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inferential statistics
Intro Stats 6th Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions
Football 2016 During the first 15 weeks of the 2016 season, the home team won 137 of the 238 regular-season National Football League games. Is this strong evidence of a home field advantage in professional football? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate
Twins A national vital statistics report indicated that about 3%of all births produced twins. Is the rate of twin births the same among very young mothers? Data from a large city hospital found that only 7 sets of twins were born to 469 teenage girls.Test an appropriate hypothesis and state your
Scratch and dent An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the damage may be minor, the company must sell those machines at drastically reduced prices. The company
Pollution A company with a fleet of 150 cars found that the emissions systems of 7 out of the 22 they tested failed to meet pollution control guidelines. Is this strong evidence that more than 20% of the fleet might be out of compliance? Test an appropriate hypothesis and state your conclusion. Be
Take the offer II We saw in Chapter 13, Exercise 36 that First USA tested the effectiveness of a double miles campaign by recently sending out offers to a random sample of 50,000 cardholders. Of those, 1184 registered for the promotion. Even though this is nearly a 2.4% rate, a staff member
Contributions, please II We learned in Chapter 13, Exercise 35 that the Paralyzed Veterans of America recently sent letters to a random sample of 100,000 potential donors and received 4781 donations. They’ve had a contribution rate of 5% in past campaigns, but a staff member worries that the rate
Educated mothers The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996, 31% of students reported that their mothers had graduated from college. In 2000,
Absentees The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996, 34% of students had not been absent from school even once during the previous month. In a 2000
Abnormalities In the 1980s, it was generally believed that congenital abnormalities affected about 5% of the nation’s children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384
Dowsing In a rural area, only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by “dowsing”—using a forked stick to indicate where the well should be drilled. You check with 80 of his customers and find
Obesity 2018 In 2018, the Centers for Disease Control and Prevention reported that 42.4% of adults in the United States are obese. A county health service planning a new awareness campaign polls a random sample of 750 adults living there. In this sample, 228 people were found to be obese based on
Smartphones Many people have trouble setting up all the features of their smartphones, so a company has developed what it hopes will be easier instructions. The goal is to have at least 96%of customers succeed. The company tests the new system on 200 people, of whom 188 were successful. Is this
Candy Someone hands you a box of a dozen chocolate-covered candies, telling you that half are vanilla creams and the other half peanut butter. You pick candies at random and discover the first three you eat are all vanilla.a) If there really were 6 vanilla and 6 peanut butter candies in the box,
He cheats? A friend of yours claims that when he tosses a coin he can control the outcome. You are skeptical and want him to prove it. He tosses the coin, and you call heads; it’s tails.You try again and lose again.a) Do two losses in a row convince you that he really can control the toss?
Cars A survey investigating whether the proportion of today’s high school seniors who own their own cars is higher than it was a decade ago finds a P-value of 0.017. Is it reasonable to conclude that more high schoolers have cars? Explain.
Relief A company’s old antacid formula provided relief for 70% of the people who used it. The company tests a new formula to see if it is better and gets a P-value of 0.27. Is it reasonable to conclude that the new formula and the old one are equally effective? Explain.
Dice The seller of a loaded die claims that it will favor the outcome 6. We don’t believe that claim, and roll the die 200 times to test an appropriate hypothesis. Our P-value turns out to be 0.03. Which conclusion is appropriate? Explain.a) There’s a 3% chance that the die is fair.b) There’s
Negatives After the political ad campaign described in Exercise 15, parta, pollsters check the governor’s negatives. They test the hypothesis that the ads produced no change against the alternative that the negatives are now below 30% and find a P-value of 0.22.Which conclusion is appropriate?
More hypotheses Write the null and alternative hypotheses you would use to test each situation.a) In the 1950s, only about 40% of high school graduates went on to college. Has the percentage changed?b) Twenty percent of cars of a certain model have needed costly transmission work after being driven
Hypotheses Write the null and alternative hypotheses you would use to test each of the following situations:a) A governor is concerned about his “negatives”—the percentage of state residents who express disapproval of his job performance. His political committee pays for a series of TV ads,
Expensive medicine Developing a new drug can be an expensive process, resulting in high costs to patients. A pharmaceutical company has developed a new drug to reduce cholesterol, and it will conduct a clinical trial to compare the effectiveness to the most widely used current treatment. The
Bad medicine Occasionally, a report comes out that a drug that cures some disease turns out to have a nasty side effect. For example, some antidepressant drugs may cause suicidal thoughts in younger patients. A researcher wants to study such a drug and look for evidence of a side effect.a) If the
Golf balls The United States Golf Association (USGA) sets performance standards for golf balls. For example, the initial velocity of the ball may not exceed 250 feet per second when measured by an apparatus approved by the USGA. Suppose a manufacturer introduces a new kind of ball and provides a
Pizza A researcher 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.
Marriage In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years. It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased since then.a) Write appropriate
GRE performance again Instead of advertising the percentage of customers who improve by at least 10 points, a manager suggests testing whether the mean score improves at all. For each customer they record the difference in score before and after taking the course (After - Before).a) State the null
Empty houses According to the 2010 Census, 11.4% of all housing units in the United States were vacant. A county supervisor wonders if her county is different from this. She randomly selects 850 housing units in her county and finds that 129 of the housing units are vacant.a) State the
Hispanic origin According to the Census Bureau, 18.1% of the people in the United States are of Hispanic or Latino origin.One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent survey data, which was a
GRE performance A test preparation company claims that more than 50% of the students who take their GRE prep course improve their scores by at least 10 points.a) Is the alternative to the null hypothesis more naturally one-sided or two-sided? Explain.b) A test run with randomly selected
Better than aspirin again? Referring to the study of Exercise 1:a) Is the alternative to the null hypothesis more naturally onesided or two-sided? Explain.b) The P-value from a clinical trial testing the hypothesis is 0.0028. What do you conclude?c) What would you have concluded if the P-value had
Hypotheses and parameters As in Exercise 3, for each of the following situations, define the parameter and write the null and alternative hypotheses in terms of parameter values.
Parameters and hypotheses For each of the following situations, define the parameter (proportion or mean) and write the null and alternative hypotheses in terms of parameter values.Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = the proportion of up
Psychic A friend of yours claims to be psychic. You are skeptical. To test this you take a stack of 100 playing cards and have your friend try to identify the suit (hearts, diamonds, clubs, or spades), without looking, of course! State the null hypothesis for your experiment.
Better than aspirin? A very large study showed that aspirin reduced the rate of first heart attacks by 44%. A pharmaceutical company thinks they have a drug that will be more effective than aspirin, and plans to do a randomized clinical trial to test the new drug. What is the null hypothesis the
Wind power Should you generate electricity with your own personal wind turbine? That depends on whether you have enough wind on your site. To produce enough energy, your site should have an annual average wind speed above 8 miles per hour, according to the Wind Energy Association. One candidate
Golf drives 2019 The Professional Golfers Association reported the average distance that 199 professional golfers drove the ball (in yd) during a week in 2019. Here is a histogram of those drives. Assume this is a representative sample of all professional golfers.
Stopping distance 60 A tire manufacturer is considering a newly designed tread pattern for its all-weather tires. Tests have indicated that these tires will provide better gas mileage and longer tread life. The last remaining test is for braking effectiveness. The company hopes the tire will allow
Maze Psychology experiments sometimes involve testing the ability of rats to navigate mazes. The mazes are classified according to difficulty, as measured by the mean length of time it takes rats to find the food at the end. One researcher needs a maze that will take rats an average of about one
Yogurt 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) Create a 95% confidence interval for the average calorie content of vanilla yogurt.c) A diet guide claims
Chips Ahoy! 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 Air Force Academy (no kidding) purchased some
Ski wax Bjork Larsen was trying to decide whether to use a new racing wax for cross-country 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 course 8 times. His 8 race times were
Popcorn 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 average. After experimenting with several bags,
Doritos 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 assumptions for inference?Explain.b) Find the mean and
Ruffles Students investigating the packaging of potato chips 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, 28.7, 28.9, 28.5.a) Do these data satisfy the
At work Some business analysts estimate that the length of time people work at a job has a mean of 6.2 years and a standard deviation of 4.5 years.a) Explain why you suspect this distribution may be skewed to the right.b) Explain why you could estimate the probability that 100 people selected at
Pregnant again The duration of human pregnancies may not actually follow the Normal model described in Exercise 51.a) Explain why it may be somewhat skewed to the left.b) If the correct model is in fact skewed, does that change your answers to partsa, b, and c of Exercise 51? Explain why or why not
Rainfall Statistics from Cornell’s Northeast Regional Climate Center indicate that Ithaca, New York, gets an average of 35.4"of rain each year, with a standard deviation of 4.2". Assume that a Normal model applies.a) During what percentage of years does Ithaca get more than 40" of rain?b) Less
Pregnancy Assume that the duration of human pregnancies can be described by a Normal model with mean 266 days and standard deviation 16 days.a) What percentage of pregnancies should last between 270 and 280 days?b) At least how many days should the longest 25% of all pregnancies last?c) Suppose a
Safe cities Allstate Insurance Company identified the 10 safest and 10 least-safe U.S. cities from among the 200 largest cities in the United States, based on the mean number of years drivers went between automobile accidents. The cities on both safety lists were all smaller than the 10 largest
Lucky spot? A reporter working on a story about the New York lottery contacted one of the authors of this book, wanting help analyzing data to see if some ticket sales outlets were more likely to produce winners. His data for each of the 966 New York lottery outlets are graphed below; the
Home values Assessment records indicate that the value of homes in a small city is skewed right, with a mean of $140,000 assessment data, officials plan to conduct a detailed appraisal of 100 homes selected at random. Using the 68–95–99.7 Rule, draw and label an appropriate sampling model for
GPAs A college’s data about the incoming first years indicate that the mean of their high school GPAs was 3.4, with a standard deviation of 0.35; the distribution was roughly mound-shaped and only slightly skewed. The students are randomly assigned to first-year writing seminars in groups of 25.
CEOs, revisited In Exercise 44, you looked at the annual compensation for 800 CEOs, for which the true mean and standard deviation were (in thousands of dollars) 10,307.31 and 17,964.62, respectively. A simulation drew samples of sizes 30, 50, 100, and 200 (with replacement) from the total annual
Waist size, revisited Researchers measured the waist sizes of 250 men in a study on body fat. The true mean and standard deviation of Waist for the 250 men are 36.33 inches and 4.019 inches, respectively. In Exercise 43, you looked at the histograms of simulations that drew samples of sizes 2, 5,
CEO compensation The total compensation of the chief executive officers (CEOs) of the 800 largest U.S. companies(the Fortune 800) averaged (in thousands of dollars) 10,307.31 with a standard deviation (also in $1000) of 17,964.62. Here is a histogram of their annual compensations (in $1000):a)
Waist size A study measured the Waist size of 250 men, finding a mean of 36.33 inches and a standard deviation of 4.02 inches. Here is a histogram of these measurements:(Data in Bodyfat)
Socializing, relaxing, and leisure. A random sample of 100 American Time Use Survey (ATUS) respondents spent an average of 310.8 minutes in a day on socializing, relaxing, and leisure (which we’ll call leisure time), with standard deviation of 209.5 minutes. Below is a histogram of their
Caring for household members. The American Time Use Survey (ATUS) is an annual survey of Americans over the age of 15 conducted by the Bureau of Labor Statistics (http://www.bls.gov)to better understand how Americans spend their time over the course of a 24-hour period. A random sample of 100
Golf balls The United States Golf Association (USGA) sets performance standards for golf balls. For example, the mean initial velocity of the ball may not exceed 250 feet per second when measured by an apparatus approved by the USGA. Suppose a manufacturer introduces a new kind of ball and provides
Pizza A researcher investigates whether the mean cholesterol level among those who eat frozen pizza exceeds 220 mg/dL, the value considered to indicate a health risk. The confidence interval for the mean is (225.5, 240.8) mg/dL. Explain what this indicates for the health risk.
Hot dogs A nutrition lab 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. A 90% confidence interval estimated the mean sodium content for this kind of hot dog at 317.2 to 326.8 mg. Given this, what would
Farmed salmon, second look This chapter’s Examples 14.1 and 14.2 looked at mirex contamination in farmed salmon. We first found a 95% confidence interval for the mean concentration to be 0.0834 to 0.0992 parts per million (ppm). The EPA sets a limit of 0.08 ppm to be considered safe. What does
Flights on time 2019 revisited Will your flight get you to your destination on time? The Bureau of Transportation Statistics reported the percentage of flights that were delayed each month from 1994 through September of 2019. Here’s a histogram, along with some summary statistics:
Flights on time 2019 What are the chances your flight will leave on time? The Bureau of Transportation Statistics of the U.S. Department of Transportation publishes information about airline performance. We saw the data in a Just Checking exercise in Chapter 4. Here are a histogram and summary
Michelson After his first attempt to determine the speed of light (described in Exercise 33), Michelson conducted an “improved” experiment. In 1897, he reported results of 100 trials with a mean of 852.4 and a standard deviation of 79.0.a) What is the standard error of the mean for these
Speed of light In 1882, Michelson measured the speed of light(usually denoted c as in Einstein’s famous equation E = mc2).His values are in km/sec and have 299,000 subtracted from them. He reported the results of 23 trials with a mean of 756.22 and a standard deviation of 107.12.a) Find a 95%
Parking II Suppose that, for budget planning purposes, the city in Exercise 30 needs a better estimate of the mean daily income from parking fees.a) Someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first created. How would this interval be
Normal temperature, part II Consider again the statistics about human body temperature in Exercise 29.a) Would a 90% confidence interval be wider or narrower than the 98% confidence interval you calculated before? Explain.(Don’t compute the new interval.)b) What are the advantages and
Parking Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district.The city plans to pay for the structure through parking fees.During a two-month period (44 weekdays), daily fees collected averaged $126, with a standard deviation of $15.a)
Normal temperature The researcher described in Exercise 23 also measured the body temperatures of that randomly selected group of adults. Here are summaries of the data he collected.We wish to estimate the average (or “normal”) temperature among the adult population.
Pulse rates In a recent National Health and Nutrition Examination Survey (NHANES 2013/2014—wwwn.cdc.gov/nchs/nhanes), pulse rate (30 sec rate multiplied by 2) of 2536 U.S.adults averaged 71.6 beats/min with a standard deviation of 11.5 beats/min. (Data in NHANES)a) Can you apply the Central Limit
Cholesterol In a recent National Health and Nutrition Examination Survey (NHANES 2013/2014–wwwn.cdc.gov/nchs/nhanes), total cholesterol of 2515 U.S. adults averaged 188.9 mg/dL with a standard deviation of 41.6 mg/dL. (Data in NHANES)a) Can you apply the Central Limit Theorem to describe the
Credit card charges A credit card company takes a random sample of 100 cardholders to see how much they charged on their card last month. Here’s a histogram.A computer program found that the resulting 95% confidence interval for the mean amount spent in March is ( -$28,366.84, $90,691.49).
CEO compensation 2018 Forbes magazine reports the compensation of CEOs of the 500 largest firms. The average compensation of a sample of 20 CEOs is $13.5M. Here’s a histogram of all the CEOs:Based on these data, a computer program found that a 95%confidence interval for the mean annual
Crawling Data collected by child development scientists produced this confidence interval for the average age (in weeks) at which babies begin to crawl:t-Interval for m 95.00% Confidence: 30.65 6 m(age) 6 32.89a) Explain carefully what the software output means.b) What is the margin of error for
Pulse rates A medical researcher measured the pulse rates(beats per minute) of a sample of randomly selected adults and found the following Student’s t-based confidence interval:With 95.00% Confidence, 70.887604 6 m(Pulse) 6 74.497011a) Explain carefully what the software output means.
Snow Based on meteorological data for the past century, a local TV weather forecaster estimates that the region’s average winter snowfall is 23'', with a margin of error of {2 inches.Assuming he used a 95% confidence interval, how should viewers interpret this news? Comment on each of these
Meal plan After surveying students at Dartmouth College, a campus organization calculated that a 95% confidence interval for the mean cost of food for one term (of three in the Dartmouth trimester calendar) is ($1372, $1562). Now the organization is trying to write its report and is considering the
Bird counts A biology class conducts a bird count every week during the semester. Using the number of species counted each week, a student finds the following confidence interval for the mean number of species counted:95 percent confidence interval:16.34 18.69 Knowing that species have to be whole
Shoe sizes revisited Chapter 2, Exercise 16 showed the histogram of the European shoe sizes from a sample of 269 college students. Looking at the men only, a 95% confidence interval for the mean shoe size shows:95 percent confidence interval:44.3071 44.9900 The student knows that European shoes are
Student survey revisited Chapter 2, Exercise 86 introduced a student survey in which 299 students were randomly selected and asked a variety of questions. One of the questions asked “How many friends do you have on Facebook?” To find a confidence interval for the mean number, a student drew
Framingham revisited In Chapter 4, Exercise 38, we saw an ogive of the distribution of cholesterol levels (in mg/dL) of a random sample of 1406 participants (taken in 1948 from Framingham, MA). To find a bootstrap confidence interval for the mean cholesterol, a student took 1000 bootstrap samples,
Teachers Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct? What’s wrong with the others?
Cattle Livestock are given a special feed supplement to see if it will promote weight gain. Researchers report that the 77 cows studied gained an average of 56 pounds, and that a 95% confidence interval for the mean weight gain this supplement produces has a margin of error of {11 pounds.Some
Salaries A survey finds that a 95% confidence interval for the mean salary of a police patrol officer in Fresno, California, in 2016 is $52,516 to $53,509. A student is surprised that so few police officers make more than $53,509. Explain what is wrong with the student’s interpretation.
Home sales revisited For the confidence interval you found in Exercise 11, interpret this interval and explain what 95% confidence means in this context.
Home sales again In the previous exercise, you found a 95%confidence interval to estimate the average loss in home value.
Home sales The housing market recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 36 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss from the peak in 2008 was $9560 with a standard
t-models, part IV Describe how the critical value of t for a 95% confidence interval changes as the number of degrees of freedom increases.
t-models, part III Describe how the shape, center, and spread of t-models change as the number of degrees of freedom increases.
t-models, part II Using the t tables, software, or a calculator, estimatea) the critical value of t for a 95% confidence interval with dƒ = 7.b) the critical value of t for a 99% confidence interval with dƒ = 102.
t-models, part I Using the t tables, software, or a calculator, estimatea) the critical value of t for a 90% confidence interval with dƒ = 17.b) the critical value of t for a 98% confidence interval with dƒ = 88.
More groceries Suppose the store in Exercise 4 had 312 customers this Sunday.a) Estimate the probability that the store’s revenues were at least $10,000.b) If, on a typical Sunday, the store serves 312 customers, how much does the store take in on the worst 10% of such days?
More tips The server in Exercise 3 usually waits on about 40 parties over a weekend of work.a) Estimate the probability that he will earn at least $500 in tips.b) How much does he earn on the best 10% of such weekends?
Groceries A grocery store’s receipts show that Sunday customer purchases have a skewed distribution with a mean of$32 and a standard deviation of $20.a) Explain why you cannot determine the probability that the next Sunday customer will spend at least $40.b) Can you estimate the probability that
Tips A server believes the distribution of their tips has a model that is slightly skewed to the right, with a mean of $9.60 and a standard deviation of $5.40.a) Explain why you cannot determine the probability that a given party will tip at least $20.b) Can you estimate the probability that the
LSAT The LSAT (a test taken for law school admission) has a mean score of 151 with a standard deviation of 9 and a unimodal, symmetric distribution of scores. A test preparation organization teaches small classes of 9 students at a time.A larger organization teaches classes of 25 students at a
Salmon A specialty food company sells whole King Salmon to various customers. The mean weight of these salmon is 35 pounds with a standard deviation of 2 pounds. The company ships them to restaurants in boxes of 4 salmon, to grocery stores in cartons of 16 salmon, and to discount outlet stores in
Amendment A TV news reporter says that a proposed constitutional amendment is likely to win approval in the upcoming election because a poll of 1505 likely voters indicated that 52%would vote in favor. The reporter goes on to say that the margin of error for this poll was 3%.a) Explain why the poll
Another pilot study During routine screening, a doctor notices that 22% of her adult patients show higher than normal levels of glucose in their blood—a possible warning signal for diabetes. Hearing this, some medical researchers decide to conduct a large-scale study, hoping to estimate the
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