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mathematics
practice of statistics
Questions and Answers of
Practice of Statistics
Refer to Exercise 23.a. Construct and interpret a 95% confidence interval for the difference between the true proportions. Assume that the conditions for inference are met.b. Explain how the
Which of two widely prescribed drugs—Lipitor or Pravachol—helps lower “bad cholesterol” more? In an experiment, called the PROVE-IT Study, researchers recruited about 4000 people with heart
A recent study of peanut allergies—the LEAP trial—explored the relationship between early exposure to peanuts and the subsequent development of an allergy to peanuts. Infants (4 to 11 months old)
In a study of 3000 randomly selected teenagers in 1990, 450 showed some hearing loss. In a similar study of 1800 teenagers reported in 2010, 351 showed some hearing loss.a. Do these data give
Phoebe has a hunch that older students at her very large high school are more likely to bring a bag lunch than younger students because they have grown tired of cafeteria food. She takes a simple
Refer to Exercise 16.a. Explain why the sample results give some evidence for the alternative hypothesis.b. Calculate the standardized test statistic and P-value.c. What conclusion would you
Refer to Exercise 15.a. Explain why the sample results give some evidence for the alternative hypothesis.b. Calculate the standardized test statistic and P-value.c. What conclusion would you
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 ticks. The mouse population, in
Fire is a serious threat to shrubs in dry climates. Some shrubs can resprout from their roots after their tops are destroyed. Researchers wondered if fire would help with resprouting. One study of
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
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
An association of Christmas tree growers in Indiana wants to know if there is a difference in preference for natural trees between urban and rural households. So the association sponsored a survey of
A CBS News poll asked 606 randomly selected women and 442 randomly selected men, “Do you think putting a special tax on junk food would encourage more people to lose weight?” 170 of the women and
Nicotine patches are often used to help smokers quit. Does giving medicine to fight depression help? A randomized double-blind experiment assigned 244 smokers to receive nicotine patches and another
Does the appearance of the interviewer influence how people respond to a survey question? Ken (white, with blond hair) and Hassan (darker, with Middle Eastern features) conducted an experiment to
In a Pew Research poll, 287 out of 522 randomly selected U.S. men were able to identify Egypt when it was highlighted on a map of the Middle East. When 520 randomly selected U.S. women were asked,
A surprising number of young adults (ages 19 to 25) still live in their parents’ homes. The National Institutes of Health surveyed independent random samples of 2253 men and 2629 women in this age
A company that records and sells rewritable DVDs wants to compare the reliability of DVD fabricating machines produced by two different manufacturers. They randomly select 500 DVDs produced by each
The pesticide diazinon is commonly used to treat infestations of the German cockroach, Blattella germanica. A study investigated the persistence of this pesticide on various types of surfaces.
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. Randomly assign 65
The movie A Civil Action (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 east Woburn residents was
Refer to Exercise 2.a. Find the probability that the proportion of graduates who pass the test is at most 0.20 higher than the proportion of dropouts who pass, assuming that the researcher’s report
Refer to Exercise 1.a. Find the probability that the proportion of red jelly beans in the Child sample is less than or equal to the proportion of red jelly beans in the Adult sample, assuming that
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
When buying or leasing a new car, one of the factors that customers consider is the type of fuel it uses. Some people prefer vehicles that use diesel fuel, while others favor vehicles that use
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.
In the “Ask Marilyn” column of Parade magazine, a reader posed this question: “Say that a slot machine has five wheels, and each wheel has five symbols: an apple, a grape, a peach, a pear, and
“Do you feel confident or not confident that the food available at most grocery stores is safe to eat?” When a Gallup poll asked this question, 87% of the sample said they were confident. Gallup
A researcher plans to conduct a significance test at the α = 0.01 significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest.
Vigorous exercise helps people live several years longer (on average). Whether mild activities like slow walking extend life is not clear. Suppose that the added life expectancy from regular slow
The most important condition for making an inference about a population mean from a significance test is thata. The data come from a random sample.b. The population distribution is exactly Normal.c.
After checking that conditions are met, you perform a significance test of H0: μ = 1 versus Ha: μ ≠ 1. You obtain a P-value of 0.022. Which of the following must be true?a. A 95% confidence
You are testing H0: μ = 10 against Ha: μ ≠ 10 based on an SRS of 15 observations from a Normal population. What values of the t statistic are statistically significant at the α = 0.005 level?a.
You are testing H0: μ = 10 against Ha: μ < 10 based on an SRS of 20 observations from a Normal population. The t statistic is t = −2.25. The P-valuea. Falls between 0.01 and 0.02.b. Falls
The reason we use t procedures instead of z procedures when carrying out a test about a population mean is thata. z requires that the sample size be large.b. z requires that you know the population
Refer to Exercise 85.a. Suppose that H0: p = 0.08 is true. Describe the shape, center, and variability of the sampling distribution of p̂ in random samples of size 500.b. Use the sampling
Joe is writing a report on the backgrounds of American presidents. He looks up the ages of all the presidents when they entered office. Because Joe took a statistics course, he uses these numbers to
A marketing consultant observes 50 consecutive shoppers at a supermarket, recording how much each shopper spends in the store. Explain why it would not be wise to use these data to carry out a
A researcher wishes to determine if people are able to complete a certain pencil and paper maze more quickly while listening to classical music. Suppose previous research has established that the
A medical experiment investigated whether taking the herb echinacea could help prevent colds. The study measured 50 different response variables usually associated with colds, such as lowgrade fever,
A national chain of SAT-preparation schools wants to know if using a smartphone app in addition to its regular program will help increase student scores more than using just the regular program. On
You read that a significance test at the α = 0.01 significance level has probability 0.14 of making a Type II error when a specific alternative is true.a. What is the power of the test against this
A researcher looking for evidence of extrasensory perception (ESP) tests 500 subjects. Four of these subjects do significantly better (P<0.01) than random guessing.a. Is it proper to conclude that
Refer to Exercises 86 and 88.a. Explain one disadvantage of using α = 0.10 instead of α = 0.05 when performing the test.b. Explain one disadvantage of taking a random sample of 50 people instead of
A scientist calculates that a test at the α = 0.05 significance level has probability 0.23 of making a Type II error when a specific alternative is true.a. What is the power of the test against this
A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school’s students approved of the parking that was provided.
A company that manufactures classroom chairs for high school students claims that the mean breaking strength of the chairs is 300 pounds. One of the chairs collapsed beneath a 220-pound student last
A company that makes potato chips requires each shipment of potatoes to meet certain quality standards. If the company finds convincing evidence that more than 8% of the potatoes in the shipment have
Refer to Exercises 85 and 87.a. Explain one disadvantage of using α = 0.10 instead of α = 0.05 when performing the test.b. Explain one disadvantage of taking a random sample of 500 potatoes instead
Refer to Exercise 86. Determine if each of the following changes would increase or decrease the power of the test. Explain your answers.a. Use a random sample of 30 people instead of 50 people.b. Try
Refer to Exercise 85. Determine if each of the following changes would increase or decrease the power of the test. Explain your answers.a. Change the significance level to α = 0.10.b. Take a random
You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over
The P-value for a two-sided test of the null hypothesis H0: μ = 15 is 0.03.a. Does the 99% confidence interval for μ include 15? Why or why not?b. Does the 95% confidence interval for μ include
The P-value for a two-sided test of the null hypothesis H0: μ = 10 is 0.06 .a. Does the 95% confidence interval for μ include 10? Why or why not?b. Does the 90% confidence interval for μ include
A blogger claims that U.S. adults drink an average of five 8- ounce glasses (that’s 40 ounces) of water per day. Researchers wonder if this claim is true, so they ask a random sample of 24 U.S.
Refer to Exercise 78.a. Construct and interpret a 90% confidence interval for the true mean vertical jump μ (in inches) of the students at Haley, Jeff, and Nathan’s school. Assume that the
How long does it take for a chunk of information to travel from one server to another and back on the Internet? According to the site internettrafficreport.com, the average response time is 200
Refer to Exercise 77.a. Construct and interpret a 95% confidence interval for the true hardness μ of the tablets in this batch. Assume that the conditions for inference are met.b. Explain why the
Student researchers Haley, Jeff, and Nathan saw an article on the Internet claiming that the average vertical jump for teens was 15 inches. They wondered if the average vertical jump of students at
A drug manufacturer forms tablets by compressing a granular material that contains the active ingredient and various fillers. The hardness of a sample from each batch of tablets produced is measured
One company’s bottles of grapefruit juice are filled by a machine that is set to dispense an average of 180 milliliters (ml) of liquid. The company has been getting negative feedback from customers
A school librarian purchases a novel for her library. The publisher claims that the book is written at a fifth-grade reading level, but the librarian suspects that the reading level is lower than
A study was carried out with a random sample of 10 patients who suffer from insomnia to investigate the effectiveness of a drug designed to increase sleep time. The following data show the number of
Every road has one at some point— construction zones that have much lower speed limits. To see if drivers obey these lower speed limits, a police officer uses a radar gun to measure the speed (in
In the study of the candy machine from Exercise 66, the sample mean weight for the bags of candy was 19.28 ounces and the sample standard deviation was 0.81 ounce.a. Calculate the standardized test
In the study of older students’ attitudes from Exercise 65, the sample mean SSHA score was 125.7 and the sample standard deviation was 29.8.a. Calculate the standardized test statistic.b. Find and
Suppose you want to perform a test of H0: μ = 5 versus Ha: μ < 5 at the α = 0.05 significance level. A random sample of size n = 20 from the population of interest yields x¯ = 4.7 and sx =
A retailer entered into an exclusive agreement with a supplier who guaranteed to provide all products at competitive prices. To be sure the supplier honored the terms of the agreement, the retailer
Suppose you want to perform a test of H0: μ = 64 versus Ha: μ ≠ 64 at the α = 0.05 significance level. A random sample of size n = 25 from the population of interest yields x¯ = 62.8 and sx =
A tablet computer manufacturer claims that its batteries last an average of 10.5 hours when playing videos. The quality-control department randomly selects 20 tablets from each day’s production and
A machine is supposed to fill bags with an average of 19.2 ounces of candy. The manager of the candy factory wants to be sure that the machine does not consistently underfill or overfill the bags. So
The Survey of Study Habits and Attitudes (SSHA) is a psychological test with scores that range from 0 to 200. The mean score for U.S. college students is 115. A teacher suspects that older students
Will cash bonuses speed the return to work of unemployed people? The Illinois Department of Employment Security designed an experiment to find out. The subjects were 10,065 people aged 20 to 54 who
A manufacturer of digital video discs (DVDs) wants to be sure that the DVDs will fit inside the plastic cases used as packaging. Both the cases and the DVDs are circular. According to the supplier,
Which of the following 95% confidence intervals would lead us to reject H0: p = 0.30 in favor of Ha: p ≠ 0.30 at the 5% significance level?a. (0.19, 0.27)b. (0.24, 0.30)c. (0.27, 0.31)d. (0.29,
The standardized test statistic for a test of H0: p = 0.4 versus Ha: p ≠ 0.4 is z = 2.43. This test isa. not significant at either α = 0.05 or α = 0.01.b. significant at α = 0.05, but not at α
After once again losing a football game to the archrival, a college’s alumni association conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the
Which of choices (a) through (d) is not a condition for performing a significance test about a population proportion p?a. The data should come from a random sample from the population of interest.b.
The Gallup Youth Survey asked a random sample of U.S. teens aged 13 to 17 whether they thought that young people should wait until marriage to have sex. The Minitab output shows the results of a
What proportion of students are willing 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
A Gallup poll found that 59% of the people in its sample said “Yes” when asked, “Would you like to lose weight?” Gallup announced: “For results based on the total sample of national adults,
The Pew Internet and American Life Project asked a random sample of U.S. adults, “Do you ever … use Twitter or another service to share updates about yourself or to see updates about others?”
Refer to Exercise 52.a. Construct and interpret a 95% confidence interval for the true proportion p of all first-year students at the university who would identify being very well-off as an important
Refer to Exercise 51.a. Construct and interpret a 95% confidence interval for the true proportion p of all teens in the state who passed their driving test on the first attempt. Assume that the
In a recent year, 73% of first-year college students responding to a national survey identified “being very well-off financially” as an important personal goal. A state university finds that 132
A state’s Division of Motor Vehicles (DMV) claims that 60% of all teens pass their driving test on the first attempt. An investigative reporter examines an SRS of the DMV records for 125 teens; 86
When a fair coin is flipped, we all know that the probability the coin lands on heads is 0.50. However, what if a coin is spun? According to the article “Euro Coin Accused of Unfair Flipping” in
Gregor Mendel (1822–1884), an Austrian monk, is considered the father of genetics. Mendel studied the inheritance of various traits in pea plants. One such trait is whether the pea is smooth or
A political organization wants to determine if there is convincing evidence that a majority of registered voters in a large city favor Proposition X. In an SRS of 1000 registered voters, 482 favor
A consumer organization suspects that less than half of parents know their child’s cell-phone password. The Pew Research Center asked a random sample of parents if they knew their child’s
A drug manufacturer claims that less than 10% of patients who take its new drug for treating Alzheimer’s disease will experience nausea. To test this claim, researchers conduct an experiment. They
A local high school makes a change that should improve student satisfaction with the parking situation. Before the change, 37% of the school’s students approved of the parking that was provided.
The germination rate of seeds is defined as the proportion of seeds that sprout and grow when properly planted and watered. A certain variety of grass seed usually has a germination rate of 0.80. A
A test of H0: p = 0.65 against Ha: p < 0.65 based on a sample of size 400 yields the standardized test statistic z = −1.78.a. Find and interpret the P-value.b. What conclusion would you make at
A test of H0: p = 0.5 versus Ha: p > 0.5 based on a sample of size 200 yields the standardized test statistic z=2.19 . Assume that the conditions for performing inference are met.a. Find and
A media report claims that more than 75% of middle school students engage in bullying behavior. A University of Illinois study on aggressive behavior surveyed a random sample of 558 middle school
Refer to Exercise 35.a. Explain why the sample result gives some evidence for the alternative hypothesis.b. Calculate the standardized test statistic and P-value.c. What conclusion would you
Refer to Exercise 36.a. Explain why the sample result gives some evidence for the alternative hypothesis.b. Calculate the standardized test statistic and P-value.c. What conclusion would you
A college president says, “More than two-thirds of the alumni support my firing of Coach Boggs.” The president’s statement is based on 200 emails he has received from alumni in the past three
You want to determine if a coin is fair. So you toss it 10 times and record the proportion of tosses that land “heads.” You would like to perform a test of H0: p = 0.5 versus Ha: p ≠ 0.5, where
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