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essentials of statistics

The Basic Practice Of Statistics 5th Edition David S Moore - Solutions

Using credit cards. Are shoppers more or less likely to use credit cards for “im-pulse purchases”that they decide to make on the spot, as opposed to purchases that they had in mind when they went to the store? Stop every third person leaving a department store with a purchase. (This is in
Does preschool help? To study the long-term effects of preschool programs for poor children, the High/Scope Educational Research Foundation has followed two groups of Michigan children since early childhood.26 One group of 62 attended preschool as 3- and 4-year-olds. A control group of 61 children
Lyme disease. Lyme disease is spread in the northeastern United States by in-S TE Pfected ticks. The ticks are infected mainly by feeding on mice, so more mice result in more infected ticks. The mouse population in turn rises and falls with the abundance of acorns, their favored food. Experimenters
Seat belt use. The proportion of drivers who use seat belts depends on things like ST EP age (young people are more likely to go unbelted) and gender (women are more likely to use belts). It also depends on local law. In New York City, police can stop a driver who is not belted. In Boston at the
I refuse! Do our emotions influence economic decisions? One way to examine the ST EP issue is to have subjects play an “ultimatum game”against other people and against a computer. Your partner (person or computer) gets $10, on the condition that it be shared with you. The partner makes you an
The Gold Coast. A historian examining British colonial records for the Gold Coast in Africa suspects that the death rate was higher among African miners than among European miners. In the year 1936, there were 223 deaths among 33,809 African miners and 7 deaths among 1541 European miners on the
How to quit smoking. Nicotine patches are often used to help smokers quit. Does giving medicine to fight depression help? A randomized double-blind experiment assigned 244 smokers who wanted to stop to receive nicotine patches and another 245 to receive both a patch and the antidepression drug
Are urban students more successful, continued. Continue your work from Exercise 20.26. Estimate the difference between the success rates for all urban/suburban and rural/small-town students who plan to study chemical engineering at North Carolina State. (Use 90% confidence.)
Female and male students. The North Carolina State University study in the previous exercise also looked at possible differences in the proportions of female and male students who succeeded in the course. They found that 23 of the 34 women and 60 of the 89 men succeeded. Is there evidence of a
Are urban students more successful? North Carolina State University looked at the factors that affect the success of students in a required chemical engineering course. Students must get a C or better in the course in order to continue as chemical engineering majors, so a “success” is a grade
Significant does not mean important. Never forget that even small effects can be statistically significant if the samples are large. To illustrate this fact, consider a sample of 148 small businesses. During a three-year period, 15 of the 106 headed by men and 7 of the 42 headed by women
The design of the study matters. How accurate are the tests that grain-handling facilities make to detect the presence of genetically modified (GM) soybeans in shipments to countries that do not allow GM beans? Batches of soybeans containing some genetically modified (GM) beans were submitted to 23
How big a difference? Give a 95% confidence interval for the difference between the proportions of papers rejected without review when a statistician is and is not involved in the research.
How often are statisticians involved? Give a 95% confidence interval for the proportion of papers submitted to these journals that include help from a statistician.
Does statistical help make a difference? Is there a significant difference in the proportions of papers with and without statistical help that are rejected without review? State hypotheses, find the test statistic, use software or the bottom row of Table C to get a P-value, and give your
Drug testing in schools, continued. Exercise 20.18 describes a study that compared the proportions of athletes who use illegal drugs in two similar high schools, one that tests for drugs and one that does not. Drug testing is intended to reduce use of drugs. Do the data give good reason to think
Genetically altered mice. Genetic influences on cancer can be studied by manipulating the genetic makeup of mice. One of the processes that turn genes on or off (so to speak) in particular locations is called “DNA methylation.”Do low levels of this process help cause tumors? Compare mice
Drug testing in schools. In 2002 the Supreme Court ruled that schools could require random drug tests of students participating in competitive after-school activities such as athletics. Does drug testing reduce use of illegal drugs? A study compared two similar high schools in Oregon. Wahtonka High
Truthfulness in online profiles. Many teens have posted profiles on sites such as MySpace. A sample survey asked random samples of teens with online profiles if they included false information in their profiles. Of 170 younger teens (ages 12 to 14), 117 said “Yes.” Of 317 older teens (ages 15
The plus four 90% confidence interval for the difference between the proportion of rats that succeed when given M and the proportion that succeed without it is(a) 0.455 ± 0.312. (b) 0.417 ± 0.304. (c) 0.417 ± 0.185.
The z test in the previous exercise(a) may be inaccurate because the populations are too small.(b) may be inaccurate because some counts of successes and failures are too small.(c) is reasonably accurate because the conditions for inference are met.
In an experiment to learn if substance M can help restore memory, the brains of 20 rats were treated to damage their memories. The rats were trained to run a maze.After a day, 10 rats were given M and 7 of them succeeded in the maze; only 2 of the 10 control rats were successful. The z test for
The 95% large-sample confidence interval for the difference pM − pF in the proportions of college men and women who worked last summer is about(a) 0.06 ± 0.00095. (b) 0.06 ± 0.043. (c) 0.06 ± 0.036.
The z statistic for a test comparing the proportions of college men and women who worked last summer is about(a) z = 2.66. (b) z = 2.72. (c) z = 3.10.
The pooled sample proportion who worked last summer is about(a) ˆp = 1.70. (b) ˆp = 0.89. (c) ˆp = 0.85.
The sample proportions of college males and females who worked last summer are about(a) ˆpM = 0.88 and ˆpF = 0.82.(b) ˆpM = 0.82 and ˆpF = 0.88.(c) ˆpM = 0.75 and ˆpF = 0.97.
Take pM and pF to be the proportions of all college males and females who worked last summer. We conjectured before seeing the data that men are more likely to work. The hypotheses to be tested are(a) H0: pM = pF versus Ha: pM = pF .(b) H0: pM = pF versus Ha: pM > pF .(c) H0: pM = pF versus Ha: pM
Seat belt use: planning a study. How large a sample would be needed to obtain ST EP margin of error ±0.05 in the study of seat belt use among Hispanic females? Use the ˆp from Exercise 19.40 as your guess for the unknown p.
Does the double-blind method work? Many medical trials randomly assign pa-S TE Ptients to either an active treatment or a placebo. These trials are always doubleblind.Sometimes the patients can tell whether or not they are getting the active treatment. This defeats the purpose of blinding. Reports
Seat belt use, continued. Do the data in Exercise 19.40 give good reason to ST EP conclude that more than half of Hispanic female drivers in Boston wear seat belts?
Opinions about evolution, continued. Does the sample in Exercise 19.39 give ST EP good evidence to support the claim “Fewer than half of American adults think that humans developed from earlier species of animals”?
Seat belt use. The proportion of drivers who use seat belts depends on things ST EP like age, gender, ethnicity, and local law. As part of a broader study, investigators observed a random sample of 117 female Hispanic drivers in Boston; 68 of these drivers were wearing seat belts.25 Give a 95%
Opinions about evolution. A sample survey funded by the National Sci-ence Foundation asked a random sample of American adults about biological evolution.24 One question asked subjects to answer “True,” “False,” or “Not sure”to the statement “Human beings, as we know them today,
Condom usage. The National AIDS Behavioral Surveys (Example 19.1) also in-terviewed a sample of adults in the cities where AIDS is most common. This sample included 803 heterosexuals who reported having more than one sexual partner in the past year. We can consider this an SRS of size 803 from the
Shrubs that survive fires. Some shrubs have the useful ability to resprout from their roots after their tops are destroyed. Fire is a particular threat to shrubs in dry climates, as it can injure the roots as well as destroy the aboveground material.One study of resprouting took place in a dry area
Student drinking. The College Alcohol Study interviewed a sample of 14,941 college students about their drinking habits. The sample was stratified using 140 colleges as strata, but the overall effect is close to an SRS of students. The response rate was between 60% and 70% at most colleges. This is
Surveying students. You are planning a survey of students at a large university to determine what proportion favor an increase in student fees to support an expansion of the student newspaper. Using records provided by the registrar, you can select a random sample of students. You will ask each
Customer satisfaction. An automobile manufacturer would like to know what proportion of its customers are not satisfied with the service provided by the local dealer. The customer relations department will survey a random sample of customers and compute a 99% confidence interval for the proportion
The IRS plans an SRS. The Internal Revenue Service plans to examine an SRS of individual federal income tax returns from each state. One variable of interest is the proportion of returns claiming itemized deductions. The total number of tax returns in a state varies from more than 15 million in
Running red lights. A random digit dialing telephone survey of 880 drivers asked,“Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?”Of the 880 respondents, 171 admitted that at least one light had been red.21(a) Give a 95%
Detecting genetically modified soybeans. Most soybeans grown in the United States are genetically modified to, for example, resist pests and so reduce use of pesticides. Because some nations do not accept genetically modified (GM) foods, grain-handling facilities routinely test soybean shipments
Which font? Plain type fonts such as Times New Roman are easier to read than fancy fonts such as Gigi.Agroup of 25 volunteer subjects read the same text in both fonts. (This is a matched pairs design. One-sample procedures for proportions, like those for means, are used to analyze data from matched
I don’t like my life. The Pew Research Center asked a random sample of 1128 adult women, “How satisfied are you with your life overall?” Of these women, 56 said either “Mostly dissatisfied” or “Very dissatisfied.”18(a) Pew dialed residential telephone numbers at random in the
Do college students pray? Social scientists asked 127 undergraduate students“from courses in psychology and communications”about prayer and found that 107 prayed at least a few times a year.17(a) To use any inference procedure, we must be willing to regard these 127 students, as far as their
Harris announces a margin of error. Exercise 19.25 describes a Harris Poll survey of smokers in which 848 of a sample of 1010 smokers agreed that smoking would probably shorten their lives. Harris announces a margin of error of ±3 percentage points for all samples of about this size. Opinion polls
Reporting cheating. Students are reluctant to report cheating by other students.A student project put this question to an SRS of 172 undergraduates at a large university:“You witness two students cheating on a quiz. Do you go to the professor?”Only 19 answered “Yes.”16 Give a 95% confidence
Do smokers know that smoking is bad for them? The Harris Poll asked a sample of smokers, “Do you believe that smoking will probably shorten your life, or not?” Of the 1010 people in the sample, 848 said “Yes.”(a) Harris called residential telephone numbers at random in an attempt to contact
A Gallup Poll found that only 28% of American adults expect to inherit money or valuable possessions from a relative. The poll’s margin of error was 3%. This means that(a) the poll used a method that gets an answer within 3% of the truth about the population 95% of the time.(b) we can be sure
The value of the z statistic for the test of the previous exercise is about(a) z = 12. (b) z = 6. (c) z = 0.6.
Does the poll in Exercise 19.20 give reason to conclude that more than half of all seniors think their job prospects are good? The hypotheses for a test to answer this question are(a) H0: p = 0.5, Ha: p > 0.5.(b) H0: p > 0.5, Ha: p = 0.5.(c) H0: p = 0.5, Ha: p = 0.5.
The sample survey in Exercise 19.20 actually called 130 seniors, but 30 of the seniors refused to answer. This nonresponse could cause the survey result to be in error. The error due to nonresponse(a) is in addition to the margin of error found in Exercise 19.20.(b) is included in the margin of
An opinion poll asks an SRS of 100 college seniors how they view their job prospects. In all, 53 say “Good.” The plus four 95% confidence interval for estimating the proportion of all college seniors who think their job prospects are good is(a) 0.529 ± 0.096. (b) 0.529 ± 0.098. (c) 0.529 ±
How many athletes must be interviewed to estimate the proportion concerned about use of drugs within ±0.02 with 95% confidence? Use 0.5 as the conservative guess for p.(a) n = 25 (b) n = 1225 (c) n = 2401
Based on the Sports Illustrated sample, the 95% large-sample confidence interval for the proportion of all Division I athletes who think performance-enhancing drugs are a problem is(a) 0.36 ± 0.017. (b) 0.36 ± 0.034. (c) 0.36 ± 0.00030.
In fact, 273 of the 757 athletes in the Sports Illustrated sample said “Yes.”The sample proportion ˆp who said “Yes” is(a) 36. (b) 2.77. (c) 0.36.
The standard deviation of the distribution of ˆp in the previous exercise is about(a) 0.00028. (b) 0.033. (c) 0.017.
Sports Illustrated asked a random sample of 757 Division I college athletes, “Do you believe performance-enhancing drugs are a problem in college sports?” Suppose that in fact 30% of all Division I athletes think that drugs are a problem. In repeated samples, the sample proportion ˆp would
Student drinking. A professor asked her sophomore students, “How many drinks ST EP do you typically have per session? (A drink is defined as one 12 oz beer, one 4 oz glass of wine, or one 1 oz shot of liquor.)”Some of the students didn’t drink. Table 18.4 gives the responses of the female and
Tropical flowers. Different varieties of the tropical flower Heliconia are fertilized S TE Pby different species of hummingbirds. Over time, the lengths of the flowers and the forms of the hummingbirds’ beaks have evolved to match each other. Here are data on the lengths in millimeters of two
Active versus passive learning, continued.(a) Use the data in Exercise 18.46 to give a 90% confidence interval for the difference in mean number of Blissymbols identified correctly by children after active and passive lessons.(b) Give a 90% confidence interval for the mean number of Blissymbols
Each day I am getting better in math. A “subliminal” message is below our ST EP threshold of awareness but may nonetheless influence us. Can subliminal messages help students learn math? A group of students who had failed the mathematics part of the City University of New York Skills Assessment
Active versus passive learning. A study of computer-assisted learning exam-ined the learning of “Blissymbols” by children. Blissymbols are pictographs (think of Egyptian hieroglyphs) that are sometimes used to help learning-impaired children communicate. The researcher designed two computer
Thinking about money changes behavior. Kathleen Vohs of the University of ST EP Minnesota and her coworkers carried out several randomized comparative experiments on the effects of thinking about money. Here’s part of one such experiment.22 Ask student subjects to unscramble 30 sets of five words
for confidence intervals. Remember that examining the data and discussing the conditions for inference are part of the Solve step.
Year-to-year comparison. Rather than comparing the two groups in each year, we could compare the behavior of each group in the first and second years. The study report says: “Our main prediction was that females receiving additional food in the nestling period should not change laying date the
Did the treatment have an effect? The investigators expected the control group to adjust their breeding date the next year, whereas the well-fed supplemented group had no reason to change. The report continues: “but in the following year food-supplemented females were more out of synchrony with
Did the randomization produce similar groups? First, compare the two groups in the first year. The only difference should be the chance effect of the random assignment. The study report says: “In the experimental year, the degree of synchronization did not differ between food-supplemented and
How much less wrinkling? In Exercise 18.39, you found that the Hylite process results in significantly greater wrinkle resistance than the Permafresh process. How large is the difference in mean wrinkle recovery angle? Give a 90% confidence interval.Do birds learn to time their breeding? Blue
How much stronger? Continue your work from Exercise 18.38. A fabric manufacturer wants to know how large an advantage in strength fabrics treated by the Permafresh method have over fabrics treated by the Hylite process. Give a 90%confidence interval for the difference in mean breaking strengths.
Reducing wrinkles. Of course, the reason for durable press treatment is to reduce wrinkling. “Wrinkle recovery angle”measures how well a fabric recovers from wrinkles. Higher is better. Here are data on the wrinkle recovery angle (in degrees)for the same fabric swatches discussed in the
How strong are durable press fabrics? “Durable press” cotton fabrics are treated to improve their recovery from wrinkles after washing. Unfortunately, the treatment also reduces the strength of the fabric. A study compared the breaking strength of fabrics treated by two commercial durable press
IQ scores for boys and girls, continued. Use the data in Exercise 18.35 to give a 95% confidence interval for the difference between the mean IQ scores of all boys and girls in the district.
Do good smells bring good business, continued. In Exercise 18.9 (page 483)you examined the effects of a lavender odor on customer behavior in a small restaurant.Lavender is a relaxing odor. The researchers also looked at the effects of lemon, a stimulating odor. The design of the study is described
IQ scores for boys and girls. Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district:19 114 100 104 89 102 91 114 114 103 105 108 130 120 132 111 128 118 119 86 72 111 103 74 112 107 103 98 96 112 112 93 The IQ test scores of 47 seventh-grade boys in the same district
Coaching and SAT scores: critique. The data you used in the previous two problems came from a random sample of students who took the SAT twice. The response rate was 63%, which is pretty good for nongovernment surveys, so let’s accept that the respondents do represent all students who took the
Coaching and SAT scores, continued. What we really want to know is whether coached students improve more than uncoached students, and whether any advantage is large enough to be worth paying for. Use the information in the previous exercise to answer these questions:(a) Is there good evidence that
Coaching and SAT scores. Coaching companies claim that their courses can raise the SAT scores of high school students. Of course, students who retake the SAT without paying for coaching generally raise their scores. A random sample of students who took the SAT twice found 427 who were coached and
Immigrant mothers at a university. The SAFE (Social, Attitudinal, Familial, and Environmental Stress) scale measures the stress level of adults adjusting to a different culture. Scores range from 1 (not stressful) to 5 (extremely stressful). In a study of stress among immigrant mothers in a
Hispanic customers and Anglo customers. As the presence of Hispanics in the United States has grown, businesses try to understand what Hispanics like. One study sampled customers leaving a bank. Customers were classified as Hispanic if they preferred to be interviewed in Spanish or as Anglo if they
Ginkgo extract and the post-lunch dip. The post-lunch dip is the drop in mental alertness after a midday meal. Does an extract of the leaves of the ginkgo tree reduce the post-lunch dip? Assign healthy people aged 18 to 40 to take either ginkgo extract or a placebo pill. After lunch, ask them to
Is Montessori preschool beneficial? Do education programs for preschool children that follow the Montessori method perform better than other programs? A study compared 5-year-old children in Milwaukee, Wisconsin, who had been enrolled in preschool programs from the age of 3.14(a) Explain why
Whelks on the Pacific coast. In a study of the presence of whelks along the Pacific coast, investigators put down a frame that covers 0.25 square meter and counted the whelks on the sea bottom inside the frame. They did this at 7 locations in California and 6 locations in Oregon. The report says
Eating potato chips. Give healthy women aged 18 to 40 bags of potato chips and bottled water and invite them to snack freely. Some women were trying to restrain their diet out of concern about their weight. How much effect did these good intentions have on their eating habits? The table below
Do women talk more than men? Equip male and female students with a small device that secretly records sound for a random 30 seconds during each 12.5-minute period over two days. Count the words each subject speaks during each recording period, and from this, estimate how many words per day each
The two-sample t statistic for the road rage study (male mean minus female mean)is t = 3.18. The P-value for testing the hypotheses from the previous exercise satisfies(a) 0.001 < P < 0.005. (b) 0.0005 < P < 0.001.(c) 0.001 < P < 0.002.
We suspect that men are more prone to road rage than women. To see if this is true, test these hypotheses for the mean road rage scores of all male and female drivers:(a) H0: μM = μF versus Ha: μM > μF .(b) H0: μM = μF versus Ha: μM = μF .(c) H0: μM = μF versus Ha: μM < μF .
Astudy of road rage asked samples of 596 men and 523 women about their behavior while driving. Based on their answers, each subject was assigned a road rage score on a scale of 0 to 20. The subjects were chosen by random digit dialing of telephone numbers. Are the conditions for two-sample t
The 8 high-capacity rats had mean blood pressure 89 with standard deviation 9;the 8 low-capacity rats had mean blood pressure 105 with standard deviation 13.(Blood pressure is measured in millimeters of mercury.) The two-sample t statistic for comparing the population means has value(a) 0.5. (b)
A study of the effects of exercise used rats bred to have high or low capacity for exercise. There were 8 high-capacity and 8 low-capacity rats. To compare the mean blood pressure of the two types of rats using the two-sample t procedures with the conservative Option 2, the correct degrees of
One major reason that the two-sample t procedures are widely used is that they are quite robust. This means that(a) t procedures do not require that we know the standard deviations of the populations.(b) confidence levels and P-values from the t procedures are quite accurate even if the population
There are two common methods for measuring the concentration of a pollutant in fish tissue. Do the two methods differ on the average? You apply both methods to a sample of 18 carp and use(a) the one-sample t test.(b) the matched pairs t test.(c) the two-sample t test.
In the 2005 NAEP sample of Texas eighth-graders, the mean mathematics scores were 279 for female students and 283 for male students. To see if there is a significant difference between the mean scores of all female and male students in Texas, you would use(a) the one-sample t test.(b) the matched
The 2005 National Assessment of Educational Progress (NAEP) gave a mathematics test to a random sample of eighth-graders in Texas. The mean score was 281 out of 500. To give a confidence interval for the mean score of all Texas eighth-graders, you would use(a) the one-sample t interval.(b) the
Practical significance? Give a 90% confidence interval for the mean time advantage of right-hand over left-hand threads in the setting of Exercise 17.45. Do you think that the time saved would be of practical importance if the task were performed many times—for example, by an assembly-line
Comparing two drugs. Makers of generic drugs must show that they do not differ S TE Psignificantly from the “reference”drugs that they imitate. One aspect in which drugs TABLE 17.6 Absorption extent for two versions of a drug SUBJECT REFERENCE DRUG GENERIC DRUG 15 4108 1755 3 2526 1138 9 2779
Right versus left. The design of controls and instruments affects how easily people ST EP can use them. Timothy Sturm investigated this effect in a course project, asking 25 right-handed students to turn a knob (with their right hands) that moved an indicator by screw action. There were two
Mutual-fund performance. Mutual funds often compare their performance with ST EP a benchmark provided by an “index” that describes the performance of the class of assets in which the fund invests. For example, the Vanguard International Growth Fund benchmarks its performance against the EAFE
How much better does nature heal? Give a 90% confidence interval for the difference in healing rates (control minus experimental) in the previous exercise.
Does nature heal better? Our bodies have a natural electrical field that is known ST EP to help wounds heal. Does changing the field strength slow healing? A series of experiments with newts investigated this question. The data below are the healing rates of cuts (micrometers per hour) in a matched
Natural weed control? Fortunately, we aren’t really interested in the number ST EP of seeds velvetleaf plants produce (see Exercise 17.39). The velvetleaf seed beetle feeds on the seeds and might be a natural weed control. Here are the total seeds, seeds infected by the beetle, and percent of

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