Jeff, a sales manager of a car dealership, believes that his sales force sells a car to 35% of the customers who stop by the showroom. He needs the dealership to make 50 sales this month to get a special bonus of $100,000. Approximately 120 customers visit the showroom each month. You may assume that customers entering the dealership are independent of one another. a) What is the probability that he will make his bonus? b) What is the probability that he will sell between 40 and 50 cars? c) Assume that Jeff can choose to either increase the motivation of his sales force so that they increase the probability of a sale to 40%, or to increase the number of people walking into the showroom to 140. Which makes it more likely that Jeff will sell 50 cars? d) A marketing consultant suggests that she can produce an ad campaign that will increase the number of people walking into the showroom to 140 at a cost of $15,000. Assuming that Jeff is risk-neutral and has the budget, should Jeff accept this offer? e) What is the maximum amount that Jeff should be willing to pay to increase the number of people entering the showroom to 140 (assuming that he is risk-neutral and perfectly rational)? f) If 20% of customers are “Big Spenders” who earn the firm a lot of money, what is the probability that Jeff will see at least 1 “Big Spender” in the next 10 customers (not see one that buys, but just see one)?
> 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
> For the following experiment, indicate whether it was single-blind, double-blind, or not blinded at all. Explain your reasoning. Makers of a new frozen entrée arranged for it to be served to randomly selected customers at a restaurant in place of the equ
> For the bookstore of Exercise 1, the manager wants to predict Sales from Number of Sales People Working. a) Find the slope estimate, b1. b) What does it mean, in this context? c) Find the intercept, b0. d) What does it mean, in this context? Is it meanin
> For the hard drive data in Exercise 2, the correlation is 0.988 and other summary statistics are: a) If a drive has a capacity of 17.46 TB (or 1 SD above the mean), how many standard deviations above or below the mean price of $785.82 do you expect the
> For the bookstore sales data in Exercise 1, the correlation of number of sales people and sales is 0.965. a) If the number of people working is 2 standard deviations above the mean, how many standard deviations above or below the mean do you expect sales
> True or False. If False, explain briefly. a) Some of the residuals from a least squares linear model will be positive and some will be negative. b) Least Squares means that some of the squares of the residuals are minimized. c) We write y^ to denote the
> Consider the following data from a small bookstore. a) Prepare a scatterplot of Sales against Number of Sales People Working. b) What can you say about the direction of the association? c) What can you say about the form of the relationship? d) What ca
> The histogram shows the December charges (in $) for 5000 customers from one marketing segment from a credit card company. (Negative values indicate customers who received more credits than charges during the month.) a) Write a short description of this d
> For the data in Exercise 2: a) Find the quartiles using your calculator. b) Find the quartiles using the Tukey method (page 65). c) Find the IQR using the quartiles from part b. d) Find the standard deviation. Exercise 2: As the new manager of a small c
> For the data in Exercise 1: a) Find the quartiles using your calculator. b) Find the quartiles using the Tukey method (page 65). c) Find the IQR using the quartiles from part b. d) Find the standard deviation.
> Suppose the archer from Exercise 58 shoots 10 arrows. a) Find the mean and standard deviation of the number of bull’s-eyes she may get. b) What’s the probability that she never misses? c) What’s the probability that there are no more than 8 bull’s-eyes?
> Analysts from the Internet company of Exercise 5 are now concerned that customers who come directly to their site (by typing their URL into a browser) might respond differently than those referred to the site from other sites (such as search engines). Th
> Suppose we choose 12 people instead of the 5 chosen in Exercise 57. a) Find the mean and standard deviation of the number of right-handers in the group. b) What’s the probability that they’re not all right-handed? c) What’s the probability that there
> Consider our archer from Exercise 52. a) How many bull’s-eyes do you expect her to get? b) With what standard deviation? c) If she keeps shooting arrows until she hits the bull’s-eye, how long do you expect it will take?
> Consider our group of 5 people from Exercise 51. a) How many lefties do you expect? b) With what standard deviation? c) If we keep picking people until we find a lefty, how long do you expect it will take?
> The manufacturer in Exercise 54 has noticed that the number of faulty cell phones in a production run of cell phones is usually small and that the quality of one day’s run seems to have no bearing on the next day. a) What model might you use to model th
> A website manager has noticed that during the evening hours, about 3 people per minute check out from their shopping cart and make an online purchase. She believes that each purchase is independent of the others and wants to model the number of purchases
> The scatterplot shows, for 2015 cars, the carbon footprint (tons of CO2 per mile) vs. the new Environmental Protection Agency (EPA) highway mileage for 69 family sedans as reported by the U.S. government (www.fueleconomy.gov/feg/byclass.htm); the cars in
> At a small company, the head of human resources wants to examine salary to prepare annual reviews. He selects 28 employees at random with job types ranging from 01 = Stocking clerk to 99 = President. He plots Salary ($) against Job Type and finds a stron
> A sales manager for a major pharmaceutical company analyzes last year’s sales data for her 96 sales representatives, grouping them by region (1 = East Coast United States; 2 = Mid West United States; 3 = West United States; 4 = South Un
> Insurance companies carefully track claims histories so that they can assess risk and set rates appropriately. The National Insurance Crime Bureau reports that Honda Accords, Honda Civics, and Toyota Camrys are the cars most frequently reported stolen, w
> A CEO announces at the annual shareholders meeting that the new see-through packaging for the company’s flagship product has been a success. In fact, he says, “There is a strong correlation between packaging and sales.” Criticize this statement on statis
> In an effort to check the quality of their cell phones, a manufacturing manager decides to take a random sample of 10 cell phones from yesterday’s production run, which produced cell phones with serial numbers ranging (according to when they were produce
> The 30 quarterbacks in Exercise 32 had an average Salary of $13,788,022 1SD = $8,130,5362. The correlation between Salary and Total QBR = 0.278. If a player had a Total QBR rating 1 SD below the average, what Salary would you predict for it? Exercise 32
> For the data in Exercise 31, the average Sales was 52,697 pounds (SD = 10,261 pounds), and the correlation between Price and Sales was = -0.547. If the Price in a particular week was one SD higher than the mean Price, how much pizza would you predict was
> In 2016, the Los Angeles Dodgers spent nearly one quarter billion (!) dollars on salaries for their players (Spotrac). Is there a relationship between salary and team performance in Major League Baseball? For the 2016 season, a linear model fit to the nu
> Is there a relationship between total team salary and the performance of teams in the National Football League (NFL)? For the 2016–2017 season, a linear model predicting Wins (out of 16 regular season games) from the total team Salary ($M) for the 32 tea
> Quarterback performance 2017. The average salary for 30 top NFL quarterbacks in 2017 was just over $13,000,000. A linear model to predict Salary from Total QBR (an overall measure of performance based on game statistics) found the following: a) What i
> A linear model fit to predict weekly Sales of frozen pizza (in pounds) from the average Price ($/unit) charged by a sample of stores in the city of Dallas in 39 recent weeks is: (Data in Pizza prices) a) What is the explanatory variable? b) What is t
> Here are several scatterplots. The calculated correlations are -0.977, -0.021, 0.736, and 0.951. Which is which? (a) (b) (c) (d)
> Here are several scatterplots. The calculated correlations are -0.923, -0.487, 0.006, and 0.777. Which is which? (a) (b) (c) (d)
> Owners of a new coffee shop tracked sales for the first 20 days and displayed the data in a scatterplot a) Make a histogram of the daily sales since the shop has been in business. b) State one fact that is obvious from the scatterplot, but not from the
> A ceramics factory can fire eight large batches of pottery a day. Sometimes a few of the pieces break in the process. In order to understand the problem better, the factory records the number of broken pieces in each batch for three days and then creates
> A cable provider wants to contact customers in a particular telephone exchange to see how satisfied they are with the new digital TV service the company has provided. All numbers are in the 452 exchange, so there are 10,000 possible numbers from 452-0000
> Which of the scatterplots show: a) Little or no association? b) A negative association? c) A linear association? d) A moderately strong association? e) A very strong association? (1) [:.. (3) (4)
> Which of the scatterplots show: a) Little or no association? b) A negative association? c) A linear association? d) A moderately strong association? e) A very strong association? (1) (3) (4)
> Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the li
> Suppose you were to collect data for each pair of variables. You want to make a scatterplot. Which variable would you use as the explanatory variable and which as the response variable? Why? What would you expect to see in the scatterplot? Discuss the li
> The Toy Association tracks sales of toys using a tracking survey that represents approximately 80% of U.S. toy sales. Projected to the entire industry, the following table breaks down U.S. toy sales by category. a) Create an appropriate graphical display
> In 2014, Pew Research Center released the results of a survey among U.S. adults that asked nearly 2000 people how satisfied they are with their current financial situation (www.pewsocialtrends .org/datasets/). Responses were collected by gender, using a
> An insurance company is updating its payouts and cost structure for their insurance policies. Of particular interest to them is the risk analysis for customers currently on heart or blood pressure medication. The Centers for Disease Control and Preventio
> Here’s a pie chart of the data in Exercise 16. a) Which display of these data is best for comparing the market value of these brands? Explain. b) Does Pepsi or Red Bull have a larger market value? Is that comparison easier to make wit
> Here’s a bar chart of the data in Exercise 15. a) Compared to the pie chart in Exercise 15, which is better for displaying the relative portions of market share? Explain. b) What is missing from this display that might make it somewha
> An Olympic archer is able to hit the bull’seye 80% of the time. Assume each shot is independent of the others. If she shoots 6 arrows, what’s the probability of each of the following results? a) Her first bull’s-eye comes on the third arrow. b) She mis
> Tuition 2016. In 2016, the mean tuition of private colleges and universities was $18,230, with a standard deviation of $7272. The mean tuition for public colleges and universities was $9624, with a standard deviation of $4669. The distribution of tuition
> The 1057 houses described in Exercise 44 have a mean price of $167,900, with a standard deviation of $77,158. The mean living area is 1819 sq. ft., with a standard deviation of 663 sq. ft. Which is more unusual, a house in that market that sells for $400
> A second report by the National Center for Productivity analyzed the relationship between productivity and wages. They used the graph from Exercise 67, with the x-axis labeled “wages.” Comment on any problems you see with their analysis.
> The National Center for Productivity releases information on the efficiency of workers. In a recent report, they included the following graph showing a rapid rise in productivity. What questions do you have about this? 3.5 2.5 Productivity
> The claims about climate change suggest two possible effects: more storms and bigger, stronger storms. Here are plots similar to those of Exercise 65, but for major hurricanes. (Data in Hurricane history) a) Describe the distribution. Here is the time
> The North Atlantic hurricane database, or HURDAT, is a database of all tropical storms and hurricanes for the Atlantic Ocean, Gulf of Mexico, and Caribbean Sea, reporting numbers of storms each year since 1850. The older portion of the database reflects
> Holes-R-Us, an Internet company that sells piercing jewelry, keeps transaction records on its sales. At a recent sales meeting, one of the staff presented the following histogram and summary statistics of the ZIP codes of the last 500 customers, so that
> Each house listed on the multiple listing service (MLS) is assigned a sequential ID number. A recently hired real estate agent decided to examine the MLS numbers in a recent random sample of homes for sale by one real estate agency in nearby towns. To be
> The discounts negotiated by the car buyers in Exercise 32 are classified by whether the buyer was Male 1code = 02 or Female 1code = 12. Compare the discounts of men vs. women using an appropriate display and write a brief summary of the differences.
> The 70 mutual funds of Exercise 31 are classified into four types: U.S. Domestic Equity Funds, Bond Funds, International Funds, and Other Funds. Compare the 12 month returns of the four types of funds using an appropriate display and write a brief summar
> A manufacturer of game controllers is concerned that their controller may be difficult for left-handed users. They set out to find lefties to test. About 13% of the population is left-handed. If they select a sample of five customers at random in their s
> For each CEO, a code is listed that corresponds to the industry of the CEO’s company. Here are a few of the codes and the industries to which they correspond: A recently hired investment analyst has been assigned to examine the indust
> A philanthropic organization has a database of millions of donors that they contact by mail to raise money for charities. One of the variables in the database, Title, contains the title of the person or persons printed on the address label. The most comm
> A real estate agent notices that houses with fireplaces often fetch a premium in the market and wants to assess the difference in sales price of 60 homes that recently sold. The data and summary are shown in the table. Write a report summarizing the fi
> Engineers at a computer production plant tested two methods for accuracy in drilling holes into a PC board. They tested how fast they could set the drilling machine by running 10 boards at each of two different speeds. To assess the results, they measure
> Look again at the histograms of test scores for the three statistics classes in Exercise 55. a) Overall, which class do you think performed better on the test? Why? b) How would you describe the shape of each distribution? c) Match each class with the co
> Three statistics classes all took the same test. Here are histograms of the scores for each class. a) Which class had the highest mean score? b) Which class had the highest median score? c) For which class are the mean and median most different? Which
