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inferential statistics
Intro Stats 6th Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions
Enough eggs? One of the important issues for poultry farmers is the production rate—the percentage of days on which a given hen actually lays an egg. Ideally, that would be 100% (an egg every day), but realistically, hens tend to lay eggs on about 3 of every 4 days. ISA Babcock wants to advertise
Polling disclaimer A newspaper article that reported the results of an election poll included the following explanation:The Associated Press poll on the 2016 presidential campaign is based on telephone interviews with 798 randomly selected registered voters from all states except Alaska and
Living at home According to the U.S. American Community Survey (ACS), by 2014, for the first time in the history of the ACS, more U.S. 18- to 34-year-olds reported living with a parent than were living independently in their own homes.The survey found that 32.1% were living with parents vs.31.6%
Jerseys A statistics professor came home to find that all four of his children got white team shirts from soccer camp this year. He concluded that this year, unlike other years, the camp must not be using a variety of colors. But then he finds out that in each child’s age group there are 4 teams,
Who’s the boss? The 2016 State of Women-Owned Businesses Report commissioned by American Express(www.womenable.com/70/the-state-of-women-ownedbusinesses-in-the-u.s.:-2016) says that, excluding large, publicly traded firms, women-owned firms make up 38%of the privately held firm population, a
Gay marriage 2016 In March 2016, Pew Research asked a random sample of 2254 U.S. adults, “Do you strongly favor, favor, oppose, or strongly oppose allowing gays and lesbians to marry legally?”
Teen smoking The Centers for Disease Control and Prevention say that about 18% of high school students smoke tobacco (down from a high of 38% in 1997). Suppose you randomly select high school students to survey them on their attitudes toward scenes of smoking in the movies.What’s the probability
Stocks Since the stock market began in 1872, stock prices have risen in about 73% of the years. Assuming that market performance is independent from year to year, what’s the probability thata) the market will rise for 3 consecutive years?b) the market will rise 3 years out of the next 5?c) the
Bimodal We are sampling randomly from a distribution known to be bimodal.a) As our sample size increases, what’s the expected shape of the sample’s distribution?b) What’s the expected value of our sample’s mean? Does the size of the sample matter?c) How is the variability of sample means
Passing stats Molly’s college offers two sections of Statistics 101. From what she has heard about the two professors listed, Molly estimates that her chances of passing the course are 0.80 if she gets Professor Scedastic and 0.60 if she gets Professor Kurtosis. The registrar uses a lottery to
Scrabble Using a computer to play many simulated games of Scrabble, researcher Charles Robinove found that the letter “A” occurred in 54% of the hands. This study had a margin of error of {10%. (Chance, 15, no. 1 [2002])a) Explain what the margin of error means in this context.b) Why might the
Fake news In a survey of 1002 U.S. adults in December 2016 by Pew Research (www.journalism.org/2016/12/15/many-americans-believe-fake-news-is-sowing-confusion/), 64% of adult respondents say they think that made-up “news”is causing a great deal of confusion about the basic facts of current
Polling 2016 The 2016 U.S. presidential election was unusual in several ways. First, the candidate who won the most electoral votes, Donald Trump, did not win the most popular votes. Second, several minor-party candidates received enough votes to possibly affect the outcome. The official results
More twins A group of 5 women became pregnant while undergoing fertility treatments with the drug Clomid, discussed in Exercise 4. What’s the probability thata) none will have twins?b) exactly 1 will have twins?c) at least 3 will have twins?
Hamsters How large are hamster litters? Among 47 golden hamster litters recorded, there were an average of 7.72 baby hamsters, with a standard deviation of 2.5 hamsters per litter.a) Create and interpret a 90% confidence interval.b) Would a 98% confidence interval have a larger or smaller margin of
Color-blind Medical literature says that about 8% of males are color-blind. A university’s introductory psychology course is taught in a large lecture hall. Among the students, there are 325 males. Each semester when the professor discusses visual perception, he shows the class a test for color
Archery A champion archer can generally hit the bull’s-eye 80% of the time. Suppose she shoots 200 arrows during competition. Let pn represent the percentage of bull’s-eyes she gets (the sample proportion).a) What are the mean and standard deviation of the sampling distribution model for pn?b)
Babies The National Perinatal Statistics Unit of the Sydney Children’s Hospital reports that the mean birth weight of all babies born in birth centers in Australia in a recent year was 3564 grams—about 7.86 pounds. A Missouri hospital reports that the average weight of 112 babies born there
Socks In your sock drawer you have 4 blue socks, 5 gray socks, and 3 black ones. Half asleep one morning, you grab 2 socks at random and put them on. Find the probability you end up wearinga) 2 blue socks.b) no gray socks.c) at least 1 black sock.d) a green sock.e) matching socks.
Leaky gas tanks According to the website RightingInjustice.com, about 77% of all underground storage tanks, or USTs, have “confirmed releases” or leaks. Researchers in California want to know if the percentage is lower in their state. To do this, they randomly sample 47 service stations in
Twins In the United States, the probability of having twins(usually about 1 in 90 births) rises to about 1 in 10 for women who have been taking the fertility drug Clomid. Among a group of 10 pregnant women, what’s the probability thata) at least one will have twins if none were taking a fertility
Emergency switch Safety engineers must determine whether industrial workers can operate a machine’s emergency shutoff device. Among a group of test subjects, 66%were successful with their left hands, 82% with their right hands, and 51% with both hands.a) What percent of these workers could not
Workers A company’s human resources officer reports a breakdown of employees by job type and sex shown in the table.a) What’s the probability that a worker selected at random is i) female?ii) female or a production worker?iii) female, if the person works in production?iv) a production worker,
Quality control A consumer organization estimates that 29% of new cars have a cosmetic defect, such as a scratch or a dent, when they are delivered to car dealers. This same organization believes that 7% have a functional defect—something that does not work properly—and that 2% of new cars have
Farmed salmon bootstrap In Chapter 14 we saw data from samples of farmed salmon and examined the mirex content.The EPA sets a limit of 0.08 ppm as a maximum safe value. We performed a bootstrap on these data, drawing 10,000 resamples.Here is the resulting histogram of bootstrapped mean mirex
Chips Ahoy! bootstrapped Exercise 53 of Chapter 15 asked for a Student’s t-based test of the hypothesis that every bag of Chips Ahoy! cookies had at least 1000 chips. Here is a histogram of 10,000 bootstrapped means based on the sample of packages in the data file.
Pottery An artist experimenting with clay to create pottery with a special texture has been experiencing difficulty with these special pieces. About 40% break in the kiln during firing. Hoping to solve this problem, she buys some more expensive clay from another supplier. She plans to make and fire
Hoops A basketball player with a poor foul-shot record practices intensively during the off-season. He tells the coach that he has raised his proficiency from 60% to 80%. Dubious, the coach asks him to take 10 shots, and is surprised when the player hits 9 out of 10. Did the player prove that he
Faulty or not? You are in charge of shipping computers to customers. You learn that a faulty chip was put into some of the machines. There’s a simple test you can perform, but it’s not perfect. All but 4% of the time, a good chip passes the test, but unfortunately, 35% of the bad chips pass the
Two coins In a drawer are two coins. They look the same, but one coin produces heads 90% of the time when spun while the other one produces heads only 30% of the time. You select one of the coins. You are allowed to spin it once and then must decide whether the coin is the 90%- or the 30%-head
Catheters, again The catheter company in Exercise 40 is reviewing its testing procedure.a) Suppose the significance level is changed to a = 0.01.Will the probability of a Type II error increase, decrease, or remain the same?b) What is meant by the power of the test the company conducts?c) Suppose
TV safety, revisited The manufacturer of the metal TV stands in Exercise 39 is thinking of revising its safety test.a) If the company’s lawyers are worried about being sued for selling an unsafe product, should they increase or decrease the value of a? Explain.b) In this context, what is meant by
Catheters During an angiogram, heart problems can be examined via a small tube (a catheter) threaded into the heart from a vein in the patient’s leg. It’s important that the company that manufactures the catheter maintain a diameter of 2.00 mm.(The standard deviation is quite small.) Each day,
TV safety The manufacturer of a metal stand for home TV sets must be sure that its product will not fail under the weight of the TV. Since some larger sets weigh nearly 300 pounds, the company’s safety inspectors have set a standard of ensuring that the stands can support an average of over 500
Testing the ads The company in Exercise 36 contacts 600 people selected at random, and only 133 remember the ad.a) Should the company renew the contract? Support your recommendation with an appropriate test.b) Explain what your P-value means in this context.
Software, part II 203 students signed up for the Stats course in Exercise 35. They used the suggested software, and scored an average of 108 points on the final with a standard deviation of 8.7 points.a) Should the professor spend the money for this software?Support your recommendation with an
Ads A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 20% of the residents of the city have heard the ad and recognize the company’s product. The radio station conducts a random phone survey of 400 people.a) What are the
Software for learning A statistics professor has observed that for several years students score an average of 105 points out of 150 on the semester exam. A salesman suggests that she try a statistics software package that gets students more involved with computers, predicting that it will increase
Stop signs Highway safety engineers test new road signs, hoping that increased reflectivity will make them more visible to drivers. Volunteers drive through a test course with several of the new- and old-style signs and rate which kind shows up the best.a) Is this a one-tailed or a two-tailed test?
Equal opportunity? A company is sued for job discrimination because only 19% of the newly hired candidates were minorities when 27% of all applicants were minorities. Is this strong evidence that the company’s hiring practices are discriminatory?a) Is this a one-tailed or a two-tailed test?
Production Consider again the task of the quality control inspectors in Exercise 30.a) In this context, what is meant by the power of the test the inspectors conduct?b) They are currently testing 5 items each hour. Someone has proposed that they test 10 instead. What are the advantages and
Cars, again As in Exercise 29, state regulators are checking up on repair shops to see if they are certifying vehicles that do not meet pollution standards.a) In this context, what is meant by the power of the test the regulators are conducting?b) Will the power be greater if they test 20 or 40
Quality control Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items produced. If they find a significant increase in the proportion of items that must be rejected, they
Testing cars A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair
Alzheimer’s Testing for Alzheimer’s disease can be a long and expensive process, consisting of lengthy tests and medical diagnosis. A group of researchers (Solomon et al., 1998) devised a 7-minute test to serve as a quick screen for the disease for use in the general population of senior
Homeowners 2019 In 2019, the U.S. Census Bureau reported that 65.1% of American families owned their homes—up slightly from the 20-year low of 63.8% in 2016. Census data reveal that the ownership rate in one small city is much lower. The city council is debating a plan to offer tax breaks to
More spam Consider again the points-based spam filter described in Exercise 24. When the points assigned to various components of an e-mail exceed the cutoff value you’ve set, the filter rejects its null hypothesis (that the message is real) and diverts that e-mail to a junk mailbox.a) In this
Second loan Exercise 23 describes the loan score method a bank uses to decide which applicants it will lend money. Only if the total points awarded for various aspects of an applicant’s financial condition fail to add up to a minimum cutoff score set by the bank will the loan be denied.a) In this
Spam Spam filters try to sort your e-mails, deciding which are real messages and which are unwanted. One method used is a point system. The filter reads each incoming e-mail and assigns points to the sender, the subject, key words in the message, and so on. The higher the point total, the more
Loans Before lending someone money, banks must decide whether they believe the applicant will repay the loan. One strategy used is a point system. Loan officers assess information about the applicant, totaling points they award for the person’s income level, credit history, current debt burden,
Fans A survey of 81 randomly selected people standing in line to enter a football game found that 73 of them were home team fans.a) Explain why we cannot use this information to construct a confidence interval for the proportion of all people at the game who are fans of the home team.*b) Would a
Dogs Canine hip dysplasia is a degenerative disease that causes pain in many dogs. Sometimes advanced warning signs appear in puppies as young as 6 months. A veterinarian checked 42 puppies whose owners brought them to a vaccination clinic, and she found 5 with early hip dysplasia. She considers
Hard times In June 2010, a random poll of 800 working men found that 9% had taken on a second job to help pay the bills.(www.careerbuilder.com)a) Estimate the true percentage of men that are taking on second jobs by constructing a 95% confidence interval.b) A pundit on a TV news show claimed that
Approval 2016 In January 2016, at the end of his time in office, President Obama’s approval rating stood at 57% in Gallup’s daily tracking poll of 1500 randomly surveyed U.S. adults. (www.gallup.com/poll/113980/gallup-daily-obama-job-approval.aspx)a) Make a 95% confidence interval for his
Is the Euro fair? Soon after the Euro was introduced as currency in Europe, it was widely reported that someone had spun a Euro coin 250 times and gotten heads 140 times. We wish to test a hypothesis about the fairness of spinning the coin.a) Estimate the true proportion of heads. Use a 95%
Groceries Yahoo surveyed 2400 U.S. men. 1224 of the men identified themselves as the primary grocery shopper in their household.a) Estimate the percentage of all American males who identify themselves as the primary grocery shopper. Use a 98% confidence interval. Check the conditions first.b) A
Alpha, again Environmentalists concerned about the impact of high-frequency radio transmissions on birds found that there was no evidence of a higher mortality rate among hatchlings in nests near cell towers. They based this conclusion on a test using a = 0.05. Would they have made the same
Alpha A researcher developing scanners to search for hidden weapons at airports has concluded that a new device is significantly better than the current scanner. He made this decision based on a test using a = 0.05. Would he have made the same decision at a = 0.10? How about a = 0.01?Explain.
Another P-value Have harsher penalties and ad campaigns increased seat-belt use among drivers and passengers? Observations of commuter traffic failed to find evidence of a significant change compared with three years ago. Explain what the study’s P-value of 0.17 means in this context.
P-value A medical researcher tested a new treatment for poison ivy against the traditional ointment. He concluded that the new treatment is more effective. Explain what the P-value of 0.047 means in this context.
More errors For each of the following situations, state whether a Type I, a Type II, or neither error has been made.a) A test of H0: m = 25 vs. HA: m 7 25 rejects the null hypothesis. Later it is discovered that m = 24.9.b) A test of H0: p = 0.8 vs. HA: p 6 0.8 fails to reject the null hypothesis.
Errors For each of the following situations, state whether a Type I, a Type II, or neither error has been made. Explain briefly.a) A bank wants to know if the enrollment on their website is above 30% based on a small sample of customers.
Significant again? A new reading program may reduce the number of elementary school students who read below grade level. The company that developed this program supplied materials and teacher training for a large-scale test involving nearly 8500 children in several different school districts.
Significant? Public health officials believe that 98% of children have been vaccinated against measles. A random survey of medical records at many schools across the country found that, among more than 13,000 children, only 97.4% had been vaccinated. A statistician would reject the 98% hypothesis
More critical values For each of the following situations, find the critical value for z or t.a) H0: m = 105 vs. HA: m ≠ 105 at a = 0.05; n = 61.b) H0: p = 0.05 vs. HA: p 7 0.05 at a = 0.05.c) H0: p = 0.6 vs. HA: p ≠ 0.6 at a = 0.01.d) H0: p = 0.5 vs. HA: p 6 0.5 at a = 0.01; n = 500.e) H0: p =
Critical values For each of the following situations, find the critical value(s) for z or t.a) H0: p = 0.5 vs. HA: p ≠ 0.5 at a = 0.05.b) H0: p = 0.4 vs. HA: p 7 0.4 at a = 0.05.c) H0: m = 10 vs. HA: m ≠ 10 at a = 0.05; n = 36.d) H0: p = 0.5 vs. HA: p 7 0.5 at a = 0.01; n = 345.e) H0: m = 20
Alpha false and true Which of the following statements are true? If false, explain briefly.a) It is better to use an alpha level of 0.05 than an alpha level of 0.01.b) If we use an alpha level of 0.01, then a P-value of 0.001 is statistically significant.c) If we use an alpha level of 0.01, then we
Alpha true and false Which of the following statements are true? If false, explain briefly.a) Using an alpha level of 0.05, a P-value of 0.04 results in rejecting the null hypothesis.b) The alpha level depends on the sample size.c) With an alpha level of 0.01, a P-value of 0.10 results in rejecting
More P-values Which of the following are true? If false, explain briefly.a) A very low P-value provides evidence against the null hypothesis.b) A high P-value is strong evidence in favor of the null hypothesis.c) A P-value above 0.10 shows that the null hypothesis is true.d) If the null hypothesis
P-values Which of the following are true? If false, explain briefly.a) A very high P-value is strong evidence that the null hypothesis is false.b) A very low P-value proves that the null hypothesis is false.c) A high P-value shows that the null hypothesis is true.d) A P-value below 0.05 is always
False or true Which of the following are true? If false, explain briefly.a) If the null hypothesis is true, you’ll get a high P-value.b) If the null hypothesis is true, a P-value of 0.01 will occur about 1% of the time.c) A P-value of 0.90 means that the null hypothesis has a good chance of being
True or false Which of the following are true? If false, explain briefly.a) A P-value of 0.01 means that the null hypothesis is false.b) A P-value of 0.01 means that the null hypothesis has a 0.01 chance of being true.c) A P-value of 0.01 is evidence against the null hypothesis.d) A P-value of 0.01
Exam time The instructor of a large math class estimates that at the intended level of difficulty, his undergraduate midterm exams require on average 10 minutes for graduate students in his department to complete. If the average is longer than 10 minutes, then the exam is likely too hard and needs
Cookie sales A company that sells cookies decided to redesign their packaging with brighter colors with the hope of improving sales. They chose a random sample of 50 stores to pilot the new packaging, which holds the same amount of product at the same price point as before. Over the period of a
BMI According to the Centers for Disease Control (CDC)body mass index (BMI) of more than 24.9 is considered “over weight.” BMI is calculated by the formula:BMI = 703 * Weight (lb)>Height2 (in.)Using the data in Bodyfat, calculate the BMI of the 250 men in the dataset.a) Find the mean BMI of the
Cholesterol According to the National Institutes of Health(NIH), adults should have a total cholesterol level of below 240 mg/dL. The dataset Framingham contains the total cholesterol levels of 1406 participants in the Framingham Heart Study.a) Find the mean total cholesterol of these
Facebook friends again A bootstrap test of the hypothesis in Exercise 56 produced the following distribution (shifted to center the histogram at the hypothesized mean of 649): (Data in Student Survey)
Maze revisited A student resampled the Maze times from Exercise 55 1000 times. The histogram shows the distributions of the means, and a summary of the quantiles is shown below it.
Facebook friends According to www.marketingcharts.com/, the average 18–24-year-old has 649 Facebook friends. The student who collected the survey data in Student survey wanted to test if the mean number is higher at his school. Using his data, test an appropriate hypothesis and write a couple of
Maze Here are the data from the researcher studying the reaction times of rats from Chapter 14, Exercise 61. Recall that he has a requirement that the maze take about a minute to complete on average.
More yogurt As we saw in Chapter 14, Exercise 60, Consumer Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving:130 160 150 120 120 110 170 160 110 130 90a) Check the assumptions and conditions.b) A diet guide claims that you will get an average of 120 calories
Chips Ahoy! again As we learned in Chapter 14, Exercise 59, in 1998, as an advertising campaign, the Nabisco Company announced a “1000 Chips Challenge,” claiming that every 18-ounce bag of their Chips Ahoy! cookies contained at least 1000 chocolate chips. Dedicated statistics students at the
More ski wax From Chapter 14, Exercise 58, Bjork Larsen was trying to decide whether to use a new racing wax for crosscountry skis. He decided that the wax would be worth the price if he could average less than 55 seconds on a course he knew well, so he planned to study the wax by racing on the
More popcorn In Chapter 14, Exercise 57 we saw that Yvon Hopps ran an experiment to determine optimum power and time settings for microwave popcorn. His goal was to find a combination of power and time that would deliver high-quality popcorn with less than 10% of the kernels left unpopped, on
More Doritos We saw in Chapter 14, Exercise 56 that some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5.a) Do these data satisfy the
More Ruffles Recall from Chapter 14, Exercise 55 that students investigated the packaging of potato chips. They purchased 6 bags of Lay’s Ruffles marked with a net weight of 28.3 grams.They carefully weighed the contents of each bag, recording the following weights (in grams): 29.3, 28.2, 29.1,
Computer lab fees again The technology committee of Chapter 14, Exercise 42 wants to perform a test to see if the mean amount of time students are spending in the lab has increased from 55 minutes. Here are the data from a random sample of 12 students.
More pizza The researcher from Chapter 14, Exercise 39 tests whether the mean cholesterol level among those who eat frozen pizza exceeds the value considered to indicate a health risk. She gets a P-value of 0.07. Explain in this context what the “7%”represents.
Hot dogs again The nutrition lab in Chapter 14, Exercise 38 tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for “reduced sodium” franks. The mean sodium content for the sample was 322.0 mg with a standard deviation of 18 mg. Assume
Normal temperature again From the measurements of body temperature in Chapter 14, Exercise 29, you created a confidence interval for the true mean body temperature of healthy adults.a) 98.6°F is commonly assumed to be “normal.” Set up the null and alternative hypotheses for testing this.b)
Cat naps Cats typically spend 62.5% of their time sleeping.Suppose your friend noted that over 45 randomly selected days, their cat slept an average of 18 hours a day.a) Check the assumptions and conditions.b) Is this evidence that their cat sleeps more than typical cats?
Double-yolked eggs It is estimated that 1 in 1000 eggs have two yolks. A farm claims that their premium eggs have better odds. A restaurant that sources eggs from this farm discovers that over the course of a year, 50 out of 45,000 eggs were double-yolked.a) Check the assumptions and conditions.b)
John Wayne Like a lot of other Americans, John Wayne died of cancer. But is there more to this story? In 1955, Wayne was in Utah shooting the film The Conqueror. Across the state line, in Nevada, the United States military was testing atomic bombs. Radioactive fallout from those tests drifted
Lost luggage An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 90% is recovered and delivered to its owner within 24 hours. A consumer group that surveyed a large number of air
Acid rain A study of the effects of acid rain on trees in the Hopkins Forest shows that 25 of 100 trees sampled exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the
Dropouts 2020 The National Center for Education Statistics reported that the high school dropout rate for the year 2020 was 5.3%. One school district whose dropout rate has always been very close to the national average reports that 130 of their 1782 high school students dropped out last year. Is
Jury Census data for a certain county show that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty and only 9 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain
Women executives A company is criticized because only 13 of 43 people in executive-level positions are women. The company explains that although this proportion is lower than it might wish, it’s not a surprising value given that only 40%of all its employees are women. What do you think? Test an
Seeds A garden center wants to store leftover packets of vegetable seeds for sale the following spring, but the center is concerned that the seeds may not germinate at the same rate a year later. The manager finds a packet of last year’s green bean seeds and plants them as a test. Although the
WebZine A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it’s convinced that more than 25% of current readers would subscribe. The magazine contacted a simple random sample of 500 current subscribers, and 137 of those surveyed expressed interest.
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