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mathematics
statistics

Seeing Through Statistics 4th Edition Jessica M.Utts - Solutions

The headline was based on a study in which a representative sample of over 400,000 adults in the United States was asked a series of questions, including level of education and on how many of the past 30 days they felt physically and emotionally healthy. Explain how each of the “difficulties and
Read the summary of News Story 1 in the Appendix. One of the results reported was that people who participated in the meditation pro-gram had better immune system response to a flu vaccine. a. Is a cause-and-effect relationship justified in this situation? Explain. b. Explain the extent to which
Read News Story 13 in the Appendix, and consult the original source article on the website, if necessary. One of the results reported was that teens who had more than $ 25 a week in spending money were more likely to use drugs than kids with less spending money. a. Is a cause-and-effect
Find the story referenced as News Story 15 in the Appendix, and consult the original source article on the website, if necessary. One of the results reported was that kids with higher levels of stress in their lives were more likely to eat high-fat foods and snacks. a. Is a cause-and-effect
Refer to Exercise 36, about a report on the relationship between drinking alcohol and likelihood of death, with the headline “Study: Daily drink cuts death.” a. Explain whether you think the headline is justified for this study. b. The study was based on recording drinking habits for the
Read News Story 8 in the Appendix, “Education, kids strengthen marriage.” Discuss the extent to which each of these problems with observational studies may affect the conclusions based on this study: a. Confounding variables and the implications of causation b. Extending the results
A utility company was interested in knowing if agricultural customers would use less electricity during peak hours if their rates were different during those hours. (Agricultural energy use is substantial, for things like irrigation, lighting, wind turbines to reduce frost damage, and so on.)
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 hypothetical
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
Refer to Exercise 41, in which volunteers chose their preferred exercise program, and then weight loss was measured after 5 weeks. a. What are the explanatory and response variables in this study? b. Draw a picture similar to Figure 5.1 illustrating the process used in this study.
For each of the following situations, draw a picture illustrating the process used in the study. The picture should be similar to whichever of a figure 5.1, 5.2, or 5.3 is most appropriate for the situation. a. The study described in Example 5.2 on page 97, “Blindly lowering cholesterol.” b.
To test the effects of drugs and alcohol use on driving performance, 20 volunteers were each asked to take a driving test under three conditions: sober, after two drinks, and after smoking marijuana. The order in which they drove the three conditions was randomized. An evaluator watched them drive
To compare four brands of tires, one of each brand was randomly assigned to the four tire locations on each of 50 cars. These tires were specially manufactured without any labels identifying the brand. After the tires had been on the cars for 30,000 miles, the researchers removed them and measured
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 this chapter ( for example, response variable) applies to
Researchers have found that women who take oral contraceptives (birth control pills) are at higher risk of having a heart attack or stroke than women who do not take them. They also found that the risk is substantially higher for both groups if a woman smokes. Assume that the proportions of women
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.”
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.
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.
Design and carry out a single- blind study using 10 participants, as follows. 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 do left-handed people write more legibly with
Pick one of the news stories in the Appendix that describes a randomized experiment and that has one or more journal articles accompanying it on the companion website. Explain what was done in the experiment using the terminology and concepts in this chapter. Discuss the extent to which you agree
Pick one of the news stories in the Appendix that describes an observational study and that has one or more journal articles accompanying it on the companion website. Explain what was done in the experiment using the terminology and concepts in this chapter. Discuss the extent to which you agree
Find a news article about a statistical study. Evaluate it using the seven steps on page 121. If all of the required information is not available in the news article, locate the journal article or other source of the research. As part of your analysis, make sure you discuss step 7 with regard to
Choose one of the news stories in the Appendix and the accompanying material on the companion website. Evaluate it using the seven steps on page 121. If all of the required information is not available in the news article, locate the journal article or other source of the research. As part of your
Find the journal article in the New England Journal of Medicine on which Case Study 6.5 is based. Evaluate the study using the seven steps on page 121.
At the beginning of this chapter, the following “ oldest ages” were listed, and a stemplot was shown for them in Figure 7.1: 75, 90, 60, 95, 85, 84, 76, 74, 92, 62, 83, 80, 90, 65, 72, 79, 36, 78, 65, 98, 70, 88, 99, 60, 82, 65, 79, 76, 80, 52, 75 a. Create a five-number summary for these
Refer to the “oldest ages” given at the beginning of this chapter and in Exercise 1. a. Create a histogram for these ages. b. Explain how you decided how many intervals to use for the histogram in part (a). c. Comment on the shape of the histogram in part (a).
Construct an example, and draw a histogram for a measurement that you think would be skewed to the right.
Construct an example, and draw a histogram for a measurement that you think would be bimodal.
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 useful. b. Histograms are most useful. c. Boxplots are most useful.
Refer to the previous exercise and the stemplot for the “oldest ages” in Figure 7.1. a. Create a stemplot for the oldest ages using each 10s value twice instead of once on the stem. b. Compare the stemplot created in part (a) with the one in Figure 7.1. Are any features of the data apparent in
Refer to the data on median family income in Table 7.1; a five-number summary is given in Section 7.3, page 148. What income value would be an outlier at the upper end, using the definition of an outlier on page 150? Determine if there are any outliers, and if so, which values are outliers.
Refer to the data on median family income in Table 7.1; a five- number summary is given in Section 7.3, page 148. a. What is the value of the range? b. What is the value of the interquartile range?
Refer to the data on median family income in Table 7.1; a five-number summary is given in Section 7.3, page 148.In Figure 7.1a. Construct a boxplot for this data set. b. Discuss which picture is more useful for this data set: the boxplot from part (a), or the histogram in Figure 7.4.
The data on hours of sleep discussed in Example 7.5 also included whether each student was male or female. Here are the separate five-number summaries for €œhours of sleep€ for the two sexes:a. Two males reported sleeping 16 hours and one reported sleeping 12 hours. Using this information
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, skewed
Draw a boxplot illustrating a data set with each of the following features: a. Skewed to the right with no outliers. b. Bell-shaped with the exception of one outlier at the upper end. c. Values uniformly spread across the range of the data.
Suppose you had a choice of two professors 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 numerical summary measures discussed in this
The students surveyed for the data on exercising in Example 7.4 were also asked €œHow many alcoholic beverages do you consume in a typical week?€ Five-number summaries for males€™ and females€™ responses area. Draw side- by- side skeletal boxplots for the
Refer to the alcohol consumption data in Exercise 29. Students were also asked if they typically sit in the front, back, or middle of the classroom. Here are the responses to the question about alcohol consumption for the students who responded that they typically sit in the back of the
Refer to the data in Exercise 31 on alcohol consumption for students who typically sit in the back of the classroom. Using the definition of outliers on page 150, identify which value(s) are outliers in each of the two sets of values (males and females).
a. Give an example of a set of five numbers with a standard deviation of 0. b. Give an example of a set of four numbers with a mean of 15 and a standard deviation of 0. c. Is there more than one possible set of numbers that could be used to answer part (a)? Is there more than one possible set of
In each of the following cases, would the mean or the median probably be higher, or would they be about equal? a. Prices of all new cars sold in 1 month in a large city. b. Heights of all 7-year-old children in a large city. c. Shoe sizes of adult women.
In each of the following cases, would the mean or the median probably be higher, or would they be about equal? a. Salaries in a company employing 100 factory workers and two highly paid executives. b. Ages at which residents of a suburban city die, including everything from infant deaths to the
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?
Suppose the scores on a recent exam in your statistics class were as follows:78, 95, 60, 93, 55, 84, 76, 92, 62, 83, 80, 90, 64, 75, 79, 32, 75, 64, 98, 73, 88, 61, 82, 68, 79, 78, 80, 85.a. Create a stemplot for these test scores using each 10s value once on the stem.b. Create a stemplot for these
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.
The Winters (CA) Express on April 4, 2013, reported that the seasonal rainfall (since July 1, 2012) for the year was 16.75 inches, and that the “average to April 3 is 20.09 inches.” Does this mean that the area received abnormally low rain-fall in the period from July 1, 2012, to April 4, 2013?
Suppose you are interested in genealogy, and want to try to predict your potential longevity by using the ages at death of your ancestors. You find out the ages at death for the eight great-grandparents of your mother and your father. Suppose the ages (in numerical order) are as follows: Mother’s
According to the National Weather Service, there is about a 10% chance that total annual rainfall for Sacramento, CA, will be less than 11.1 inches and a 20% chance that it will be less than 13.5 inches. At the upper end, there is about a10% chance that it will exceed 29.8 inches and a 20% chance
Refer to Original Source 5 on the companion website, “Distractions in everyday driving.” Notice that on page 86 of the report, when the responses are summarized for the quantitative data in question 8, only the mean is provided. But for questions 7 and 9 the mean and median are provided. Why do
Refer to Original Source 20 on the companion website, “Organophosphorus pesticide exposure of urban and suburban preschool children with organic and conventional diets.” In Table 4 on page 381, information is presented for estimated dose levels of various pesticides for children who eat organic
Refer to the test scores in the Exercise 4. a. Create a histogram for the test scores. b. Explain how you decided how many intervals to use for the histogram in part (a). c. Comment on the shape of the histogram in part (a).
Refer to the test scores in Exercise 4. a. Find the median for the test scores. b. Find the mean for the test scores and com-pare it to the median. Which one is larger, and why? c. Find the standard deviation for the test scores. If possible, use software or a calculator to do the
Refer to the test scores in Exercise 4. a. Create a five-number summary. b. Create a boxplot. c. The test score of 32 should have been identified as an outlier. Which of the three reasons for outliers given on page 139 do you think explains this outlier? Should the outlier be removed when a
Refer to the pulse rates given in the stemplots in Figure 7.2 (page 142). a. Create a five-number summary of the pulse rates (also found in Exercise 3b). b. Create a boxplot of the pulse rates.
Give an example for which the median would be more useful than the mean as a measure of center. (Do not reuse an example already discussed in this chapter.)
Find a set of data that has meaning for you. Internet sites are good sources for data. For instance, find ads for something you would like to buy, sports scores, weather data, and so on. Using the methods given in this chapter, summarize and display the data in whatever ways are most useful. Give a
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
Using Table 8.1, a computer, or a calculator, determines the percentage of the population falling below each of the following standard scores: a. 21.00 b. 1.96 c. 0.84
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. Use Figure 8.6 as a guide.
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? (Remember that the mean is 100 and the standard deviation is 15.) b. Mensa also allows members to
Use Table 8.1 to verify that the Empirical Rule is true. You may need to round off the values slightly.
Remember that the whiskers on a boxplot can extend 1.5 interquartile ranges (IQRs) from either end of the box, and values beyond that range are considered to be outliers. For normally distributed data, the mean and median are equal and are both centered in the middle of the box in a boxplot. a.
Recall from Chapter 7 that the interquartile range (IQR) covers the middle 50% of the data. a. What range of standardized scores is covered by the interquartile range for normally distributed populations? In other words, what are the standardized scores for the lower quartile (the 25th percentile)
Recall that for Stanford-Binet IQ scores the mean is 100 and the standard deviation is 15. a. Use the Empirical Rule to specify the ranges into which 68%, 95%, and 99.7% of Stanford-Binet IQ scores fall. b. Draw a picture similar to Figure 8.6 for Stanford-Binet scores, illustrating the ranges from
For every 100 births in the United States, the number of boys follows, approximately, a normal curve with a 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.
In each of the following cases, explain how you know that the population of measurements could not be normally distributed. a. The population is all families in the world that have exactly four children, and the measurement is the number of boys in the family. b. The population is all college
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 favors the candidate can be thought of as a measurement from a normal curve with a mean of 48% and a standard deviation of 1%. Based on this
Math SAT scores for students admitted to a university are bell-shaped with a mean of 520 and a standard deviation of 60. a. Draw a picture of these SAT scores, indicating the cutoff points for the middle 68%, 95%, and 99.7% of the scores. See Figure 8.6 for guidance. b. A student had a math SAT
According to Chance magazine ([1993], 6, no. 3, 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. a. What proportion of the
Remember from Chapter 7 that the range for a data set is found as the difference between the maximum and minimum values. Explain why it makes sense that for a bell-shaped data set of a few hundred values, the range should be about 4 to 6 standard deviations.
Suppose that you were told that scores on an exam in a large class you are taking ranged from 50 to 100 and that they were approximately bell-shaped. a. Estimate the mean for the exam scores. b. Refer to the result about the relationship between the range and standard deviation in Exercise 25.
Recall that quantitative reasoning GRE scores are approximately bell- shaped with a mean of 151.3 and standard deviation of 8.7. The minimum and maximum possible scores on this part of the GRE exam are 130 and 170, respectively. a. What is the range for these GRE scores? b. Refer to the result
Refer to Example 8.1 on page 167, and the corresponding Figure 8.3 showing the distribution of heights for college women. The mean of the heights is 64.5 inches, and the standard deviation is 2.5 inches.a. Use the Empirical Rule to determine the ranges into which about 68%, 95%, and 99.7% of
Using Table 8.1, a computer, or a calculator, determines the percentage of the population falling above each of the following standard scores: a. 1.28 b. 20.25 c. 2.33
Using Table 8.1, a computer, or a calculator, determines the standard score that has the following percentage of the population below it: a. 25% b. 75% c. 45% d. 98%
Give an example of a population of measurements that would not have a normal distribution for each of the following reasons. a. The measurement can only result in a small number of possible values, instead of the continuum over a substantial range that is required for a normal distribution. b. The
Using Table 8.1, a computer, or a calculator, determines the standard score that has the following percentage of the population above it: a. 2% b. 50% c. 75% d. 10%
Using Table 8.1, a computer, or a calculator, determines the percentage of the population falling between the two standard scores given: a. 21.00 and 1.00 b. 21.28 and 1.75 c. 0.0 and 1.00
The 84th percentile for the Stanford-Binet IQ test is 115. (Recall that the mean is 100 and the standard deviation is 15.) 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,
Find the percentile for the observed value in the following situations: a. Quantitative reasoning GRE score of 146 (mean 5 151.3, s. d. 5 8.7). b. Stanford-Binet IQ score of 97 (mean 5 100, s. d. 5 15). c. Woman’s height of 68 inches (mean 5 65 inches, s. d. 5 2.5 inches). d. Man’s height of 68
Use the pie charts in Figure 9.1 to create a bar graph comparing eye colors for Caucasian boys and Caucasian girls.
According to the American Red Cross (www.redcrossblood.org/learnaboutblood/bloodtypes), the distribution of blood types in the United States is as shown in Table 9.4. a. Draw a pie chart illustrating the blood type distribution for Caucasians, ignoring the RH factor. b. Draw a statistical
According to an article in The Seattle Times (Meckler, 2003), living organ donors are most often related to the organ recipient. Table 9.5 gives the percentages of each type of relationship for all 6613 cases in which an organ was transplanted from a living donor in 2002 in the United States.
Table 9.6 provides the total number of men and women who were in the labor force in 1971, 1981, 1991, 2001, and 2011 in the United States. a. Create a bar graph for the data. b. Compare the bar graph to the one in Figure 9.2, which presents the percent of men and women who were in the labor force.
For each of the following time series, do you think the long-term trend would be positive, negative, or nonexistent? a. The cost of a loaf of bread measured monthly from 1960 to the present month. b. The temperature in Boston measured at noon on the first day of each month from 1960 to the present
For each of the time series in Exercise 15, explain whether there is likely to be a seasonal component.
Global warming is a major concern because it implies that temperatures around the world are going up on a permanent basis. Suppose you were to examine a plot of monthly temperatures in one location for the past 50 years. Explain the role that the three time series components (trend, seasonal,
The population of the United States rose from about 179 million people in 1960 to about 314 million people in 2012. Suppose you wanted to examine a time series to see if homicides had become an increasing problem over that time period. Would you simply plot the number of homicides versus time, or
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
Discuss which of the three components of a time series (trend, seasonal, and cycles) are likely to be present in each of the following series, reported monthly for the past 10 years: a. Unemployment rates b. Hours per day the average child spends watching television
Which of the three components (trend, seasonal, and cycles) are likely to be present in a time series reporting interest rates paid by a bank each month for the last 10 years?
Refer to Figure 1 on page 691 of Original Source 11, linked to the companion website, “Driving impairment due to sleepiness is exacerbated by low alcohol intake.” a. What type of picture is in the figure? b. Write a few sentences explaining what you learn from the picture about lane drifting
Refer to Figure 2 on page 691 of Original Source 11, linked to the companion website, “Driving impairment due to sleepiness is exacerbated by low alcohol intake.” a. What type of picture is in the figure? b. Write a few sentences explaining what you learn from the picture about subjective
Give the name of a type of statistical picture that could be used for each of the following kinds of data: a. One categorical variable b. One measurement variable c. Two categorical variables d. Two measurement variables
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
An article in Science (23 January 1998, 279, 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?” Results
Figure 9.12a, 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 9.6 to determine the problem; then redraw the graph correctly (but still
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
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?

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