Statistics 4th Edition David Freedman, Robert Pisani, Roger Purves - Solutions

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17.2 A farm manager was interested in studying several first-time strawberry pickers over a period of 4 weeks. He felt that there was a significant difference in the number of pints picked per hour from one week to the next. Can you help him write the null and alternative hypotheses, input the
17.1 The high school track team coach recorded the time taken for the 100-yard dash by eight team members for three consecutive track meets during the regular season. His past experience informed him that they would improve their times throughout the season as they grew stronger and smarter. He had
16.3 The inspector general for a large state’s motor vehicle department decided to collect some data on recent driving tests. The idea was to see if scores on the driving test (dependent scale variable) were significantly different for male and female (nominal independent variable)instructors. He
16.2 A psychologist had the idea that different types of music and room temperature would influence performance on simple math tasks.She had two independent variables measured at the nominal level:(1) “music type,” hard rock and classical, and (2) “room temperature,”comfortable and hot. The
16.1 A corn farmer is interested in reducing the number of days it takes for his corn to silk. He has decided to set up a controlled experiment that manipulates the nominal variable “fertilizer,” having two categories:1 = limestone and 2 = nitrogen. Another nominal variable is “soil
15.3 Bacteria counts were taken at the four Southern California beaches of Santa Monica, Malibu, Zuma, and Ventura. The researcher’s idea was that the different beaches would yield significantly different bacteria counts. The Santa Monica beach count was 16.2, 12.0, 16.4, 15.5, 16.5, 22.0, and
15.2 A chemical engineer had three different formulas for a gasoline additive that she thought would significantly change automobile gas mileage.She had three groups of 15 test standard eight-cylinder engines that simulated normal driving conditions. Each group received a different gasoline
15.1 An El Salvadorian pig farmer, Jose, had the idea to add a by-product from the production of cane sugar to his pig feed. The idea was that the pigs would eat more, gain weight, and be worth more at market time. He had 24 weaner pigs weighing from 20 to 40 pounds. He randomly divided the pigs
14.3 The chemical engineer added a chemical to a fast-burning compound that changed the oxygen consumption once the reaction started. He did a pretest to measure the oxygen consumption index; then he added the chemical and recorded the posttest oxygen index. The pretest values are 120, 139, 122,
14.2 Data were collected from 10 major oil well drilling operators that recorded the number of hours lost per week due to work-related accidents.A rigorous safety program was instituted, and the number of lost hours was once again recorded following the introduction of the safety program. The
14.1 The researcher has the idea that listening to hard rock music can directly influence one’s perception of the world. The professor randomly selects a group of 15 individuals from his “Introduction to Psychology” lecture hall class of 300 freshman students. He wishes to test his theory on
13.3 For this review exercise, you will select and open the SPSS sample file called bankloan.sav. You will test for significant differences in the categories of education (“ed”) and whether they have previously defaulted on a loan (“default”). There are five educational categories and two
13.2 The local bank president had the idea that the money held in individual savings accounts would be significantly different for males and females.A random sample of the dollars in male and female savings accounts was recorded as follows. Males: 5,600, 5,468, 5,980, 7,890, 8,391, 9,350, 10,570,
13.1 Two 12-man teams of Marines were randomly selected from Marine Corps Air Stations Miramar and Yuma to be compared on their Combat Fitness Test. Their scores ranged from a low of 263 to a perfect score of 300. Miramar scores: 267, 278, 295, 280, 268, 286, 300, 276, 278, 297, 298, and 279. Yuma
12.3 An instructor in a community college auto mechanics class asked his students if they thought that gas consumption, as measured in miles per gallon (mpg), had improved for the Ford Focus in the past 5 years.It was a team project, so they got together and found that on average the Ford Focus was
12.2 There is an annual race to reach the top of Kendall Mountain in the small town of Silverton, Colorado. A health scientist believes that the time to reach the top has significantly changed over the past 10 years.The average time for the first 12 runners to reach the summit in the 2005 race was
12.1 You are a seller of heirloom garden seeds. You have several machines that automatically load the seeds into packages. One of your machines is suspected of sometimes being inaccurate and of underloading or overloading the packages. You take a random sample of 20 packages and record their
11.3 Open the SPSS sample database called bankloan.sav, and determine if the variables “age” and “household income in thousands” are normally distributed.
11.2 Open the SPSS sample database called bankloan.sav, and build frequency tables for all variables measured at the nominal or ordinal level.
11.1 Open the SPSS sample database called bankloan.sav, and calculate the following statistics for all variables measured at the scale level:mean, std. deviation, variance, range, minimum, maximum, S.E., mean, kurtosis, and skewness. Print the SPSS descriptive statistics output produced in answer
9.3 For this exercise, you will open the SPSS sample file called workprog.sav and select two discrete variables and one continuous variable to build a histogram paneled on both columns and rows. For the x-axis use the variable labeled as Age in years and named “Age.” The discrete variable named
9.2 Use the same database as in the previous exercise (autoaccidents.sav), and select the variable named “Age” having the label Age of insured.Build the boxplot, and answer the following questions: (a) What are the minimum and maximum ages, excluding outliers and extremes? (b) What is the age
9.1 For this exercise, you will build a simple histogram using the SPSS sample file known as autoaccidents.sav. Open the file, select the variable named“accident” and labeled Number of accidents in the past 5 years, and build the simple histogram. Use the graph you build to answer the following
8.3 You must visually display the relationship between two categorical variables using the population pyramid graphing method. The variables you use are found in the SPSS sample file called workprog.sav. The variable “prog” (program status) is the split variable, and “ed” (level of
8.2 You must summarize the data for 8,083 individuals. Specifically, you are tasked with building a 3-D pie graph showing the number and percentage of people in each of four regions. Open dmdata3.sav, select the discrete variable named “Region,” and build a pie graph. Embellish the graph to
8.1 You are given the task of building a pie chart that summarizes the five age categories of 582 individuals recorded in an SPSS sample file titled satisf.sav. The variable is named “agecat” and labeled Age category.Build a 3-D pie graph that displays the names of the categories, the numbers
7.3 You have a large database opened in SPSS, and now you must summarize and describe the data it contains. You decide to click Analyze on the Main Menu, then Frequencies; the Frequencies window opens, and you realize that you need help—what do you do next?
7.2 You need help to find out how to summarize categorical (nominal)data for a PowerPoint presentation, and you want to use a graph made from data stored in SPSS. Hint: Use the SPSS Help on the Main Menu and the Tutorial.
7.1 How can you use the SPSS Help function to get information on transforming data in an attempt to get a more normal distribution of values?
6.3 You have been given the following scale data (test scores): 100, 109, 114, 118, 125, 135, 135, 138, 139, and 140. You must set up a database in SPSS and then transform the data using the Compute Variable and arithmetic functions to calculate new variables giving the log and square root of the
6.2 Use the data from the variable (“avgspeed”) created in the previous exercise to recode the values into a nominal (string) variable. Your task is to use SPSS’s Recode into Different Variables feature and form two categories for the average walking speeds of the individuals. The two
6.1 An urban planner was tasked with recording the walking speeds (in miles per hour) of people at a downtown government center. He recorded walking speeds of the same individuals over a period of 5 days. A sample of the data is provided below along with the variable information. There are three
5.3 The following sample data were collected by the owner of a private 640-acre forest reserve. He did a sample of 10 acres as a trial survey for the entire reserve. He needs to set up and test a computer file system using SPSS’s Data Editor. The 10-acre sample was subdivided into 2.5 parcels,
5.2 A child psychologist is investigating the behavior of children in the play area of Balboa Park. Help him set up an SPSS file to measure the following variables on individual children: time the child was observed, pieces of play equipment used, other children in the play area, interaction with
5.1 The highway patrol officer wants to set up an SPSS file to record traffic violations. She wishes to record data at the nominal, ordinal, and scale levels of measurement. The first item of interest (the largest source of income for the highway patrol) is speeding. Input three variables that
4.3 A political consultant wished to measure the level of politicization of the candidates for a job at the White House. He decided that the following variables would provide at least some of the evidence required to assess the extent of their interest in politics: vote (did you vote in the
4.2 A social researcher is interested in measuring the level of religiosity of a sample of senior citizens. Help her in establishing the levels of measurement for the following variables: pray (do you pray?), services(number of times you attend formal church services per year), money(donated to
4.1 The following is a list of variables that an investigator wishes to use to measure the health and survival of a particular species of earthworm:age, length, weight, moisture content, breed, environmental factors, and acid content of the soil. Your job is to assist this researcher in specifying
3.3 Open another one of SPSS’s sample files called customer_dbase.sav (it has 132 variables and 5,000 cases), and save it in your documents file.It’s another database that you will use several times throughout this book.
3.2 In this exercise, you must import an Excel file from your computer and show the appearance of the Open Excel Data Source window and the first six rows of the Variable View screen. There should be an Excel file used as a demonstration for the Excel data program within your system files. Its name
3.1 With this review exercise, you will open an SPSS sample file workprog.sav. Once it is opened, you will save it in your documents file, making it easy to access as you will need this database frequently as you progress through this book.
2.3 You are the range safety officer at a long-distance firearms training facility.You have collected the ballistic information on four rifles—data are given below. You would like to set up a data file in SPSS to collect many hundreds of similar cases in the future. The variables are (1)
2.2 You must set up the SPSS Data Editor to analyze the three variables listed below on 30,000 individuals. The variables are (1) age (label is age in years, no decimals, center-aligned and scale data), (2) education(label is years beyond H.S., no decimals, center-aligned and scale data), and (3)
2.1 You have designed a data-collecting instrument that has the following five variables measured at the scale level (labels are given in parentheses;decimals are set to 3 and align to center): (1) miles (speed in miles per hour), (2) kilometers (speed in kilometers per hour) (3) hours,(4) minutes,
1.3 There was a quarter-mile drag race held at the abandoned airport last week. The makes of the winning cars were recorded by an interested fan. The results of her observations were as follows: Chevrolets won 23 races, Fords won 19 times, Toyota won 3, Hondas won 18, and KIAs won 8 races. As in
1.2 One day you are sitting in your professor’s office getting help on regression analysis. His phone rings; he apologizes but says that he must take the call. As you wait for him to end his phone call, you scan his bookshelves and make mental notes of the titles. You arrive at the following:15
1.1 You have classified the size of several fish that were caught in a “catch and release” fishing contest for children as small, medium, and large.The number of fish caught by the children are 32 small, 21 medium, and 11 large. Note: When inputting these data and information, you are not
If the average of *y* depends on *x* in a non-linear way, the regression line can be quite misleading. pl875
With a controlled experiment, the slope can tell you the average change in *y* that would be caused by a change in *x*. With an observational study, however, the slope cannot be relied on to predict the results of interventions. It takes a lot of hard work to draw causal inferences from
How does the average of one variable depend on the values of the other variable? The regression line can be used to answer that question. pl875
In this part of the book, scatter diagrams are used to graph the associ-ation between two variables. If the scatter diagram is football-shaped, it can be summarized by the average and SD of the two variables, with *r* to measure the strength of the association. pl875
Sometimes, two quantities are thought to be connected by a linear rela-tionship (for example, length and weight in Hooke's law). The statistical problem is to estimate the slope and intercept of the line. The least squares estimates are the slope and intercept of the regression line. pl875
Among all lines, the regression line for y on x makes the smallest r.m.s.error in predicting y from x. For that reason, the regression line is often called the least squares line. pl875
The equation can be used to make all the regression predictions, by sub-stitution. pl875
The equation of the regression line for y on x is$$y = slope \times x + intercept$$. pl875
The intercept of the regression line equals the regression estimate for y, when x is 0. pl875
The slope of the regression line for y on x is the average change in y, per unit change in x. This equals$$r \times SD \ of \ y/SD \ of \ x$$. pl875
The regression line can be specified by two descriptive statistics: the slope and the intercept. pl875
An investigator wants to use a straight line to predict IQ from lead levels in the blood, for a representative group of children aged 5-9.14 There is a weak positive association in the data. True or false, and explain-(a) He can use many different lines.(b) He has to use the regression line.(c)
A statistician is doing a study on a group of undergraduates. On average, these students drink 4 beers a month, with an SD of 8. They eat 4 pizzas a month, with an SD of 4. There is some positive association between beer and pizza, and the regression equation is 13 predicted number of beers =
(Continues exercise 5.) The couples in the previous exercise are followed for a year. Suppose everyone's income goes up by 10%. Find the new regression line for predicting wife's income from husband's income. pl875
A study is made of working couples. The regression equation for predicting wife's income from husband's income is wife's income = 0.1667 x husband's income + $24,000.Another investigator solves this equation for husband's income, and gets husband's income = 6 x wife's income - $144,000.True or
(a) Is the r.m.s. error of the line below around 0.1, 0.3, or 1?(b) Is it the regression line? pl875
For men age 18-24 in the HANES5 sample, the regression equation for pre-dicting height from weight is predicted height = (0.0267 inches per pound) x (weight) + 65.2 inches(Height is measured in inches and weight in pounds.) If someone puts on 20 pounds, will he get taller by 20 pounds x 0.0267
For women age 25-34 in the HANES5 sample, the relationship between height and income can be summarized as follows: 12 average height ≈ 64 inches, SD ≈ 2.5 inches average income ≈ $21,000, SD ≈ $20,000, r ≈ 0.2 What is the regression equation for predicting income from height? What does
Exercise 3 describes one way to predict V-SAT from M-SAT; exercise 4 describes a second way; and regression is a third way. Which way will have the smallest r.m.s.error? pl875
Repeat exercise 3, if the investigator always predicts a V-SAT of 540. pl875
A study is made of Math and Verbal SAT scores for the entering class at a certain college. The summary statistics:average M-SAT = 560, SD = 120 average V-SAT = 540, SD = 110, r = 0.66 The investigator uses the SD line to predict V-SAT score from M-SAT score.(a) If a student scores 680 on the M-SAT,
For the data in table 1 (p. 209), the regression equation for predicting length from weight is predicted length = (0.05 cm per kg) x (weight) + 439.01 cm Predict the length of the wire when the weight is 3 kg; 5 kg. Does putting more weight on the spring make it longer? Explain. pl875
The International Rice Research Institute in the Philippines developed the hybrid rice IR 8, setting off "the green revolution" in tropical agriculture. Among other things, they made a thorough study of the effects of fertilizer on rice yields. These experiments involved a number of experimental
For the men in figure 1, the regression equation for predicting average income from education is predicted income = $2,000 per year x education + $5,000.Predict the income for one of these men who has(a) 8 years of schooling-elementary education(b) 12 years of schooling-a high-school diploma(c) 16
Suppose that a scatter diagram is football-shaped. Take the points inside a narrow vertical strip. Their y-values are a new data set. The new average is estimated by the regression method. The new SD is about equal to the r.m.s. error for the regression line. And the normal approximation can be
When all the vertical strips in a scatter diagram show similar amounts of spread, the diagram is homoscedastic: the prediction errors are similar in size all along the regression line. When the scatter diagram is heteroscedastic, the prediction errors are different in different parts of the scatter
After carrying out a regression, statisticians often graph the residuals. If the residual plot shows a pattern, the regression may not have been appropriate. pl875
The SD of y is equal to the r.m.s. error of a horizontal line through the av-erage of y. The r.m.s. error of the regression line is smaller, by the factor $$√1-r^2$$.Therefore, the r.m.s. error for the regression line of y on x can be figured as$$√1-r^2$$ x the SD of y. pl875
The r.m.s. error of the regression line is the root-mean-square of the resid-uals. This measures the accuracy of the regression predictions. The predictions are off by amounts similar in size to the r.m.s. error. For many scatter diagrams, about 68% of the predictions will be right to within one
In a scatter diagram, the vertical distance of a point above or below the regression line is the graphical counterpart of the prediction error made by the regression method. pl875
When the regression line is used to predict y from x, the difference be-tween the actual value and the predicted value is a residual, or prediction error. pl875
The bends are caused by rapid changes in air pressure, resulting in the for-mation of nitrogen bubbles in the blood. The symptoms are acute pain, and sometimes paralysis leading to death. In World War II, pilots got the bends during certain battle maneuvers. It was feasible to simulate these
The freshmen at a large university are required to take a battery of aptitude tests. Students who score high on the mathematics test also tend to score high on the physics test. On both tests, the average score is 60; the SDs are the same too. The scatter diagram is football-shaped. Of the students
In a study of high-school students, a positive correlation was found between hours spent per week doing homework, and scores on standardized achieve-ment tests. The investigators concluded that doing homework helps prepare students for these tests. Does the conclusion follow from the data? Answer
Use the data in exercise 4 to answer the following questions.(a) About what percentage of students scored over 80 on the final?(b) Of the students who scored 80 on the midterm, about what percentage scored over 80 on the final?Explain your answers. pl875
A statistical analysis was made of the midterm and final scores in a large course, with the following results:average midterm score ≈ 50, SD ≈ 25 average final score ≈ 55, SD≈ 15, r≈ 0.60 pl875
Tuddenham and Snyder obtained the following results for 66 California boys at ages 6 and 18 (the scatter diagram is football-shaped):9average height at 6 ≈ 3 feet 10 inches, SD ≈ 1.7 inches, average height at 18≈ 5 feet 10 inches, SD≈ 2.5 inches, r ≈ 0.80(a) Find the r.m.s. error for the
A computer program is developed to predict the GPA of college freshmen from their high-school GPAs. This program is tried out on a class whose college GPAs are known. The r.m.s. error is 3.12. Is anything wrong? Answer yes or no, and explain. pl875
The r.m.s. error of the regression line for predicting y from x is _______.(i) SD of y(ii) SD of x(iii) r x SD of y(iv) r x SD of x(v) 1-r2 x SD of y(vi) √1-r2 x SD of x
From the same study:average height of men ≈ 68 inches, SD ≈ 2.7 inches average forearm length ≈ 18 inches, SD ≈ 1 inch, r ≈ 0.80(a) What percentage of men have forearms which are 18 inches long, to the nearest inch?(b) Of the men who are 68 inches tall, what percentage have forearms which
From the same study:average height of father ≈ 68 inches, SD ≈ 2.7 inches average height of son ≈ 69 inches, SD ≈ 2.7 inches, r ≈ 0.50(a) What percentage of the sons were over 6 feet tall?(b) What percentage of the 6-foot fathers had sons over 6 feet tall? pl875
Pearson and Lee obtained the following results for about 1,000 families:average height of husband ≈ 68 inches, SD ≈ 2.7 inches average height of wife ≈ 63 inches, SD ≈ 2.5 inches, r≈ 0.25(a) What percentage of the women were over 5 feet 8 inches?(b) Of the women who were married to men of
The data in figure 9 can be summarized as follows:average education ≈ 13.0 years, SD ≈ 3.4 years average income ≈ $18,000, SD ≈ $20,000, r ≈ 0.37(a) Find the r.m.s. error of the regression line for predicting income from education.(b) Predict the income of a woman with 16 years of
The data in figure 8 can be summarized as follows:average height of fathers ≈ 68 inches, SD ≈ 2.7 inches average height of sons ≈ 69 inches, SD≈2.7 inches, r≈ 0.5(a) Find the r.m.s. error of the regression line for predicting son's height from father's height.(b) If a father is 72 inches
In 1937, the Stanford-Binet IQ test was restandardized with two forms (L and M). A large number of subjects took both tests. The results can be summarized as follows: Form L average 100, SD 15 Form M average 100, SD 15, r 0.80 (a) True or false, and explain: the regression line for predicting the
Several regression lines are used to predict the monthly salaries in a certain com- pany, from different independent variables. Residual plots from each regression are shown below. Match the description with the plot. Explain. (You may use the same description more than once.) (a) r.m.s. error =
Several different regression lines are used to predict the price of a stock (from different independent variables). Histograms for the residuals from each line are sketched below. Match the description with the histogram: (a) r.m.s. error = $5 (b) r.m.s. error= $15 (c) something's wrong? pl875
The scatter diagram on the next page shows incomes for a sample of 168 working couples in Louisiana. Summary statistics are as follows:average husband's income = $45,000, SD = $25,000 average wife's income = $28,000, SD = $20,000(a) If you predict wife's income as $28,000, ignoring husband's
A regression line for predicting test scores has an r.m.s. error of 8 points.(a) About 68% of the time, the predictions will be right to within ___ points.(b) About 95% of the time, the predictions will be right to within ___ points. pl875
An admissions officer is trying to choose between two methods of predicting first-year scores. One method has an r.m.s. error of 12. The other has an r.m.s. error of 7. Other things being equal, which should he choose? Why? pl875
A regression line for predicting income has an r.m.s. error of $2,000. It predicts someone's income as $20,000. This is likely to be right give or take: a few hundred dollars, a few thousand dollars, ten or twenty thousand dollars. pl875
A regression line is fitted to a small data set. For each subject, the table shows the actual value of y and the predicted value from the regression line. (The value of x is not shown.) Compute the prediction errors, and the r.m.s. error of the regression line. pl875
Look at figure 1, then say whether each statement is true or false:(a) E is above average in weight.(b) E is above average in weight, for men of his height. pl875

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Statistics 4th Edition David Freedman, Robert Pisani, Roger Purves - Solutions

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