The Practice Of Statistics 6th Edition Daren S. Starnes, Josh Tabor - Solutions

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 confidence interval provides more information than the test in Exercise 23.Exercise 23.A recent study of
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 disease as subjects. These volunteers were randomly assigned to one of two treatment groups: Lipitor
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) who had shown evidence of other kinds of allergies were randomly assigned to one of two groups.
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 convincing evidence that the proportion of all teens with hearing loss has increased at the α = 0.01
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 random sample of 80 sophomores and finds that 52 of them bring a bag lunch. A simple random sample of
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 make?Exercise 16.A study by the National Athletic Trainers Association surveyed random samples of 1679 high
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 make?Exercise 15.Many new products introduced into the market are targeted toward children. The choice
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 turn, rises and falls with the abundance of acorns, their favored food. Experimenters studied two
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 resprouting took place in a dry area of Mexico. The researchers randomly assigned shrubs to treatment
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 sometimes used in an
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 different age groups
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 Indiana households that had a Christmas tree last year to find out. In a random sample of 160 rural
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 102 of the men said “Yes.” A 99% confidence interval for the difference (Women – Men) in the
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 245 to receive both a patch and the antidepressant drug bupropion. After a year, 40 subjects in the
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 address this question. They took turns (in a random order) walking up to people on the main street of a
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, 233 were able to do so.a. Construct and interpret a 95% confidence interval for the difference in the
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 group.7 The survey found that 986 of the men and 923 of the women lived with their parents.a.
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 fabricator and find that 484 of the disks produced by the first machine are acceptable and 480 of the
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. Researchers applied a 0.5% emulsion of diazinon to glass and plasterboard. After 14 days, they randomly
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 newly baked crackers to the microwave and another 65 to a control group that is not microwaved. After 1
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 contaminated by industrial chemicals. During the period that residents drank water from this well, 16 of
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 is correct.b. Suppose that the difference (Graduate – Dropout) in the sample proportions who pass
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 the company’s claim is true.b. Suppose that the Child and Adult samples contain an equal proportion
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 of 75 high
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 regular unleaded gasoline. Which of these two types of fuel costs more at the pump, on average? Does the
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 beans from
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 a plum. I pull the lever five times. What are the chances that I’ll get at least one apple?”
“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 announced the poll’s margin of error for 95% confidence as ±3 percentage points. Which of the
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. The probability that the researcher will commit a Type II error for the particular alternative value
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 walking is just 2 months. A significance test is more likely to find a significant increase in mean
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. The data contain no outliers.d. The sample size is less than 10% of the population size.e. The
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 interval for μ will include the value 1.b. A 95% confidence interval for μ will include the value
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. t >3.326b. t > 3.286c. t > 2.977d. t < −3.326 or t > 3.326e. t < −3.286
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 between 0.02 and 0.04.c. Falls between 0.04 and 0.05.d. Falls between 0.05 and 0.25.e. Is greater than
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 standard deviation σ.c. z requires that the data come from a random sample.d. z requires that the
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 distribution from part (a) to find the value of p̂ with an area of 0.05 to the right of it. If the supervisor
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 perform a significance test about the mean age of all U.S. presidents. Explain why this makes no
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 significance test about the mean amount spent by all shoppers at this supermarket.
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 mean time needed for people to complete a certain maze (without music) is 40 seconds. The researcher
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, congestion, frequency of coughing, and so on. At the end of the study, those taking echinacea
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 average, the students in the regular program increase their scores by 128 points during the 3-month
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 alternative?b. What’s the probability of making a Type I error?
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 these four people have ESP? Explain your answer.b. What should the researcher now do to test
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 30 people.Exercises 86 and 88.You are thinking about opening a restaurant and are searching for a
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 alternative?b. What’s the probability of making a Type I error?
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. After the change, the principal surveys an SRS of students at the school. She would like to perform a
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 week. You suspect that the manufacturer is exaggerating the breaking strength of the chairs, so you
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 “blemishes,” the truck will be sent back to the supplier to get another load of potatoes.
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 of 250 potatoes from the shipment.Exercises 85 and 87.A company that makes potato chips requires
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 to detect that μ = $85,500 instead of μ=$86,000.c. Change the significance level to α =
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 sample of 250 potatoes instead of 500 potatoes.c. The true proportion is p = 0.10 instead of p =
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 $85,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random
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 15? Why or why not?
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 10? Why or why not?
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. adults about their daily water intake. A graph of the data shows a roughly symmetric shape with no
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 conditions for inference are met.b. Explain why the interval in part (a) is consistent with the result of
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 milliseconds (about one-fifth of a second). Researchers wonder if this claim is true, so they collect
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 interval in part (a) is consistent with the result of the test in Exercise 77.Exercise 77.A drug
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 their school differed from 15 inches, so they obtained a list of student names and selected a random
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 to control the compression process. The target value for the hardness is μ = 11.5. The hardness
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 about underfilled bottles. To investigate, a quality-control inspector takes a random sample of 40
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 that. The librarian selects a random sample of 40 pages and uses a standard readability test to assess
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 additional hours of sleep per night gained by each subject after taking the drug. A negative value
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 miles per hour, or mph) of a random sample of 10 drivers in a 25 mph construction zone. Here are the
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 statistic.b. Find and interpret the P-value.c. What conclusion would you make?Exercise 66.A machine
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 interpret the P-value.c. What conclusion would you make?Exercise 65.The Survey of Study Habits 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 = 0.74. Assume that the conditions for carrying out the test are met.a. Explain why the sample result
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 had an audit performed on a random sample of 25 invoices. The percent of purchases on each invoice
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 = 5.36. Assume that the conditions for carrying out the test are met.a. Explain why the sample result
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 tests the fully charged batteries by playing a video repeatedly until the battery dies. The
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 manager plans to conduct a significance test at the α = 0.10 significance level ofH0: μ =
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 have better attitudes toward school. She gives the SSHA to an SRS of 45 students from the more than
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 were filing claims for unemployment insurance. Some were offered $500 if they found a job within 11
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, the diameters of the plastic cases vary Normally with mean μ = 5.3 inches and standard deviation
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, 0.38)e. None of theseSelect the best answer.
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 = 0.01.c. significant at α = 0.01, but not at α = 0.05.d. significant at both α = 0.05 and 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 population of all living alumni was taken, and 64 of the alumni in the sample were in favor of firing 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. Both np0 and n(1 − p0) should be at least 10.c. If you are sampling without replacement from a
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 significance test and a 95% confidence interval based on the survey data.a. Define the parameter of
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 cheating on a quiz. Do you go to the professor?” The Minitab output shows the results of a
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, one can say with 95% confidence that the margin of (sampling) error is ±3 percentage points.”
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?” According to Pew, the resulting 95% confidence interval is (0.123, 0.177). Based on the confidence
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 personal goal. Assume that the conditions for inference are met.b. Explain why the interval in part
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 conditions for inference are met.b. Explain why the interval in part (a) provides more information than
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 of an SRS of 200 of its first-year students say that this goal is important. Is there convincing
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 of them passed the test on their first try. Is there convincing evidence at the α = 0.05
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 the New Scientist, two Polish math professors and their students spun a Belgian euro coin 250 times.
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 wrinkled. Mendel predicted a ratio of 3 smooth peas for every 1 wrinkled pea. In one experiment, he
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 the proposition. Explain why it isn’t necessary to carry out a significance test in this setting.
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 cell-phone password. Of the 1060 parents surveyed, 551 reported that they knew the password. Explain why it
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 give the new drug to a random sample of 300 out of 5000 Alzheimer’s patients whose families have
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. After the change, the principal surveys an SRS of 200 from the more than 2500 students at the school.
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 company wants to see if spraying the seeds with a chemical that is known to increase germination
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 the α = 0.10 significance level? Would your conclusion change if you used α = 0.05 instead?
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 interpret the P-value.b. What conclusion would you make at the α = 0.01 significance level? Would your
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 students. When asked to describe their behavior in the last 30 days, 445 students admitted that they
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 make?Exercise 35.Jason reads a report that says 80% of U.S. high school students have a computer at home. He
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 make?Exercise 36.A recent report claimed that 13% of students typically walk to school. DeAnna thinks that
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 months. The college’s athletic director wants to perform a test of H0: p = 2/3 versus Ha: p >
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 p = the proportion of all tosses of the coin that would land “heads.” Check if the conditions

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The Practice Of Statistics 6th Edition Daren S. Starnes, Josh Tabor - Solutions

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