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business statistics in practice
The Practice Of Statistics 5th Edition Daren S. Starnes, Josh Tabor - Solutions
Perform a significance test to compare two proportions.
How can we find formulas for the mean and standard deviation of the sampling distribution of p^ 1− p^ 2?
Goldfish Refer to the example on page 615. Suppose that your teacher decides to take SRSs of 100 crackers from both bags instead.(a) What is the shape of the sampling distribution of p^1− p^2? Why?(b) Find the mean of the sampling distribution. Show your work.(c) Find the standard deviation of
Homework Refer to page 612. Suppose that both school counselors decide to take SRSs of 150 students instead.(a) What is the shape of the sampling distribution of p^1− p^2? Why?(b) Find the mean of the sampling distribution. Show your work.(c) Find the standard deviation of the sampling
I want red! A candy maker offers Child and Adult bags of jelly beans with different color mixes. The company claims that the Child mix has 30% red jelly beans, while the Adult mix contains 15% red jelly beans. Assume that the candy maker’s claim is true.Suppose we take a random sample of 50 jelly
Literacy A researcher reports that 80% of high school graduates, but only 40% of high school dropouts, would pass a basic literacy test.5 Assume that the researcher’s claim is true. Suppose we give a basic literacy test to a random sample of 60 high school graduates and a separate random sample
Don’t drink the water! The movie A Civil Action(Touchstone Pictures, 1998) tells the story of a major legal battle that took place in the small town of Woburn, Massachusetts. A town well that supplied water to eastern Woburn residents was contaminated by industrial chemicals. During the period
In-line skaters A study of injuries to in-line skaters used data from the National Electronic Injury Surveillance System, which collects data from a random sample of hospital emergency rooms. The researchers interviewed 161 people who came to emergency rooms with injuries from in-line skating.Wrist
Shrubs and fire Fire is a serious threat to shrubs in dry climates. Some shrubs can resprout from their roots after their tops are destroyed. One study of resprouting took place in a dry area of Mexico.7 The investigators randomly assigned shrubs to treatment and control groups. They clipped the
Broken crackers We don’t like to find broken crackers when we open the package. How can makers reduce breaking? One idea is to microwave the crackers for 30 seconds right after baking them. Breaks start as hairline cracks called “checking.” Randomly assign 65 newly baked crackers to the
Who tweets? Do younger people use Twitter more often than older people? In a random sample of 316 adult Internet users aged 18 to 29, 26% used Twitter.In a separate random sample of 532 adult Internet users aged 30 to 49, 14% used Twitter.9(a) Calculate the standard error of the sampling
Listening to rap Is rap music more popular among young blacks than among young whites?A sample survey compared 634 randomly chosen blacks aged 15 to 25 with 567 randomly selected whites in the same age group. It found that 368 of the blacks and 130 of the whites listened to rap music every
Young adults living at home A surprising number of young adults (ages 19 to 25) still live in their parents’homes. A random sample by the National Institutes of Health included 2253 men and 2629 women in this age group.11 The survey found that 986 of the men and 923 of the women lived with their
Fear of crime The elderly fear crime more than younger people, even though they are less likely to be victims of crime. One study recruited separate random samples of 56 black women and 63 black men over the age of 65 from Atlantic City, New Jersey. Of the women, 27 said they “felt
Who owns iPods? As part of the Pew Internet and American Life Project, researchers surveyed a random sample of 800 teens and a separate random sample of 400 young adults. For the teens, 79% said that they own an iPod or MP3 player. For the young adults, this figure was 67%. Do the data give
Steroids in high school A study by the National Athletic Trainers Association surveyed random samples of 1679 high school freshmen and 1366 high school seniors in Illinois. Results showed that 34 of the freshmen and 24 of the seniors had used anabolic steroids. Steroids, which are dangerous, are
Who owns iPods? Refer to Exercise 13. Carry out a significance test at the a = 0.05 level.
Steroids in high school Refer to Exercise 14. Carry out a significance test at the a = 0.05 level.
Who owns iPods? Refer to Exercise 13. Construct and interpret a 95% confidence interval for the difference between the population proportions. Explain how the confidence interval is consistent with the results of the test in Exercise 15.
Steroids in high school Refer to Exercise 14. Construct and interpret a 95% confidence interval for the difference between the population proportions.Explain how the confidence interval is consistent with the results of the test in Exercise 16.
Children make choices Many new products introduced into the market are targeted toward children.The choice behavior of children with regard to new products is of particular interest to companies that design marketing strategies for these products. As part of one study, randomly selected children in
Marriage and status “Would you marry a person from a lower social class than your own?” Researchers asked this question of a random sample of 385 black, never-married college students. Of the 149 men in the sample, 91 said “Yes.” Among the 236 women, 117 said “Yes.”15 Did a
Driving school A driving school owner believes that Instructor A is more effective than Instructor B at preparing students to pass the state’s driver’s license exam. An incoming class of 100 students is randomly assigned to two groups, each of size 50. One group is taught by Instructor A; the
Preventing strokes Aspirin prevents blood from clotting and so helps prevent strokes. The Second European Stroke Prevention Study asked whether adding another anticlotting drug, named dipyridamole, would be more effective for patients who had already had a stroke. Here are the data on strokes
Prayer and pregnancy Two hundred women who were about to undergo IVF served as subjects in an experiment. Each subject was randomly assigned to either a treatment group or a control group.Women in the treatment group were intentionally prayed for by several people (called intercessors)who did not
Acupuncture and pregnancy A study reported in the medical journal Fertility and Sterility sought to determine whether the ancient Chinese art of acupuncture could help infertile women become pregnant.18 One hundred sixty healthy women who planned to have IVF were recruited for the study.Half of the
Take pM and pF to be the proportions of all college males and females who worked last summer. The hypotheses to be tested are(a) H0: pM − pF = 0 versus Ha: pM − pF ≠ 0.(b) H0: pM − pF = 0 versus Ha: pM − pF > 0.(c) H0: pM − pF = 0 versus Ha: pM − pF < 0.(d) H0: pM − pF > 0 versus
The researchers report that the results were statistically significant at the 1% level. Which of the following is the most appropriate conclusion?(a) Because the P-value is less than 1%, fail to reject H0.There is not convincing evidence that the proportion of male college students in the study who
Which of the following is the correct margin of error for a 99% confidence interval for the difference in the proportion of male and female college students who worked for pay last summer?(a) 2.576Å0.851(0.149)550+0.851(0.149)500(b) 2.576Å0.851(0.149)1050(c)
In an experiment to learn whether Substance M can help restore memory, the brains of 20 rats were treated to damage their memories. First, the rats were trained to run a maze. After a day, 10 rats(determined at random) were given M and 7 of them succeeded in the maze. Only 2 of the 10 control rats
Drive my car (3.2)(a) What is the equation of the least-squares regression line? Be sure to define any symbols you use.(b) Interpret the slope of the least-squares line in the context of this problem.(c) One student reported that her 10-year-old car had 110,000 miles on it. Find and interpret the
Drive my car (3.2, 4.3)(a) Explain what the value of r2 tells you about how well the least-squares line fits the data.(b) The mean age of the students’ cars in the sample was x– = 8 years. Find the mean mileage of the cars in the sample. Show your work.(c) Interpret the value of s in the
Describe the shape, center, and spread of the sampling distribution of x–1 − x–2.
Determine whether the conditions are met for doing inference about m1 − m2.
Construct and interpret a confidence interval to compare two means.
Perform a significance test to compare two means.
Determine when it is appropriate to use two-sample t procedures versus paired t procedures.
Does Polyester Decay?
Cholesterol The level of cholesterol in the blood for all men aged 20 to 34 follows a Normal distribution with mean 188 milligrams per deciliter (mg/dl) and standard deviation 41 mg/dl. For 14-year-old boys, blood cholesterol levels follow a Normal distribution with mean 170 mg/dl and standard
How tall? The heights of young men follow a Normal distribution with mean 69.3 inches and standard deviation 2.8 inches. The heights of young women follow a Normal distribution with mean 64.5 inches and standard deviation 2.5 inches. Suppose we select independent SRSs of 16 young men and 9 young
Shoes How many pairs of shoes do teenagers have?To find out, a group of AP® Statistics students conducted a survey. They selected a random sample of 20 female students and a separate random sample of 20 male students from their school. Then they recorded the number of pairs of shoes that each
Household size How do the numbers of people living in households in the United Kingdom (U.K.) and South Africa compare? To help answer this question, we used CensusAtSchool’s random data selector to choose independent samples of 50 students from each country. Here is a Fathom dotplot of the
Literacy rates Do males have higher average literacy rates than females in Islamic countries? The table below shows the percent of men and women who were literate in the major Islamic nations at the time of this writing.27 (We omitted countries with populations of less than 3 million.)Country Male
Long words Mary was interested in comparing the mean word length in articles from a medical journal and an airline’s in-flight magazine. She counted the number of letters in the first 400 words of an article in the medical journal and in the first 100 words of an article in the airline magazine.
Is red wine better than white wine? Observational studies suggest that moderate use of alcohol by adults reduces heart attacks and that red wine may have special benefits. One reason may be that red wine contains polyphenols, substances that do good things to cholesterol in the blood and so may
Tropical flowers Different varieties of the tropical flower Heliconia are fertilized by different species of hummingbirds.Researchers believe that 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
Paying for college College financial aid offices expect students to use summer earnings to help pay for college. But how large are these earnings? One large university studied this question by asking a random sample of 1296 students who had summer jobs how much they earned. The financial aid office
Happy customers As the Hispanic population in the United States has grown, businesses have tried to understand what Hispanics like. One study interviewed a random sample of customers leaving a bank. Customers were classified as Hispanic if they preferred to be interviewed in Spanish or as Anglo if
Baby birds Do birds learn to time their breeding?Blue titmice eat caterpillars. The birds would like lots of caterpillars around when they have young to feed, but they must breed much earlier. Do the birds learn from one year’s experience when to time their breeding next year? Researchers
DDT in rats Poisoning by the pesticide DDT causes convulsions in humans and other mammals.Researchers seek to understand how the convulsions are caused. In a randomized comparative experiment, they compared 6 white rats poisoned with DDT with a control group of 6 unpoisoned rats.Electrical
Who talks more—men or women? Researchers equipped random samples of 56 male and 56 female students from a large university with a small device that secretly records sound for a random 30 seconds during each 12.5-minute period over two days. Then they counted the number of words spoken by each
Competitive rowers What aspects of rowing technique distinguish between novice and skilled competitive rowers? Researchers compared two randomly selected groups of female competitive rowers: a group of skilled rowers and a group of novices. The researchers measured many mechanical aspects of rowing
Teaching reading An educator believes that new reading activities in the classroom will help elementary school pupils improve their reading ability. She recruits 44 third-grade students and randomly assigns them into two groups. One group of 21 students does these new activities for an 8-week
Does breast-feeding weaken bones? Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from their bones, so mothers may lose bone mineral. Researchers compared a random sample of 47 breast-feeding women with a random sample of 22 women of similar age who were neither
Who talks more—men or women? Refer to Exercise 43. Construct and interpret a 95% confidence interval for the difference in mean number of words spoken in a day. Explain how this interval provides more information than the significance test in Exercise 43.
DDT in rats Refer to Exercise 42. Construct and interpret a 95% confidence interval for the difference in mean relative height of the second spike’s electrical response. Explain how this interval provides more information than the significance test in Exercise 42.
A better drug? In a pilot study, a company’s new cholesterol-reducing drug outperforms the currently available drug. If the data provide convincing evidence that the mean cholesterol reduction with the new drug is more than 10 milligrams per deciliter of blood (mg/dl) greater than with the
Down the toilet A company that makes hotel toilets claims that its new pressure-assisted toilet reduces the average amount of water used by more than 0.5 gallon per flush when compared to its current model. To test this claim, the company randomly selects 30 toilets of each type and measures the
Rewards and creativity Dr. Teresa Amabile conducted a study involving 47 college students who were randomly assigned to two treatment groups.The 23 students in one group were given a list of statements about external reasons (E) for writing, such as public recognition, making money, or pleasing
Sleep deprivation Does sleep deprivation linger for more than a day? Researchers designed a study using 21 volunteer subjects between the ages of 18 and 25. All 21 participants took a computer-based visual discrimination test at the start of the study. Then the subjects were randomly assigned into
Paired or unpaired? In each of the following settings, decide whether you should use paired t procedures or two-sample t procedures to perform inference. Explain your choice.39(a) To test the wear characteristics of two tire brands, A and B, each brand of tire is randomly assigned to 50 cars of the
Paired or unpaired? In each of the following settings, decide whether you should use paired t procedures or two-sample t procedures to perform inference. Explain your choice.40(a) To compare the average weight gain of pigs fed two different rations, nine pairs of pigs were used. The pigs in each
Coaching and SAT scores Let’s first ask if students who are coached increased their scores significantly.(a) You could use the information on the Coached line to carry out either a two-sample t test comparing Try 1 with Try 2 for coached students or a paired t test using Gain. Which is the
Coaching and SAT scores 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 above to answer these questions:(a) How much more do coached students gain on the
There are two common methods for measuring the concentration of a pollutant in fish tissue. Do the two methods differ, on average? You apply both methods to each fish in a random sample of 18 carp and use(a) the paired t test for md.(b) the one-sample z test for p.(c) the two-sample t test for m1
Which of the following describes a Type II error in the context of this study?(a) Finding convincing evidence that the true means are different for males and females, when in reality the true means are the same(b) Finding convincing evidence that the true means are different for males and females,
The P-value for the stated hypotheses is 0.002. Interpret this value in the context of this study.(a) Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability of getting a difference in sample means.(b) Assuming that the true mean road rage score
Based on the P-value in Exercise 59, which of the following must be true?(a) A 90% confidence interval for mM − mF will contain 0.(b) A 95% confidence interval for mM − mF will contain 0.(c) A 99% confidence interval for mM − mF will contain 0.(d) A 99.9% confidence interval for mM − mF
Which inference method?(a) Drowning in bathtubs is a major cause of death in children less than 5 years old. A random sample of parents was asked many questions related to bathtub safety. Overall, 85% of the sample said they used baby bathtubs for infants. Estimate the percent of all parents of
Which inference method?(a) How do young adults look back on adolescent romance?Investigators interviewed 40 couples in their midtwenties. The female and male partners were interviewed separately. Each was asked about his or her current relationship and also about a romantic relationship that lasted
Quality control (2.2, 5.3, 6.3) Many manufacturing companies use statistical techniques to ensure that the products they make meet standards. One common way to do this is to take a random sample of products at regular intervals throughout the production shift.Assuming that the process is working
Information online (8.2, 10.1) A random digit dialing sample of 2092 adults found that 1318 used the Internet.42 Of the users, 1041 said that they expect businesses to have Web sites that give product information;294 of the 774 nonusers said this.(a) Construct and interpret a 95% confidence
Coaching and SAT scores: Critique (4.1, 4.3) The data in Exercises 55 and 56 came from a random sample of students who took the SAT twice. The response rate was 63%, which is fairly good for nongovernment surveys.(a) Explain how nonresponse could lead to bias in this study.(b) We can’t be sure
Which procedure? For each of the following settings, say which inference procedure from Chapter 8, 9, or 10 you would use. Be specific. For example, you might say, “Two-sample z test for the difference between two proportions.” You do not need to carry out any procedures.43(a) Do people smoke
Seat belt use The proportion of drivers who use seat belts depends on things like 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 time of
Expensive ads Consumers who think a product’s advertising is expensive often also think the product must be of high quality. Can other information undermine this effect? To find out, marketing researchers did an experiment. The subjects were 90 women from the clerical and administrative staff of
Men versus women The National Assessment of Educational Progress (NAEP) Young Adult Literacy Assessment Survey interviewed a random sample of 1917 people 21 to 25 years old. The sample contained 840 men and 1077 women.46 The mean and standard deviation of scores on the NAEP’s test of quantitative
Treating AIDS The drug AZT was the first drug that seemed effective in delaying the onset of AIDS. Evidence for AZT’s effectiveness came from a large randomized comparative experiment.The subjects were 870 volunteers who were infected with HIV, the virus that causes AIDS, but did not yet have
Conditions Explain why it is not safe to use the methods of this chapter to perform inference in each of the following settings.(a) Lyme disease is spread in the northeastern United States by infected ticks. The ticks are infected mainly by feeding on mice, so more mice result in more infected
Each day I am getting better in math A “subliminal”message is below our threshold of awareness but may nonetheless influence us. Can subliminal messages help students learn math? A group of 18 students who had failed the mathematics part of the City University of New York Skills Assessment Test
A study of road rage asked separate random samples of 596 men and 523 women about their behavior while driving. Based on their answers, each respondent was assigned a road rage score on a scale of 0 to 20. Are the conditions for performing a two-sample t test satisfied?(a) Maybe; we have
Thirty-five people from a random sample of 125 workers from Company A admitted to using sick leave when they weren’t really ill. Seventeen employees from a random sample of 68 workers from Company B admitted that they had used sick leave when they weren’t ill. A 95% confidence interval for the
The power takeoff driveline on tractors used in agriculture is a potentially serious hazard to operators of farm equipment. The driveline is covered by a shield in new tractors, but for a variety of reasons, the shield is often missing on older tractors. Two types of shields are the bolt-on and the
A quiz question gives random samples of n = 10 observations from each of two Normally distributed populations. Tom uses a table of t distribution critical values and 9 degrees of freedom to calculate a 95% confidence interval for the difference in the two population means. Janelle uses her
The correct test statistic is(a) z =(6 − 5) − 0Å3 60+2 40(b) z =(6 − 5) − 0Å32 60+22 40(c) t =(6 − 5) − 0 3"60+2"40(d) t =(6 − 5) − 0Å3 60+2 40(e) t =(6 − 5) − 0Å32 60+22 40
The P-value for the test is 0.048. A correct conclusion is to(a) fail to reject H0 at the a = 0.05 level. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.(b) fail to reject H0 at the a = 0.05
At a baseball game, 42 of 65 randomly selected people own an iPod. At a rock concert occurring at the same time across town, 34 of 52 randomly selected people own an iPod. A researcher wants to test the claim that the proportion of iPod owners at the two venues is different. A 90% confidence
An SRS of size 100 is taken from Population A with proportion 0.8 of successes. An independent SRS of size 400 is taken from Population B with proportion 0.5 of successes. The sampling distribution for the difference (Population A –Population B) in sample proportions has what mean and standard
How much more effective is exercise and drug treatment than drug treatment alone at reducing the rate of heart attacks among men aged 65 and older? To find out, researchers perform a completely randomized experiment involving 1000 healthy males in this age group. Half of the subjects are assigned
Researchers are interested in evaluating the effect of a natural product on reducing blood pressure.This will be done by comparing the mean reduction in blood pressure of a treatment (natural product) group and a placebo group using a two-sample t test. The researchers would like to be able to
Researchers wondered whether maintaining a patient’s body temperature close to normal by heating the patient during surgery would affect wound infection rates. Patients were assigned at random to two groups: the normothermic group(patients’ core temperatures were maintained at near normal,
A random sample of 100 of a certain popular car model last year found that 20 had a certain minor defect in the brakes. The car company made an adjustment in the production process to try to reduce the proportion of cars with the brake problem.A random sample of 350 of this year’s model found
Pat wants to compare the cost of one- and twobedroom apartments in the area of her college campus. She collects data for a random sample of 10 advertisements of each type. The table below shows the rents (in dollars per month) for the selected apartments.1 bedroom: 500 650 600 505 450 550 515 495
Suppose the probability that a softball player gets a hit in any single at-bat is 0.300. Assuming that her chance of getting a hit on a particular time at bat is independent of her other times at bat, what is the probability that she will not get a hit until her fourth time at bat in a game?(a) a
The probability that Color Me Dandy wins a horse race at Batavia Downs given good track conditions is 0.60. The probability of good track conditions on any given day is 0.85. What is the probability that Color Me Dandy wins or the track conditions are good?(a) 0.94 (b) 0.51 (c) 0.49 (d) 0.06(e) The
Sports Illustrated planned to ask a random sample of Division I college athletes, “Do you believe performance-enhancing drugs are a problem in college sports?” How many athletes must be interviewed to estimate the proportion concerned about use of drugs within ±2% with 90% confidence?(a) 17
The distribution of grade point averages for a certain college is approximately Normal with a mean of 2.5 and a standard deviation of 0.6. Within which of the following intervals would we expect to find approximately 81.5% of all GPAs for students at this college?(a) (0.7, 3.1) (c) (1.9, 3.7) (e)
Which of the following will increase the power of a significance test?(a) Increase the Type II error probability.(b) Decrease the sample size.(c) Reject the null hypothesis only if the P-value is smaller than the level of significance.(d) Increase the significance level a.(e) Select a value for the
You can find some interesting polls online. Anyone can become part of the sample just by clicking on a response. One such poll asked, “Do you prefer watching first-run movies at a movie theater, or waiting until they are available to watch at home or on a digital device?” In all, 8896 people
A certain candy has different wrappers for various holidays. During Holiday 1, the candy wrappers are 30% silver, 30% red, and 40% pink. During Holiday 2, the wrappers are 50% silver and 50% blue. Forty pieces of candy are randomly selected from the Holiday 1 distribution, and 40 pieces are
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