For their class project, a group of Business students decides to survey the student body to assess opinions about a proposed new student coffee shop to judge how successful it might be. Their sample of 200 contained 50 first-year students, 50 sophomores, 50 juniors, and 50 seniors. a) Do you think the group was using an SRS? Why? b) What kind of sampling design do you think they used?
> In Exercise 35, you calculated probabilities of getting various colors of M&M’s. a) If you draw one M&M, are the events of getting a red one and getting an orange one disjoint or independent or neither? b) If you draw two M&M’s one after the other, are
> The American Red Cross must track their supply and demand for various blood types. They estimate that about 45% of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest Type AB. a) If someone volunteers to give blood, what is the pr
> The Mars company says that before the introduction of purple, yellow made up 20% of their plain M&M candies, red made up another 20%, and orange, blue, and green each made up 10%. The rest were brown. a) If you picked an M&M at random from a pre-purple
> Employment data at a large company reveal that 72% of the workers are married, 44% are college graduates, and half of the college grads are married. What’s the probability that a randomly chosen worker is: a) Neither married nor a college graduate? b)
> In a sample of real estate ads, 64% of homes for sale had garages, 21% have swimming pools, and 17% have both features. What is the probability that a home for sale has: a) A pool, a garage, or both? b) Neither a pool nor a garage? c) A pool but no ga
> Final consulting team project. You used the Multiplication Rule to calculate probabilities about the telecommunications experience of your consulting teammates in Exercise 30. a) What must be true about the groups in order to make that approach valid? b)
> You used the Multiplication Rule to calculate repair probabilities for your cars in Exercise 29. a) What must be true about your cars in order to make that approach valid? b) Do you think this assumption is reasonable? Explain.
> You are assigned to be part of a team of three analysts of a global management consulting company as described in Exercise 28. What is the probability that of your other two teammates: a) Neither has any telecommunications experience? b) Both have some t
> Consider again the auto repair rates described in Exercise 27. If you bought two new cars, what is the probability that: a) Neither will need repair? b) Both will need repair? c) At least one car will need repair? Exercise 27: In developing their warran
> The probability model below describes the number of repair calls that an appliance repair shop may receive during an hour. a) How many calls should the shop expect per hour? b) What is the standard deviation? Repair Calls 1 3 Probability 0.1 0.3 0.
> You work for a large global management consulting company. Of the entire work force of analysts, 55% have had no experience in the telecommunications industry, 32% have had limited experience (less than 5 years), and the rest have had extensive experienc
> In developing their warranty policy, an automobile company estimates that over a 1-year period 17% of their new cars will need to be repaired once, 7% will need repairs twice, and 4% will require three or more repairs. If you buy a new car from them, wha
> For a sales promotion, the manufacturer places winning symbols under the caps of 10% of all Pepsi bottles. If you buy a six-pack of Pepsi, what is the probability that you win something?
> A tire manufacturer recently announced a recall because 2% of its tires are defective. If you just bought a new set of four tires from this manufacturer, what is the probability that at least one of your new tires is defective?
> Many stores run “secret sales”: Shoppers receive cards that determine how large a discount they get, but the percentage is revealed by scratching off that black stuff (what is that?) only after the purchase has been to
> A toy company is preparing to market an electronic game for young children that “randomly” generates a color. They suspect, however, that the way the random color is determined may not be reliable, so they ask the prog
> Here are engine size (displacement, in liters) and gas mileage (estimated combined city and highway) for a random sample of 35 2016 model cars (taken from Fuel Economy 2016 and identified in the data with Sample = “Yes”). a) Make a scatterplot for these
> Since 1985, average mortgage interest rates have f luctuated from a low of nearly 3% to a high of over 14%. Is there a relationship between the amount of money people borrow and the interest rate that’s offered? Here is a scatterplot of
> The Office of Federal Housing Enterprise Oversight (www.fhfa.gov) collects data on various aspects of housing costs around the United States. Here is a scatterplot of the Housing Cost Index versus the Median Family Income for each of the 50 states. The c
> Concern over the weather associated with El Niño has increased interest in the possibility that the climate on Earth is getting warmer. The most common theory relates an increase in atmospheric levels of carbon dioxide (CO2), a greenhouse
> Suppose occurrences of sales on a small company’s website are well modeled by a Poisson model with l = 5>hour. a) If a sale just occurred, what is the expected waiting time until the next sale? b) What is the probability that the next sale will happen
> Numbeo.com collects data from users in cities around the world on prices of a basket of goods and services and uses these data to determine a cost of living index. This index scales New York City as 100 and expresses the cost of living in other cities as
> Use the advertised prices for BMW 8’s given in Exercise 63 to create a linear model for the relationship between a car’s Model Year and its Price. a) Find the equation of the regression line. b) Explain the meaning of the slope of the line. c) Explain th
> A business student needs cash, so he decides to sell his car. The car is a classic BMW “8 series” that was only made over the course of a few years in the 1990s. He would like to sell it on his own, rather than through a dealer so he’d like to predict th
> A popular magazine annually publishes rankings of both U.S. business programs and international business programs. The latest issue claims to have developed a linear model predicting the school’s ranking (with “1” being the highest ranked school) from it
> An analyst at a business school’s admissions office claims to have developed a valid linear model predicting success (measured by starting salary ($) at time of graduation) from a student’s undergraduate performance (measured by GPA). Describe how you wo
> An economist investigated the association between a country’s Literacy Rate and Gross Domestic Product (GDP) and used the association to draw the following conclusions. Explain why each statement is incorrect. (Assume that all the calculations were done
> An advertising agent who created a regression model using amount spent on Advertising to predict annual Sales for a company made these two statements. Assuming the calculations were done correctly, explain what is wrong with each interpretation. a) My R2
> If you create a regression model for estimating a student’s business school GPA (on a scale of 1–5) based on his math SAT (on a scale of 200–800), is the slope most likely to be closer to 0.01, 1, or 10? Explain.
> If you create a regression model for predicting the sales ($ million) from money spent on advertising the prior month ($ thousand), is the slope most likely to be closer to 0.03, 300, or 3000? Explain.
> An actuary at a mid-sized insurance company is examining the sales performance of the company’s sales force. She has data on the average size of the policy ($) written in two consecutive years by 200 salespeople. She fits a linear model and finds the slo
> Lifetimes of electronic components can often be modeled by an exponential model. Suppose quality control engineers want to model the lifetime of a hard drive to have a mean lifetime of 3 years. a) What value of l should they use? b) With this model, wh
> An analyst at a large credit card bank is looking at the relationship between customers’ charges to the bank’s card in two successive months. He selects 150 customers at random, regresses charges in March ($) on charges in February ($), and finds an R2 o
> Tell what each of the following residual plots indicates about the appropriateness of the linear model that was fit to the data. a) b) c)
> Tell what each of the following residual plots indicates about the appropriateness of the linear model that was fit to the data. a) b) c)
> An online clothing retailer examined their transactional database to see if total yearly Purchases ($) were related to customers’ Incomes ($). (You may assume that the assumptions and conditions for regression are met.) The least square
> As the nature of investing shifted in the 1990s (more day traders and faster f low of information using technology), the relationship between mutual fund monthly performance (Return) in percent and money f lowing (Flow) into mutual funds ($ million) shif
> Perhaps fans are just more interested in teams that win. The displays below are based on American League teams for the 2016 season. (Data in Attendance 2016) a) Do winning teams generally enjoy greater attendance at their home games? Describe the assoc
> American League baseball games are played under the designated hitter rule, meaning that pitchers, often weak hitters, do not come to bat. Baseball owners believe that the designated hitter rule means more runs scored, which in turn means higher attendan
> From the linear model fit to the data on GDP growth of Exercise 46: a) Write the equation of the regression line. b) What is the meaning of the intercept? Does it make sense in this context? c) Interpret the meaning of the slope. d) In a year in whic
> From the linear model fit to the data on GDP growth in Exercise 45: a) Write the equation of the regression line. b) What is the meaning of the intercept? Does it make sense in this context? c) Interpret the meaning of the slope. d) In a year in which
> Is economic growth in Europe related to growth in the United States? Here’s a scatterplot of the average growth in the 19 European countries (% of Gross Domestic Product) vs. the growth in the United States. Each point represents one of
> The U.S. Fish and Wildlife Service plans to study the fishing industry around Saginaw Bay. To do that, they decide to randomly select five fishing boats at the end of a randomly chosen fishing day and count the numbers and types of all the fish on those
> For the following experiment, identify the experimental units, the treatments, the response, and the random assignment. An investment club decided to compare investment strategies. Starting with nine equal investment amounts, three invested in the “dogs
> Is economic growth in the developing world related to growth in the industrialized countries? Here’s a scatterplot of the growth (in % of Gross Domestic Product) of the least developed countries (as classified by the UN) vs. the growth
> An economics student is studying the American economy and finds that the correlation between the inflation-adjusted Dow Jones Industrial Average and the Gross Domestic Product (GDP) (also inflation adjusted) is 0.85 for the years 1961 to 2016. (www.measu
> Is the number of total rooms in the house associated with the price of a house? Here is the scatterplot of a random sample of homes for sale: a) Is there an association? b) Check the assumptions and conditions for correlation. Homes for Sale 6 4+ 1
> In 2008, the EPA revised their methods for estimating the fuel efficiency (mpg) of cars—a factor that plays an increasingly important role in car sales. How do the new highway and city estimated mpg values relate to each other? Here&aci
> The environmental advocacy group from Exercise 5 that was interested in gauging perceptions about climate change among organic farmers has decided to use a different method to sample. Instead of randomly selecting members from a shuffled list, they liste
> As discussed in the chapter, GfK Roper Consulting conducts a global consumer survey to help multinational companies understand different consumer attitudes throughout the world. In India, the researchers interviewed 1000 people aged 13–65 (www.gfkamerica
> An airline company is interested in the opinions of their frequent f lyer customers about their proposed new routes. Specifically they want to know what proportion of them plan to use one of their new hubs in the next six months. They take a random sampl
> An environmental advocacy group is interested in the perceptions of farmers about global climate change. Specifically, they wish to determine the percentage of organic farmers who are concerned that climate change will affect their crop yields. They use
> Indicate whether each statement below is true or false. If false, explain why. a) To get a representative sample, you must sample a large fraction of the population. b) Using modern methods, it is best to select a representative subset of a population
> For your marketing class, you’d like to take a survey from a sample of all the Catholic Church members in your city to assess the market for a DVD about Pope Francis’s first year as pope. A list of churches shows 17 Catholic churches within the city limi
> Indicate whether each statement below is true or false. If false, explain why. a) We can eliminate sampling error by selecting an unbiased sample. b) Randomization helps to ensure that our sample is representative. c) Sampling error refers to sample-t
> For the following observational studies, indicate whether they are prospective or retrospective studies. a) An airline was concerned that new security measures might discourage air travelers. A year after the new security restrictions were put into plac
> For Exercises 11 and 12, identify the following if possible. (If not, say why.) a) The population b) The population parameter of interest c) The sampling frame d) The sample e) Any potential sources of bias you can detect and any problems you see in
> For Exercises 11 and 12, identify the following if possible. (If not, say why.) a) The population b) The population parameter of interest c) The sampling frame d) The sample e) Any potential sources of bias you can detect and any problems you see in
> The airline company from Exercise 6, interested in the opinions of their frequent f lyer customers about their proposed new routes, has decided that different types of customers might have different opinions. Of their customers, 50% are silver-level, 30%
> What percent of a standard Normal model is found in each region? Be sure to draw a picture first. a) z > 1.5 b) z < 2.25 c) -1 < z < 1.15 d) z > 0.5
> Some IQ tests are standardized to a Normal model with a mean of 100 and a standard deviation of 16. a) Draw the model for these IQ scores. Clearly label it, showing what the 68–95–99.7 Rule predicts about the scores. b) In what interval would you expec
> The Environmental Protection Agency (EPA) fuel economy estimates for automobiles suggest a mean of 24.8 mpg and a standard deviation of 6.2 mpg for highway driving. Assume that a Normal model can be applied. a) Draw the model for auto fuel economy. Clea
> The pediatrician in Exercise 4 explains to the parents that the most extreme 5% of cases often require special treatment or attention. a) Does this child fall into that group? b) What do you need to assume about the heights of 2-year-olds to find your
> Indicate whether each statement below is true or false. If false, explain why. a) Asking viewers to call into an 800 number is a good way to produce a representative sample. b) When writing a survey, it’s a good idea to include as many questions as pos
> Your company will admit to the executive training program only people who score in the top 3% on the executive aptitude test discussed in Exercise 3. a) With your z-score of 2.20, did you make the cut? b) What do you need to assume about test scores to
> After examining a child at his 2-year checkup, the boy’s pediatrician said that the z-score for his height relative to American 2-year-olds was -1.88. Write a sentence to explain to the parents what that means.
> Your company’s Human Resources department administers a test of “Executive Aptitude.” They report test grades as z-scores, and you got a score of 2.20. What does this mean?
> 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 first statistics exam had a mean of 65 and a standard deviation of 10 points; the second had a mean of 80 and a standard deviation of 5 points. Derrick scored an 80 on both tests. Julie scored a 70 on the first test and a 90 on the second. They both
> 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
> Shortly after the introduction of the Belgian euro coin, newspapers around the world published articles claiming the coin is biased. The stories were based on reports that someone had spun the coin 250 times and gotten 140 heads—that’s 56% heads. a) Use
> Because many passengers who make reservations do not show up, airlines often overbook f lights (sell more tickets than there are seats). A Boeing 767-400ER holds 245 passengers. If the airline believes the rate of passenger no-shows is 5% and sells 255 t
> In the 4 * 100 medley relay event, four swimmers swim 100 yards, each using a different stroke. A college team preparing for the conference championship looks at the times their swimmers have posted and creates a model based on the following assumptions:
> For a new type of tire, a NASCAR team found the average distance a set of tires would run during a race is 168 miles, with a standard deviation of 14 miles. Assume that tire mileage is independent and follows a Normal model. a) If the team plans to chang
> Indicate whether each statement below is true or false. If false, explain why. a) A local television news program that asks viewers to call in and give their opinion on an issue typically results in a biased voluntary response sample. b) Convenience sa
> Has the Consumer Price Index (CPI) fluctuated around its mean according to a Normal model? Here are some displays. Is a Normal model appropriate for these data? Explain. 800 E 600 400 200 0.0 75.0 150.0 225.0 CPI 200 150 100 50 + -2 2 Nscores
> Speeds of cars were measured as they passed one point on a road to study whether traffic speed controls were needed. Here’s a histogram and normal probability plot of the measured speeds. Is a Normal model appropriate for these data? Ex
> In a standard Normal model, what value(s) of z cut(s) off the region described? Remember to draw a picture first. a) the lowest 12% b) the highest 30% c) the highest 7% d) the middle 50%
> In a standard Normal model, what value(s) of z cut(s) off the region described? Don’t forget to draw a picture. a) the highest 20% b) the highest 75% c) the lowest 3% d) the middle 90%
> What percent of a standard Normal model is found in each region? Draw a picture first. a) z > -2.05 b) z < -0.33 c) 1.2 < z < 1.8 d) | z | < 1.28
> An incoming MBA student took placement exams in economics and mathematics. In economics, she scored 82 and in math 86. The overall results on the economics exam had a mean of 72 and a standard deviation of 8, while the mean math score was 68, with a stan
> Given independent random variables, X and Y, with means and standard deviations as shown, find the mean and standard deviation of each of the variables in parts a to d. a) 3X b) Y + 6 c) X + Y d) X - Y Mean SD 10 20 5 2.
> A marketing agency has developed three vacation packages to promote a timeshare plan at a new resort. They estimate that 20% of potential customers will choose the Day Plan, which does not include overnight accommodations; 40% will choose the Overnight P
> An orthodontist has three financing packages, and each has a different service charge. He estimates that 30% of patients use the first plan, which has a $10 finance charge; 50% use the second plan, which has a $20 finance charge; and 20% use the third pl
> Find the standard deviation of the day trader’s option value in Exercise 4. Exercise 4: A day trader buys an option on a stock that will return $100 profit if the stock goes up today and lose $400 if it goes down. If the trader thinks there is a 75% cha
> Here are more proposed survey questions for the survey in Exercise 15: Question 3: Do you find that the slow speed of DSL Internet access reduces your enjoyment of web services? Question 4: Given the growing importance of high-speed Internet access for y
> Find the standard deviation of the book purchases in Exercise 3. Exercise 3: Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.5, 0.3, and 0.2, respectively. What is the expected number of books a customer w
> A day trader buys an option on a stock that will return $100 profit if the stock goes up today and lose $400 if it goes down. If the trader thinks there is a 75% chance that the stock will go up, a) What is her expected value of the option’s profit? b)
> Suppose that the probabilities of a customer purchasing 0, 1, or 2 books at a book store are 0.5, 0.3, and 0.2, respectively. What is the expected number of books a customer will purchase?
> For the website described in Exercise 21, let Y = the total time (in minutes) that a customer spends during a visit to the website. a) What are the possible values of this random variable? b) Is the random variable discrete or continuous?
> You have just launched the website for your company that sells nutritional products online. Suppose X = the number of different pages that a customer hits during a visit to the website. a) Assuming that there are n different pages in total on your websi
> Replacing the buttons with snaps increases the probability of a flaw to 0.003, but the inspector can check 70 shirts an hour (still with 6 snaps each). Now what is the probability she finds no snap f laws
> The database also, of course, includes each employee’s compensation. a) Is this variable discrete or continuous? b) What are the possible values it can take on?
> A manufacturer of clothing knows that the probability of a button f law (broken, sewed on incorrectly, or missing) is 0.002. An inspector examines 50 shirts in an hour, each with 6 buttons. Using a Poisson probability model: a) What is the probability t
> As in Exercise 17, you are phoning local businesses. You call three firms. What is the probability that all three are owned by women?
> The U.S. Census Bureau’s 2012 Survey of Business Owners (www.census.gov/newsroom/press-releases/2015/ cb15-209.html) showed that 35.8% of all non-farm businesses are owned by women. You are phoning local businesses and assume that the national percentage
> An intern is working for Pacific TV (PTV), a small cable and Internet provider, and has proposed some questions that might be used in the survey to assess whether customers are willing to pay $50 for a new service. Question 1: If PTV offered state-of-the
> Through the career services office, you have arranged preliminary interviews at four companies for summer jobs. Each company will either ask you to come to their site for a follow-up interview or not. Let X be the random variable equal to the total numbe
> At many airports, a traveler entering the U.S. is sent randomly to one of several stations where his passport and visa are checked. If each of the 6 stations is equally likely, can the probabilities of which station a traveler will be sent be modeled wit
> At the airport entry sites, a computer is used to randomly decide whether a traveler’s baggage should be opened for inspection. If the chance of being selected is 12%, can you model your chance of having your baggage opened with a Bernoulli model? Check
