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Seeing Through Statistics 2nd Edition Jessica M. Utts - Solutions

9. Explain how two variables can have a perfect curved relationship and yet have zero correlation. Draw a picture of a set of data meeting those criteria.
8. Give an example of a pair of variables that are likely to have a positive correlation and a pair of variables that are likely to have a negative correlation.
7. Which implies a stronger linear relationship, a correlation of +.4 or a correlation of –.6? Explain.
6. The relationship between height and weight is a well-established and obvious fact. Suppose you were to sample heights and weights for a small number of your friends, and you failed to find a statistically significant relationship between the two variables. Would you conclude that the
5. Suppose a weak relationship exists between two variables in a population.Which would be more likely to result in a statistically significant relationship between the two variables: a sample of size 100 or a sample of size 10,000?Explain.
4. Are each of the following pairs of variables likely to have a positive correlation or a negative correlation?a. Daily temperature at noon in New York City and in Bostonb. Weight of an automobile and its gas mileage in average miles per gallonc. Hours of television watched and grade-point average
3. A pint of water weights 1.04 pounds, so 1 pound of water is 0.96 pint. Suppose a merchant sells water in containers weighing 0.5 pound, but customers can fill them to their liking. It is easier to weigh the filled container than to measure the volume of water the customer is purchasing. Define x
2. In Figure 10.2, we observed that the correlation between husbands’ and wives’heights, measured in millimeters, was .36. Can you determine what the correlation would be if the heights were converted to inches? Explain.
1. Suppose 100 different researchers each did a study to see if there was a relationship between coffee consumption and height. Suppose there really is no such relationship in the population. Would you expect any of the researchers to find a statistically significant relationship? If so,
3. Find some data that represent change over time for a topic of interest to you.Present a line graph of the data in the best possible format. Explain what you have done to make sure the picture is as useful as possible.
2. Collect two measurement variables on each of at least ten individuals. Represent them in a statistical picture. Describe the picture in terms of possible outliers, variability, and relationship between the two variables.
1. Collect some categorical data on a topic of interest to you and represent it in a statistical picture. Explain what you have done to make sure the picture is as useful as possible.
12. Find a graph that does not start at zero. Redraw the picture to start at zero. Discuss the pros and cons of the two versions.
11. Find an example of a statistical picture in a newspaper or magazine that has at least one of the problems listed in Section 9.4, “Difficulties and Disasters in Plots, Graphs, and Pictures.” Explain the problem. If you think anything should have been done differently, explain what and why.
10. According to the American Medical Association Family Medical Guide (1982, p. 422), the distribution of blood types among Americans is as shown in Table 9.3.a. Draw a pie chart illustrating the blood-type distribution for white Americans, ignoring the RH factor.b. Draw a statistical picture
9. Find an example of a statistical picture in a newspaper or magazine, or on the Internet. Answer the ten questions in Section 9.5 for the picture. In the process of answering the questions, explain what (if any) features you think should have been added or changed to make it a good picture.
8. Table 9.2 indicates the population (in millions) and the number of violent crimes (in millions) in the United States from 1982 to 1991, as reported in the World Almanac and Book of Facts (1993, p. 948).a. Draw two line graphs representing the trend in violent crime over time.Draw the first graph
7. Figure 10.4 in Chapter 10 displays the success rate for professional golfers when putting at various distances. Discuss the figure in the context of the material in this chapter. Are there ways in which the picture could be improved?
6. In its February 24–26, 1995, edition (p. 7), USA Weekend gave statistics on the changing status of which parent children live with. As noted in the article, the numbers don’t total 100% because they are drawn from two sources: the U.S.Census Bureau and America’s Children: Resources from
5. Figure 9.10, which displays rising postal rates, is an example of a graph with misleading units because the prices are not adjusted for inflation. The graph actually has another problem as well. Use the checklist in Section 9.5 to determine the problem; then redraw the graph correctly (but still
4. An article in Science (vol. 279, 23 January, 1998, p. 487) reported on a “telephone survey of 2600 parents, students, teachers, employers, and college professors”in which people were asked the question, “Does a high school diploma mean that a student has at least learned the basics?”
3. One method used to compare authors or to determine authorship on unsigned writing is to look at the frequency with which words of different lengths appear in a piece of text. For this exercise, you are going to compare your own writing with that of the author of this book.a. Using the first full
2. Suppose a real estate company in your area sold 100 houses last month, whereas their two major competitors sold 50 houses and 25 houses, respectively.The top company wants to display its better record with a pictogram using a simple two-dimensional picture of a house. Draw two pictograms
1. Give the name of a type of statistical picture that could be used for each of the following kinds of data.a. One categorical variableb. One measurement variablec. Two categorical variablesd. Two measurement variables
20. According to Chance magazine (vol. 6, no. 3 [1993], p. 5), the mean healthy adult temperature is around 98.2° Fahrenheit, not the previously assumed value of 98.6°. Suppose the standard deviation is 0.6 degree and the population of healthy temperatures is bell-shaped. What proportion of the
19. Assuming heights for each sex are bell-shaped, with means of 70 inches for men and 65 inches for women, and with standard deviations of 3 inches for men and 2.5 inches for women, what proportion of your sex is shorter than you are?(Be sure to mention your sex and height in your answer!)
18. Suppose you record how long it takes you to get to work or school over many months and discover that the times are approximately bell-shaped with a mean of 15 minutes and a standard deviation of 2 minutes. How much time should you allow to get there to make sure you are on time 90% of the time?
17. Suppose a candidate for public office is favored by only 48% of the voters. If a sample survey randomly selects 2500 voters, the percentage in the sample who favor the candidate can be thought of as a measurement from a normal curve with a mean of 48% and standard deviation of 1%. Based on this
16. For every 100 births in the United States, the number of boys follows, approximately, a normal curve with mean of 51 boys and standard deviation of 5 boys.If the next 100 births in your local hospital resulted in 36 boys (and thus 64 girls), would that be unusual? Explain.
15. Use the Empirical Rule to specify the ranges into which 68%, 95%, and 99.7%of Stanford-Binet IQ scores fall. (Recall the mean is 100 and the standard deviation is 16.)
14. A graduate school program in English will admit only students with GRE verbal ability scores in the top 30%. What is the lowest GRE score they will accept? (Recall the mean is 497 and the standard deviation is 115.)
13. Give an example of a population of measurements that you do not think has a normal curve, and draw its frequency curve.
12. Recall from Chapter 7 that the interquartile range covers the middle 50% of the data. For a bell-shaped population:a. The interquartile range covers what range of standardized scores? In other words, what are the standardized scores for the lower and upper quartiles?(Hint: Draw a standard
11. Use Table 8.1 to verify that the Empirical Rule is true. You may need to round off the values slightly.
10. Every time you have your cholesterol measured, the measurement may be slightly different due to random fluctuations and measurement error. Suppose that for you, the population of possible cholesterol measurements if you are healthy has a mean of 190 and a standard deviation of 10. Further,
9. Mensa is an organization that allows people to join only if their IQs are in the top 2% of the population.a. What is the lowest Stanford-Binet IQ you could have and still be eligible to join Mensa?b. Mensa also allows members to qualify on the basis of certain standard tests.If you were to try
8. Find the percentile for the observed value in the following situations:a. GRE score of 450 (mean = 497, s.d. = 115)b. Stanford-Binet IQ score of 92 (mean = 100, s.d. = 16)c. Woman’s height of 68 inches (mean = 65 inches, s.d. = 2.5 inches)
7. Draw a picture of a bell-shaped curve with a mean value of 100 and a standard deviation of 10. Mark the mean and the intervals derived from the Empirical Rule in the appropriate places on the horizontal axis. You do not have to mark the vertical axis.
6. The 84th percentile for the Stanford-Binet IQ test is 116. (Recall that the mean is 100 and the standard deviation is 16.)a. Verify that this is true by computing the standardized score and using Table 8.1.b. Draw pictures of the original and standardized scores to illustrate this situation,
5. Using Table 8.1, a computer, or calculator, determine the percentage of the population falling between the two standard scores given:a. –1.00 and 1.00b. –1.28 and 1.75c. 0.0 and 1.00
4. Using Table 8.1, a computer, or a calculator, determine the standard score that has the following percentage of the population above it:a. 2%b. 50%c. 75%d. 10%
3. Using Table 8.1, a computer, or a calculator, determine the standard score that has the following percentage of the population below it:a. 25%b. 75%c. 45%d. 98%
2. Using Table 8.1, a computer, or a calculator, determine the percentage of the population falling above each of the following standard scores:a. 1.28b. –0.25c. 2.33
1. Using Table 8.1, a computer, or a calculator, determine the percentage of the population falling below each of the following standard scores:a. –1.00b. 1.96c. 0.84
2. Measure your pulse rate 25 times over the next few days, but don’t take more than one measurement in any 10-minute period. Record any unusual events related to the measurements, such as if one was taken during exercise or one was taken immediately upon awakening. Create a stemplot and a
1. Find a set of data that has meaning for you. Some potential sources are the Internet, the sports pages, and the classified ads. Using the methods given in this chapter, summarize and display the data in whatever ways are most useful.Give a written description of interesting features of the data.
27. Draw a boxplot illustrating a data set with each of the following features:a. Skewed to the right with no outliersb. Bell-shaped with the exception of one outlier at the upper endc. Values uniformly spread across the range of the data
26. Suppose you had a choice of two professors to take for a class in which your grade was very important. They both assign scores on a percentage scale (0 to 100). You can have access to three summary measures of the last 200 scores each professor assigned. Of the summary measures discussed in
25. Which set of data is more likely to have a bimodal shape: daily New York City temperatures at noon for the summer months or daily New York City temperatures at noon for an entire year? Explain.
24. Find a set of data of interest to you, such as rents from a newspaper or test scores from a class, with at least 12 numbers. Include the data with your answer.a. Create a five-number summary of the data.b. Create a boxplot of the data.c. Describe the data in a paragraph that would be useful to
23. Give one advantage a stemplot has over a histogram and one advantage a histogram has over a stemplot.
22. What is the variance for the Stanford-Binet IQ test?
21. Would outliers more heavily influence the range or the quartiles? Explain.
20. Three types of pictures were presented in this chapter: stemplots, histograms, and boxplots. Explain the features of a data set for which:a. Stemplots are most usefulb. Histograms are most usefulc. Boxplots are most useful
19. Suppose a set of test scores is approximately bell-shaped, with a mean of 70 and a range of 50. Approximately, what would the minimum and maximum test scores be?
18. Explain the following statement in words that someone with no training in statistics would understand: The heights of adult males in the United States are bell-shaped, with a mean of about 70 inches and a standard deviation of about 3 inches.
17. Give an example of a measurement for which the mode would be more useful than the median or the mean as an indicator of the “typical” value.
16. Construct an example and draw a histogram for a measurement that you think would be bimodal.
15. Construct an example and draw a histogram for a measurement that you think would be skewed to the right.
14. Construct an example and draw a histogram for a measurement that you think would be bell-shaped.
13. Suppose an advertisement reported that the mean weight loss after using a certain exercise machine for 2 months was 10 pounds. You investigate further and discover that the median weight loss was 3 pounds.a. Explain whether it is most likely that the weight losses were skewed to the right,
12. In each of the following cases, which would probably be higher, the mean or the median, or would they be about equal?a. Salaries in a company employing 100 factory workers and 2 highly paid executivesb. Ages at which residents of a suburban city die, including everything from infant deaths to
11. Refer to the data on per capita income in Table 7.1; a five-number summary is given in Section 7.3, page 116).a. Construct a boxplot for this data set.b. Discuss which picture is more useful for this data set: the boxplot from parta, or the histogram in Figure 7.3.
10. The data on hours of sleep discussed in Example 1 also included whether each student was male or female. Here are the separate five-number summaries for“hours of sleep” for the two sexes:Males Females 7 7 6 8 6 8 3 16 3 11a. Two males reported sleeping 16 hours and one reported sleeping 12
9. Refer to the pulse rate data displayed in the stemplots in Figure 7.2.a. Find the median.b. Create a five-number summary.
8. Find the mean and standard deviation of the following set of numbers: 10, 20, 25, 30, 40.
7. All the information contained in the five-number summary for a data set is required for constructing a boxplot. What additional information is required?
6. Give an example of a set of more than five numbers that has a five-number summary of 40 30 70 10 80
5. Give an example of a set of five numbers with a standard deviation of 0.
4. Give an example for which the median would be more useful than the mean as a measure of center.
3. Create a histogram for the test scores in Exercise 1. Comment on the shape.
2. Refer to the test scores in Exercise 1.a. Create a five-number summary.b. Create a boxplot.
1. At the beginning of this chapter, the following exam scores were listed: 75, 95, 60, 93, 85, 84, 76, 92, 62, 83, 80, 90, 64, 75, 79, 32, 78, 64, 98, 73, 88, 61, 82, 68, 79, 78, 80, 55.a. Create a stemplot for the test scores.b. Describe the scores as illustrated by the stemplot, including
5. Design and carry out a single-blind study using ten participants. Your goal is to establish whether people write more legibly with their dominant hand. In other words, do right-handed people write more legibly with their right hand and vice versa for left-handed people? Explain exactly what you
4. Go to the library or the Internet and locate a journal article that describes an observational study. Explain how it was done using the terminology of this chapter and whether you agree with the conclusions drawn by the authors.
3. Go to the library or the Internet and locate a journal article that describes a randomized experiment. Explain what was done correctly and incorrectly in the experiment and whether you agree with the conclusions drawn by the authors.
2. Design an observational study to test something of interest to you. Explain how your design addresses each of the three complications listed in Section 5.5,“Difficulties and Disasters in Observational Studies.”
1. Design an experiment to test something of interest to you. Explain how your design addresses each of the four complications listed in Section 5.3, “Difficulties and Disasters in Experiments.”
23. Explain which of the “difficulties and disasters” is most likely to be a problem in each of the following observational studies, and why:a. A study measured the number of writing courses taken by students and their subsequent scores on the quantitative part of the Graduate Record Exam.The
22. Explain which of the “difficulties and disasters” is most likely to be a problem in each of the following experiments, and why:a. To see if eating just before going to bed causes nightmares, volunteers are recruited to spend the night in a sleep laboratory. They are randomly assigned to be
21. Give an example of an experiment that would have poor ecological validity.
20. Is the “experimenter effect” most likely to be present in a double-blind experiment, a single-blind experiment, or an experiment with no blinding? Explain.
19. Explain why each of the following is used in experiments:a. Placebo treatmentsb. Blindingc. Control groups
18. Refer to Case Study 5.2, “Exercise Yourself to Sleep.”a. Discuss each of the “difficulties and disasters in experiments” (Section 5.3)as applied to this experiment.b. Explain whether the authors can conclude that exercise actually caused improvements in sleep.
17. Explain why a randomized experiment allows researchers to draw a causal conclusion whereas an observational study does not.
16. Is it possible to conduct an experiment to compare two conditions using volunteers recruited through the newspaper? If not, explain why not. If so, explain how it would be done and explain any “difficulties and disasters” that would be encountered.
15. A headline in the Sacramento Bee (11 December 1997, p. A15) read, “Study:Daily drink cuts death,” and the article began with the statement, “One drink a day can be good for health, scientists are reporting, confirming earlier research in a new study that is the largest to date of the
14. A case-control study claimed to have found a relationship between drinking coffee and pancreatic cancer. The cases were people recently hospitalized with pancreatic cancer, and the controls were people hospitalized for other reasons.When asked about their coffee consumption for the past year,
13. Suppose an observational study finds that people who use public transportation to get to work have better knowledge of current affairs than those who drive to work, but that the relationship is weaker for well-educated people. What term from the chapter (for example, response variable) applies
12. Suppose you wanted to know if men or women students spend more money on clothes. You consider two different plans for carrying out an observational study:Plan 1: Ask the participants how much they spent on clothes during the last 3 months; then compare the men and women.Plan 2: Ask the
11. Refer to Exercise 10. What are the explanatory and response variables?
10. Researchers ran an advertisement in a campus newspaper asking for sedentary volunteers who were willing to begin an exercise program. The volunteers were allowed to choose which of three programs they preferred: jogging, swimming or aerobic dance. After 5 weeks on the exercise programs, weight
9. A researcher was interested in teaching couples to communicate more effectively.She had 20 volunteer couples, 10 of which were randomly assigned to receive the training program and 10 of which were not. After they had been trained (or not), she presented each of the 20 couples with a
8. To study the effectiveness of vitamin C in preventing colds, a researcher recruited 200 volunteers. She randomly assigned 100 of them to take vitamin C for 10 weeks and the remaining 100 to take nothing. The 200 participants recorded how many colds they had during the 10 weeks. The two groups
7. Researchers have found that women who take oral contraceptives (birth control pills) are at higher risk of having a heart attack or stroke and that the risk is substantially higher if a woman smokes. In investigating the relationship between taking oral contraceptives (the explanatory variable)
6. Suppose researchers were interested in determining the relationship, if any, between brain cancer and the use of cellular telephones. Would it be better to use an experiment or a case-control study? Explain.
5. A study to see whether birds remember color was done by putting birdseed on a piece of red cloth and letting the birds eat the seed. Later, empty pieces of cloth of varying colors (red, purple, white, and blue) were displayed. The birds headed for the red cloth. The researcher concluded that the
4. Refer to Thought Question 5 at the beginning of this chapter. The headline was based on a study in which a representative sample of over 400,000 adults in the United States were asked a series of questions, including level of education and on how many of the past 30 days they felt physically and
3. Designate the explanatory variable and the response variable for each of the three studies in Exercise 2.
2. In each of the following examples, explain whether the experiment was doubleblind, single-blind, or neither, and explain whether it was a matched-pair or block design or neither.a. A utility company was interested in knowing if agricultural customers would use less electricity during peak hours

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