Question: A company is interested in estimating the

> 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

> For the data in Exercise 4, a) Test the null hypothesis at a = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.) b) Find a 95% confidence interval using the pooled degrees of freedom. c) Are your answers different from wha

> 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 8

> In 2016, the Centers for Disease Control and Prevention reported that 36.5% 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 w

> 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 who

> 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 a

> 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

> 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.

> 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?

> 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% ch

> After the political ad campaign described in Exercise 15, part a, 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.

> 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 tra

> For the data in Exercise 3, a) Test the null hypothesis at a = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.) b) Find a 95% confidence interval using the pooled degrees of freedom. c) Are your answers different from wha

> 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

> During the week of April 15, 2013, a Gallup Poll asked 1500 U.S. adults, aged 18 or over, how they rated economic conditions. Only 17% rated the economy as Excellent/Good. Construct a 95% confidence interval for the true proportion of Americans who rated

> In a survey on downloading music, the Gallup Poll asked 703 Internet users if they “ever downloaded music from an Internet site that was not authorized by a record company, or not,” and 18% responded “yes.” Construct a 95% confidence interval for the tru

> The mayor of a small city has suggested that the state locate a new prison there, arguing that the construction project and resulting jobs will be good for the local economy. A total of 183 residents show up for a public hearing on the proposal, and a sh

> Some food retailers propose subjecting food to a low level of radiation in order to improve safety, but sale of such “irradiated” food is opposed by many people. Suppose a grocer wants to find out what his customers think. He has cashiers distribute surv

> Direct mail advertisers send solicitations (“junk mail”) to thousands of potential customers in the hope that some will buy the company’s product. The response rate is usually quite low. Suppose a company wants to test the response to a new f lyer and se

> An insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel in 91 of them. a) Create a 95% confidence interval for the percentage of all auto accidents that involve teenage drivers. b) Expla

> A biotechnology firm in Boston is planning its investment strategy for future products and research labs. A poll found that only 8% of a random sample of 1012 U.S. adults approved of attempts to clone a human. a) Find the margin of error for this poll i

> A small company involved in e-commerce is interested in statistics concerning the use of e-mail. A poll found that 38% of a random sample of 1012 adults, who use a computer at their home, work, or school, said that they do not send or receive e-mail. a)

> For quality control purposes, 900 ceramic tiles were inspected to determine the proportion of defective (e.g., cracked, uneven finish, etc.) tiles. Assuming that these tiles are representative of all tiles manufactured by an Italian tile company, what ca

> Look back at the prices for the external disk drives we saw in Exercise 10. The least squares line is The assumptions and conditions for regression are met. a) Disk drives keep growing in capacity. Some tech experts now talk about Petabyte 1PB = 100

> A student is considering publishing a new magazine aimed directly at owners of Japanese automobiles. He wanted to estimate the fraction of cars in the United States that are made in Japan. The computer output summarizes the results of a random sample of

> How far do professional golfers drive a ball? (For non-golfers, the drive is the shot hit from a tee at the start of a hole and is typically the longest shot.) Here’s a histogram of the average driving distances of the 199 leading profe

> 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 90 a) Check the assumptions and conditions for inference. b) Create a 95% confidence interval for the averag

> After the sub-prime crisis of late 2007, real estate prices fell almost everywhere in the United States. In 2006–2007 before the crisis, the average selling price of homes in a region in upstate New York was $191,300. A real estate agen

> 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 of at least 8 miles per hour, according to the Wi

> While reviewing the sample of audit fees, a senior accountant for the firm notes that the fee charged by the firm’s accountants depends on the complexity of the return. A comparison of actual charges therefore might not provide the information needed to

> Certified public accountants are often required to appear with clients if the IRS audits the client’s tax return. Some accounting firms give the client an option to pay a fee when the tax return is completed that guarantees tax advice and support from th

> The speed-measuring machines must measure accurately to maximize effectiveness in slowing traffic. The accuracy of the machines will be tested before placement on city streets. To ensure that error rates are estimated accurately, the researchers want to

> Police departments often try to control traffic speed by placing speed-measuring machines on roads that tell motorists how fast they are driving. Traffic safety experts must determine where machines should be placed. In one recent test, police recorded t

> At one time, Nevada was the only U.S. state that allowed gambling. Although gambling continues to be one of the major industries in Nevada, the proliferation of legalized gambling in other areas of the country has required state and local governments to

> Recall the small bookstore we saw in Exercise 9. The regression line is: and the assumptions and conditions for regression are met. Calculations with technology find that se = 1.477. a) Find the predicted sales on a day with 500 employees working. b)

> Government officials have difficulty attracting new business to communities with troubled reputations. Nevada has been one of the fastest growing states in the country for a number of years. Accompanying the rapid growth are massive new construction proj

> A company that produces cell phones claims its standard phone battery lasts longer on average than other batteries in the market. To support this claim, the company publishes an ad reporting the results of a recent experiment showing that under normal us

> The technology committee has stated that the average time spent by students per lab visit has increased, and the increase supports the need for increased lab fees. To substantiate this claim, the committee randomly samples 12 student lab visits and notes

> Will your flight get you to your destination on time? The U.S. Bureau of Transportation Statistics reported the percentage of f lights that were late each month from 1995 through early 2016. Here’s a histogram, along with some summary s

> What are the chances your f light will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. Here are a histogram and summary statistics for the percentage of f li

> Suppose the state in Exercise 33 sampled 16 small retailers instead of 51, and for the sample of 16, the sample mean increase again equaled $2350 in additional sales tax revenue collected per retailer compared to the previous quarter. Also assume the sam

> States that rely on sales tax for revenue to fund education, public safety, and other programs often end up with budget surpluses during economic growth periods (when people spend more on consumer goods) and budget deficits during recessions (when people

> In Exercise 30, we found a 95% confidence interval to estimate the average value of foreclosed homes. a) Suppose the standard deviation of the values was $300,000 instead of the $196,196 used for that interval. What would the larger standard deviation d

> Suppose that for budget planning purposes the city in Exercise 29 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 cr

> In 2012, a large number of foreclosed homes in the Washington, DC, metro area were sold. In one community, a sample of 30 foreclosed homes sold for an average of $443,705 with a standard deviation of $196,196. a) What assumptions and conditions must be c

> In Exercise 5, we saw a regression to predict the sales per person at a movie theater in terms of the time (in minutes) before the show. The model was: a) A 90% prediction interval for sales to a concessions customer 10 minutes before the movie starts

> 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. For a random sample of 44 weekdays, daily fees collected averaged $126, with

> A credit card company takes a random sample of 100 cardholders to see how much they charged on their card last month. A histogram and boxplot are as follows: A computer program found that the 95% confidence interval for the mean amount spent in Januar

> A sample of 20 CEOs from the Forbes 500 shows total annual compensations ranging from a minimum of $0.1 to $62.24 million. The average for these 20 CEOs is $7.946 million. The histogram and boxplot are as follows: Based on these data, a computer progr

> A feed supply company has developed a special feed supplement to see if it will promote weight gain in livestock. Their researchers report that the 77 cows studied gained an average of 56 pounds and that a 95% confidence interval for the mean weight gain

> Markets have become interested in the potential of social networking sites. But they need to understand the demographics of social networking users. Pew Research has conducted surveys since 2012 that address these questions. (www.pewinternet.org/Reports/

> A market researcher working for the bank in Exercise 2 wants to know if the distribution of applications by card is the same for the past three mailings. She takes a random Inference for Counts: Chi-Square Tests sample of 200 from each mailing and counts

> An analyst at a local bank wonders if the age distribution of customers coming for service at his branch in town is the same as at the branch located near the mall. He selects 100 transactions at random from each branch and researches the age information

> For the data in Exercise 2, a) Compute the standardized residual for each type of card. b) Are any of these particularly large? (Compared to what?) c) What does the answer to part b say about this new group of customers? Exercise 2: At a major credit ca

> For the data in Exercise 1, a) Compute the standardized residual for each season. b) Are any of these particularly large? (Compared to what?) c) Why should you have anticipated the answer to part b? Exercise 1: If there is no seasonal effect on human bi

> A survey designed to study how much households spend on eating out finds the following regression model, relating the amount respondents said they spent individually to eat out each week to their household income in $1000’s. a) A 95%

> For the customers in Exercise 2, a) If the customers apply for the three cards according to the historical proportions, about how big, on average, would you expect the χ2 statistic to be (what is the mean of the χ2 distribution)? b) Does the statistic yo

> For the births in Exercise 1, a) If there is no seasonal effect, about how big, on average, would you expect the x2 statistic to be (what is the mean of the χ2 distribution)? b) Does the statistic you computed in Exercise 1 seem large in comparison to th

> At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are 60%, 30%, and 10%, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silve

> For the data in Exercise 2, a) Test the null hypothesis at a = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.) b) Find a 95% confidence interval using the pooled degrees of freedom. c) Are your answers different from wha

> For the data in Exercise 1, a) Test the null hypothesis at a = 0.05 using the pooled t-test. (Show the t-statistic, P-value, and conclusion.) b) Find a 95% confidence interval using the pooled degrees of freedom. c) Are your answers different from wha

> As part of the poll in Exercise 11, Pew asked whether the respondent owned a smartphone. Are Internet use and smartphone ownership independent? a) Under the usual null hypothesis, what are the expected values? b) Compute the χ2 statistic. c)

> A similar Pew poll in 2016 asked people how often they used the Internet. (Data in Income and internet) How often do you use the Internet? a) Under the usual null hypothesis, what are the expected values? b) Compute the χ2 statistic. c) Ho

> From the same survey as in Exercise 9, 294 of the 409 respondents who reported earning less than $30,000 per year said they were social networking users. At the other end of the income scale, 333 of the 504 respondents reporting earnings of $75,000 or mo

> If there is no seasonal effect on human births, we would expect equal numbers of children to be born in each season (winter, spring, summer, and fall). A student takes a census of her statistics class and finds that of the 120 students in the class, 25 w

> Using the data in Exercise 1, and assuming that the data come from a distribution that is Normally distributed, a) Find a 95% confidence interval for the mean difference in ages of houses in the two neighborhoods. b) Is 0 within the confidence interval

> The study of external disk drives from Chapter 4, Exercise 2 (with the outlier removed) finds the following: The least squares line was found to be: a) Find the predicted Price of a 2 TB hard drive. b) Find a 95% confidence interval for the mean Pric

> A website that rents movies online recorded the age and the number of movies rented during the past month for some of their customers. Here are their data: Make a scatterplot for these data. What does it tell you about the relationship between these t

> The histogram of the ages of the respondents in Exercise 22 looks like this: What might you suggest for the next step of the analysis? 15 - 10 40 80 120 160 200 240 Count

> The histogram of the total revenues (in $M) of the movies in Exercise 21 looks like this: What might you suggest for the next step of the analysis? 80 60 40 20 100 200 300 400 500 600 700 800 Gross (SM) Count

> Are the following data time series? If not, explain why. a) Reports from the Bureau of Labor Statistics on the number of U.S. adults who are employed full time in each major sector of the economy. b) The quarterly Gross Domestic Product (GDP) of France f

> Are the following data time series? If not, explain why. a) Quarterly earnings of Microsoft Corp. b) Unemployment in August 2010 by education level. c) Time spent in training by workers in NewCo. d) Numbers of e-mails sent by employees of SynCo each hour

> You wish to explain to your boss what effect taking the base-10 logarithm of the salary values in the company’s database will have on the data. As simple, example values you compare a salary of $10,000 earned by a part-time shipping clerk, a salary of $1

> When analyzing data on the number of employees in small companies in one town, a researcher took square roots of the counts. Some of the resulting values, which are reasonably symmetric were: 4, 4, 6, 7, 7, 8, 10 What were the original values, and how ar

> For the disk drive data of Exercise 2 (as corrected in Exercise 12), find and interpret the value of R2. Exercise 2: Disk drives have been getting larger. Their capacity is now often given in terabytes (TB) where 1 TB = 1000 gigabytes, or about a trilli

> Indicate which of the following represent independent events. Explain briefly. a) Prices of houses on the same block. b) Successive measurements of your heart rate as you exercise on a treadmill. c) Measurements of the heart rates of all students in t

> For the regression model for the bookstore of Exercise 1, what is the value of R2 and what does it mean? Exercise 1: Consider the following data from a small bookstore. Number of Sales People Working Sales (in $1000) 10 3 11 7 13 14 10 18 10 20 12

> Here are residual plots (residuals plotted against predicted values) for three linear regression models. Indicate which condition appears to be violated (linearity, outlier, or equal spread) in each case. a) 15+ 10 5+ -5+ -10+ -10 0 10 20 30 40 50

> Is the experiment of Exercise 1 blind? Could it be made double blind? Explain. Exercise 1: For the following experiment, identify the experimental units, the treatments, the response, and the random assignment. A commercial food lab compared recipes fo

> Here are the residuals for a regression of Sales on Number of Sales People Working for the bookstore of Exercise 1: a) What are the units of the residuals? b) Which residual contributes the most to the sum that was minimized according to the Least Squa

> U.S. Customs and Border Protection has been testing automated kiosks that may be able to detect lies (www .wired.com/threatlevel/2013/01/ff-lie-detector/all/). One measurement used (among several) is involuntary eye movements. Using this method alone, te

> According to U.S. Census data, 68% of the civilian U.S. labor force self-identifies as White, 11% as Black, and the remaining 21% as Hispanic/Latino or Other. Among Whites in the labor force, 54% are Male, and 46% Female. Among Blacks, 52% are Male and 4

> The company in Exercise 13 performed another experiment in which they tested three website designs to see which one would lead to the highest probability of purchase. The first (design A) used enhanced product information, the second (design B) used exte

> Summit Projects provides marketing services and website management for many companies that specialize in outdoor products and services. To understand customer Web behavior, the company experiments with different offers and website design. The results of

> Facebook reports that 70% of their users are from outside the United States and that 50% of their users log on to Facebook every day. Suppose that 20% of their users are United States users who log on every day. a) What percentage of Facebook’s users are

> A national survey indicated that 30% of adults conduct their banking online. It also found that 40% are under the age of 50, and that 25% are under the age of 50 and conduct their banking online. a) What percentage of adults do not conduct their banking

> Using the table from Exercise 8, a) What is the probability that a randomly selected Black multigenerational family is a two-adult-generation family? b) What is the probability that a randomly selected multigenerational family is White, given that it is

> Indicate which of the following represent independent events. Explain brief ly. a) The gender of customers using an ATM machine. b) The last digit of the social security numbers of students in a class. c) The scores you receive on the first midterm, s

> True or False. If False, explain briefly. a) We choose the linear model that passes through the most data points on the scatterplot. b) The residuals are the observed y-values minus the y-values predicted by the linear model. c) Least squares means that

> For the following experiment, indicate whether it was single-blind, double-blind, or not blinded at all. Explain your reasoning. Does a “stop smoking” program work better if it costs more? Smokers responding to an advertisement offering to help them stop

> A study finds that during blizzards, online sales are highly associated with the number of snow plows on the road; the more plows, the more online purchases. The director of an association of online merchants suggests that the organization should encoura

> A larger firm is considering acquiring the bookstore of Exercise 1. An analyst for the firm, noting the relationship seen in Exercise 1, suggests that when they acquire the store they should hire more people because that will drive higher sales. Is his c

> If we assume that the conditions for correlation are met, which of the following are true? If false, explain briefly. a) A correlation of 0.02 indicates a strong positive association. b) Standardizing the variables will make the correlation 0. c) Addi

> If we assume that the conditions for correlation are met, which of the following are true? If false, explain briefly. a) A correlation of -0.98 indicates a strong, negative association. b) Multiplying every value of x by 2 will double the correlation.

> A company that relies on Internet-based advertising linked to key search terms wants to understand the relationship between the amount it spends on this advertising and revenue (in $). a) Which variable is the explanatory or predictor variable? b) Whic

> The human resources department at a large multinational corporation wants to be able to predict average salary for a given number of years’ experience. Data on salary (in $1000s) and years of experience were collected for a sample of employees. a) Which

> Disk drives have been getting larger. Their capacity is now often given in terabytes (TB) where 1 TB = 1000 gigabytes, or about a trillion bytes. A search of prices for external disk drives on Amazon.com in mid-2016 found the following data: (Data in Dis

> An online investment blogger advises investing in mutual funds that have performed badly the past year because “regression to the mean tells us that they will do well next year.” Is he correct?

> A CEO complains that the winners of his “rookie junior executive of the year” award often turn out to have less impressive performance the following year. He wonders whether the award actually encourages them to slack off. Can you offer a better explanat

> For the disk drives in Exercise 2, we want to predict Price from Capacity. a) Find the slope estimate, b1 and interpret it in words. b) Does the slope seem reasonable? Explain. c) Find the intercept, b0. d) What does it mean, in this context? Is it meani