A company selling glass ornaments by mail-order expects, from previous history, that 6% of the ornaments it ships will break in shipping. You purchase two ornaments as gifts and have them shipped separately to two different addresses. What is the probability that both arrive safely? What did you assume?
> 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
> Which of these situations fit the conditions for using Bernoulli trials? Explain. a) You are rolling 5 dice and need to get at least two 6s to win the game. b) We record the distribution of home states of customers visiting our website. c) A committee co
> A broker has calculated the expected values of two different financial instruments X and Y. Suppose that E(X) = $100, E(Y) = $90, SD(X) = $12, and SD(Y) = $8. Find each of the following. a) E(X + 10) and SD(X + 10) b) E(5Y) and SD(5Y) c) E(X + Y) and SD(
> 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) X - 20 b) 0.5Y c) X + Y d) X - Y Mean SD X 80 12 Y 12 3.
> A company’s employee database includes data on whether or not the employee includes a dependent child in his or her health insurance. a) Is this variable discrete or continuous? b) What are the possible values it can take on?
> Using the table from Exercise 7, a) What is the probability that a randomly selected U.S. adult who is a Republican believes that global warming is a serious issue? b) What is the probability that a randomly selected U.S. adult is a Republican given that
> Multigenerational families can be categorized as having two adult generations, such as parents living with adult children, “skip” generation families, such as grandparents living with grandchildren, and three or more g
> The airline company in Exercise 6 has realized that some of its customers don’t have e-mail or don’t read it regularly. They decide to restrict the mailing only to customers who have recently registered for a “Win a trip to Miami” contest, figuring that
> The following contingency table shows opinion about global warming among U.S. adults, broken down by political party affiliation (based on a poll in October 2012 by Pew Research found at www.people-press.org/2012/10/15/ more-say-there-is-solid-evidence-o
> For the data in Exercise 2: a) Would you expect the mean purchase to be smaller than, bigger than, or about the same size as the median? Explain. b) Find the mean purchase. c) Find the median purchase.
> For the data in Exercise 1: a) Would you expect the mean age to be smaller than, bigger than, or about the same size as the median? Explain. b) Find the mean age. c) Find the median age.
> At your school, 10% of the class are marketing majors. If you are randomly assigned to two partners in your statistics class, a) What is the probability that the first partner will be a marketing major? b) What is the probability that the first partner
> For the histogram you made in Exercise 2a: a) Is the distribution unimodal or multimodal? b) Where is (are) the mode(s)? c) Is the distribution symmetric? d) Are there any outliers?
> For the histogram you made in Exercise 1a: a) Is the distribution unimodal or multimodal? b) Where is (are) the mode(s)? c) Is the distribution symmetric? d) Are there any outliers?
> The five-number summary for the ages of 100 respondents to a survey on cell phone use looks like this: Are there any outliers in these data? How can you tell? What might your next steps in the analysis be? Min Q1 Med Q3 Max 13 24 38 49 256
> The five-number summary for the total revenue (in $M) of the top 100 movies of 2015 looks like this: (Data selected from Movies 06-15) Are there any outliers in these data? How can you tell? What might your next steps in the analysis be? Min Q1 Med
> Recall the distributions of the weekly sales for the regional stores in Exercise 19. Following are boxplots of weekly sales for this same food store chain for three stores of similar size and location for two different states: Massachusetts (MA) and Conn
> As the new manager of a small convenience store, you want to understand the shopping patterns of your customers. You randomly sample 20 purchases from yesterday’s records (all purchases in U.S. dollars): a) Make a histogram of the dat
> An intern for the environmental group in Exercise 5 has decided to make the survey process simpler by calling 150 of the members who attended the recent symposium on coping with climate change that was recently held in Burlington, VT. He has all the phon
> Here are boxplots of the weekly sales (in $ U.S.) over a two-year period for a regional food store for two locations. Location #1 is a metropolitan area that is known to be residential where shoppers walk to the store. Location #2 is a suburban area wher
> The store manager from Exercise 2 has collected data on purchases from weekdays and weekends. Here are some summary statistics (rounded to the nearest dollar): Weekdays: n = 230 Min = 4, Q1 = 28, Median = 40, Q3 = 68, Max = 95 Weekends: n = 150 Min = 10,
> The survey from Exercise 1 had also asked the customers to say whether they were male or female. Here are the data: Construct boxplots to compare the ages of men and women and write a sentence summarizing what you find. Age Sex Age Sex Age Sex Age
> A survey of major universities asked what percentage of incoming freshmen usually graduate “on time” in 4 years. Use the summary statistics given to answer these questions. a) Would you describe this distribution as
> A recent survey found that, despite airline requests, about 40% of passengers don’t fully turn off their cell phones during takeoff and landing (although they may put them in “airplane mode”). The two passengers across the aisle (in seats A and B) clearl
> Here are summary statistics for the sizes (in acres) of upstate New York vineyards from Exercise 10. a) From the summary statistics, would you describe this distribution as symmetric or skewed? Explain. b) From the summary statistics, are there any ou
> For the data in Exercise 2: a) Draw a boxplot using the quartiles from Exercise 8b. b) Does the boxplot nominate any outliers? c) What purchase amount would be considered a high outlier? Exercise 2: As the new manager of a small convenience store, you w
> For the data in Exercise 1: a) Draw a boxplot using the quartiles from Exercise 7b. b) Does the boxplot nominate any outliers? c) What age would be considered a high outlier?
> Using the purchases from Exercise 2: a) Standardize the minimum and maximum purchase using the mean from Exercise 6b and the standard deviation from Exercise 8d. b) Which has the more extreme z-score, the min or the max? c) How large a purchase would a p
> Using the ages from Exercise 1: a) Standardize the minimum and maximum ages using the mean from Exercise 5b and the standard deviation from b) Which has the more extreme z-score, the min or the max? c) How old would someone with a z-score of 3 be?
> The investment club described in Exercise 2 decided to repeat their experiment in a different way. Three members of the club took responsibility for one of each of the three investment “strategies,” making the final choices and allocations of investment
> Adair Vineyard is a 10-acre vineyard in New Paltz, New York. The winery itself is housed in a 200-year-old historic Dutch barn, with the wine cellar on the first f loor and the tasting room and gift shop on the second. Since they are relatively small and
> For the table in Exercise 7: b) Looking at the column percentages in part a, does the tenure distribution (how long the employee has been with the company) for each educational level look the same? Comment briefly. c) Make a segmented or stacked bar char
> In addition to their age levels, the movie audiences in Exercise 2 were also asked if they had seen the movie before (Never, Once, More than Once). Here is a table showing the responses by age group: a) Find the marginal distribution of their previous
> From Exercise 1, we also have data on how long each person has been with the company (tenure) categorized into three levels: less than 1 year, between 1 and 5 years, and more than 5 years. A table of the two variables together looks like: a) Find the m
> For the same kind of lottery as in Exercise 3, which of the following strategies can improve your chance of winning? If the method works, explain why. If not, explain why using appropriate statistics terms. a) Choose randomly from among the numbers that
> For the ages described in Exercise 2: a) Write two to four sentences summarizing the distribution. b) What possible problems do you see in concluding that the age distribution from these surveys accurately represents the ages of the national audience for
> For the educational levels described in Exercise 1: a) Write two to four sentences summarizing the distribution. b) What conclusions, if any, could you make about the educational level at other companies? Exercise 1: As part of the human resource group
> From the age distribution data described in Exercise 2: a) Make a bar chart using counts on the y-axis. b) Make a relative frequency bar chart using percentages on the y-axis. c) Make a pie chart.
> From the educational level data described in Exercise 1: a) Make a bar chart using counts on the y-axis. b) Make a relative frequency bar chart using percentages on the y-axis. c) Make a pie chart.
> In the experiment described in Exercise 1, in fact the study also compared the use of butter or margarine in the recipes. The design was balanced, with each combination of chip type and oil type tested. a) What were the factors and factor levels? b) Wh
> As part of the marketing group at Pixar, you are asked to find out the age distribution of the audience of Pixar’s latest film. With the help of 10 of your colleagues, you conduct exit interviews by randomly selecting people to question at 20 different m
> A student finds data on an Internet site that contains financial information about selected companies. He plans to analyze the data and use the results to develop a stock investment strategy. What kind of data source is he using? What concerns might you
> For the real estate data of Exercise 1, do the data appear to have come from a designed survey or experiment? What concerns might you have about drawing conclusions from this data set? Data Table from Exercise 1: House_ID Neighborhood Mail_ZIP Acre
> Referring to the bookstore data table of Exercise 2, a) For each variable, would you describe it as primarily categorical, or quantitative? If quantitative, what are the units? If categorical, is it ordinal or simply nominal? b) Are these data a time se
> Referring to the real estate data table of Exercise 1, a) For each variable, would you describe it as primarily categorical, or quantitative? If quantitative, what are the units? If categorical, is it ordinal or simply nominal? b) Are these data a time
> A local bookstore is keeping a database of its customers to find out more about their spending habits so that the store can start to make personal recommendations based on past purchases. Here are the first five rows of their database: a) What does a row
> In many state lotteries, you can choose which numbers to play. Consider a common form in which you choose 5 numbers. Which of the following strategies can improve your chance of winning? If the method works, explain why. If not, explain why using appropr
> A real estate major collected information on some recent local home sales. The first 6 lines of the database appear below. The columns correspond to the house identification number, the community name, the ZIP code, the number of acres of the property, t
> For the table in Exercise 8: a) Find the column percentages. b) Looking at the column percentages in part a, does the distribution of how many times someone has seen the movie look the same for each age group? Comment briefly. c) Make a segmented bar cha
> As part of the human resource group of your company you are asked to summarize the educational levels of the 512 employees in your division. From company records, you find that 164 have no college degree (None), 42 have an associate’s degree (AA), 225 ha
> Is the experiment of Exercise 5 blind? Could it be made double blind? Explain. Exercise 5: An Internet sale site randomly sent customers to one of three versions of its welcome page. It recorded how long each visitor stayed in the site. Here is a diagra
> For the following experiment, identify the experimental units, the treatments, the response, and the random assignment. A commercial food lab compared recipes for chocolate chip cookies. They baked cookies with different kinds of chips (milk chocolate,
> Product R is normally sold for $52 per unit. A special price of $42 is offered for the export market. The variable production cost is $30 per unit. An additional export tariff of 30% of revenue must be paid for all export products. Assume there is suffic
