure, so perhaps giving them an antidepressant drug will help. A 3-year study with 72 chronic cocaine users compared an antidepressant drug called
The students decided to compare the average ratings of the cafeteria food on the two scales.a. Find the mean and standard deviation of the ratings for the students who were given the 1-to-5 scale.b.
a. Was this an observational study or an experiment? Justify your answer.b. Explain why it would not be appropriate to perform a chi-square test in this setting.For their final project, a group of
For these data, χ2 = 69.8 with a P-value of approximately 0. Assuming that the researchers used a significance level of 0.05, which of the following is true?a. A Type I error is possible.b. A Type
In each of the following settings, state which inference procedure from Chapter 8, 9, 10, or 11 you would use. Be specific. For example, you might answer, “Two-sample z test for the difference
When analyzing survey results from a two-way table, the main distinction between a test for independence and a test for homogeneity is a. How the degrees of freedom are calculated.b. How the
Which of the following is the correct number of degrees of freedom for the chi-square test using these data?a. 4b. 8c. 10d. 20e. 4876The National Longitudinal Study of Adolescent Health interviewed a
Which of the following is the expected count of females who respond “Almost certain”?a. 487.7b. 525c. 965d. 1038.8e. 1174The National Longitudinal Study of Adolescent Health interviewed a random
A survey by the National Institutes of Health asked a random sample of young adults (aged 19 to 25 years), “Where do you live now? That is, where do you stay most often?” Here is the full two way
The General Social Survey (GSS) asked separate random samples of people with only a high school degree and people with a bachelor’s degree, “Do you favor or oppose the death penalty for persons
Which of the following is the appropriate null hypothesis for performing a chi-square test?a. Equal proportions of female and male teenagers are almost certain they will be married in 10 years.b.
Gastric freezing was once a recommended treatment for ulcers in the upper intestine. Use of gastric freezing stopped after experiments showed it had no effect. One randomized comparative experiment
A study of first-year college students asked separate random samples of students from private and public universities the following question: “How many miles is this university from your permanent
Conduct a follow-up analysis for the test in Exercise 49.Exercise 49.A survey by the National Institutes of Health asked a random sample of young adults (aged 19 to 25 years), “Where do you live
Determine which chi-square test is appropriate in each of the following settings. Explain your reasoning.a. Does chocolate help heart-attack victims live longer? Researchers in Sweden randomly
Determine which chi-square test is appropriate in each of the following settings. Explain your reasoning.a. With many babies being delivered by planned cesarean section, Mrs. McDonald’s statistics
A recent poll conducted by the Pew Research Center asked a random sample of 1846 Internet users if they do any of their banking online. The table summarizes their responses by age. Is there
A random sample of U.S. adults was recently asked, “Would you support or oppose major new spending by the federal government that would help undergraduates pay tuition at public colleges without
The National Gun Policy Survey asked a random sample of adults, “Do you think there should be a law that would ban possession of handguns except for the police and other authorized persons?” Here
Is your index finger longer than your ring finger? Or is it the other way around? It isn’t the same for everyone. To investigate if there is a relationship between gender and relative finger
Researchers followed a random sample of 2315 middle-aged men from eastern Finland for up to 30 years. They recorded how often each man went to a sauna and whether or not he suffered sudden cardiac
The General Social Survey (GSS) asked a random sample of adults their opinion about whether astrology is very scientific, sort of scientific, or not at all scientific. Here is a two-way table of
Refer to Exercise 38. Which treatment seems to be most effective? Least effective? Justify your choices.Exercise 38.Aspirin prevents blood from clotting and so helps prevent strokes. The Second
Refer to Exercise 37. Which treatment seems to be most effective? Least effective? Justify your choices.Exercise 37.It’s hard for smokers to quit. Perhaps prescribing a drug to fight depression
Courtney and Lexi wondered if the distribution of color was the same for name-brand gummy bears (Haribo Gold) and store-brand gummy bears (Great Value). To investigate, they randomly selected 6 bags
The UR Nuts Company sells Deluxe and Premium nut mixes, both of which contain only cashews, Brazil nuts, almonds, and peanuts. The Premium nuts are much more expensive than the Deluxe nuts. A
Aspirin prevents blood from clotting and so helps prevent strokes. The Second European Stroke Prevention Study asked whether adding another anticlotting drug named dipyridamole would be more
It’s hard for smokers to quit. Perhaps prescribing a drug to fight depression will work as well as the usual nicotine patch. Perhaps combining the patch and the drug will work better than either
The nonprofit group Public Agenda conducted telephone interviews with three randomly selected groups of parents of high school children. There were 202 black parents, 202 Hispanic parents, and 201
How do U.S. residents who travel overseas for leisure differ from those who travel for business? The following is the breakdown by occupation.Explain why we can’t use a chi-square test to learn
Refer to Exercises 28 and 30.a. Verify that the conditions for inference are met.b. Use Table C to find the P-value. Then use your calculator’s χ2 cdf command.c. Interpret the P-value from the
The two-way table shows the results of the experiment described in Exercise 28.a. State the appropriate null and alternative hypotheses.b. Show the calculation for the expected count in the Cold/Yes
Refer to Exercises 27 and 29.a. Verify that the conditions for inference are met.b. Use Table C to find the P-value. Then use your calculator’s χ2 cdf command.c. Interpret the P-value from the
The two-way table shows the results of the experiment described in Exercise 27.a. State the appropriate null and alternative hypotheses.b. Show the calculation for the expected count in the Red/Red
How is the hatching of water python eggs influenced by the temperature of the snake’s nest? Researchers randomly assigned newly laid eggs to one of three water temperatures: hot, neutral, or cold.
The scatterplot shows the number of books read and the English grade for all 79 students in the study. The least-squares regression line ŷ = 3.42 + 0.024x has been added to the graph.a. Interpret
Inspired by the example about how background music influences choice of entrée at a restaurant, a statistics student decided to investigate other ways to influence a person’s behavior. Using 60
Summary statistics for the two groups from Minitab are provided.a. Explain why it is acceptable to use two-sample t procedures in this setting.b. Construct and interpret a 95% confidence interval for
To determine if there is a relationship between age and playing video games, the Pew Research Center asked randomly selected adults for their age and if they “ever play video games on a computer,

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