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mathematics
statistics

Questions and Answers of Statistics

Look again at the histograms of test scores for the three Statistics classes in Exercise 57.a) Overall, which class do you think performed better on the test? Why?b) How would you describe the shape
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
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
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
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
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
The 70 mutual funds of Exercise 31 are classified into four types: U.S. Domestic Equity Funds, Bond Funds, International Funds, and Other Funds. Com-pare the 12 month returns of the four types of
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
Each house listed on the multiple listing services (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
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
Buying insurance for property loss from hurricanes has become increasingly difficult since Hurricane Katrina caused record property loss damage. Many companies have refused to renew policies or write
Using the hurricanes data set, examine the number of major hurricanes (category 3, 4, or 5) by every full decade from 1851 to 2000.a) Create a histogram of these data.b) Describe the distribution.c)
For the data in Exercise 1: a) Find the quartiles using your calculator. b) Find the quartiles using Tukey’s method (page 58). c) Find the IQR using the quartiles from part b. d) Find the standard
The 1057 houses described in Exercise 46 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
The data set provided contains the aver-age tuition of private four-year colleges and universities as well as the average 2007–2008 tuitions for each state. The mean tuition charged by a public
FAOSTAT, the Food and Agriculture Organization of the United Nations, collects in-formation on the production and consumption of more than 200 food and agricultural products for 200 countries around
The World Bank, through their Doing Business project (www.doingbusiness.org), ranks nearly 200 economies on the ease of doing business. One of their rankings measures the ease
The data set provided contains U.S. regular retail gasoline prices (cents/gallon) from August 20, 1990 to January 2, 2012, from a national sample of gasoline stations obtained from the U.S.
Standard and Poor’s Case-Shiller® Home Price Index measures the residential housing market in metropolitan regions across the United States. The national index, Composite.10, is a composite of
The histogram shows the monthly U.S. unemployment rate from January 2003 to January 2013 (data.bls.gov/timeseries/LNS14000000).Here is the time series plot for the same data.a) What features of the
Here is a histogram of the monthly CPI as reported by the Bureau of Labor Statistics (ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt) from 2008 through 2012:Here is the time series plot for the
Here is a histogram of the assets (in millions of dollars) of 79 companies chosen from the Forbes list of the nation€™s top corporations.a) What aspect of this distribution makes it
For the data in Exercise 1: a) Find the quartiles using your calculator. b) Find the quartiles using Tukey’s method. c) Find the IQR using the quartiles from part b. d) Find the standard deviation.
Here are the same data you saw in Exercise 79 after re-expressions as the square root of assets and the logarithm of assets.a) Which re-expression do you prefer? Why? b) In the square root
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
The S&P/Case-Shiller Home Price Indices provide measures of the U.S. residential housing market. They track changes in the value of residential real estate nationally and in 20 metropolitan
The dataset States contains various educational and economic measures of the 50 U.S. states, including the District of Columbia. Examine the variables, commenting on their shape, center, and spread
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
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
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
For the hard drive data in Exercise 2, some research on the prices discovered that the 200 GB hard drive was a special €œhardened€ drive designed to resist physical shocks and
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,
For the disk drives in Exercise 2 (as corrected in Exercise 12), we want to predict Price from Capacity. a) Find the slope estimate, b1. b) What does it mean, in this context? c) Find the intercept,
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
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?
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
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
For the regression model for the bookstore of Exercise 1, what is the value of R2 and what does it mean?
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 survey of prices for external disk drives found the
For the disk drive data of Exercise 2 (as corrected in Exercise 12), find and interpret the value of R2.
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,
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
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
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?
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)(2) (3) (4)
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
Owners of a new coffee shop tracked sales for the first 20 days and displayed the data in a scatterplot (by day).a) Make a histogram of the daily sales since the shop has been in business. b) State
Here are several scatterplots. The calculated correlations are €”0.923, €”0.487, 0.006, and 0.777. Which is which?a)b) c) d)
Here are several scatterplots. The calculated correlations are €”0.977, €”0.021, 0.736, and 0.951. Which is which?a)b) c) d)
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: Saks = 141,865.53 -
Price of a 2012 Honda Civic EX (in $) from its Mileage (in miles) was fit to 18 cars that were available during the week of March 1, 2013 (Kelly’s Blue Book, www.kbb.com) within 200 miles of San
Is there a relationship between total team salary and the performance of teams in the National Football League (NFL)? For the 2012-2013 season, a linear model predicting Wins (out of 16 regular
In 2012, the New York Yankees won 95 games and spent $198 million on salaries for their players (USA Today). Is there a relationship between salary and team performance in Major League Baseball? For
Pizza sales and price, part 2. 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
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
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.
The scatterplot shows, for 2013 cars, the carbon footprint (tons of CO2 per mile) vs. the new Environmental Protection Agency (EPA) high-way mileage for 76 family sedans as reported by the U.S.
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
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
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
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 180 developing
Is economic growth in Europe related to growth in the United States? Here€™s a scatterplot of the average growth in 25 European countries (in % of Gross Domestic Product) vs. the growth in
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)
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)
American League baseball games are played under the designated hitter rule, meaning that weak-hitting pitchers do not come to bat. Baseball owners believe that the designated hitter rule means more
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)
Perhaps fans are just more interested in teams that win. Here are displays of other variables in the dataset of exercise 49 (espn.go.com). Are the teams that win necessarily those that score the most
As the nature of investing shifted in the 1990s (more day traders and faster flow of information using technology), the relationship between mutual fund monthly performance (Return) in percent and
An online clothing retailer examined their transactional database to see if total yearly Purchases ($) were related to customers’ Incomes ($). (You may assume that the assumptions and conditions
Tell what each of the following residual plots indicates about the appropriateness of the linear model that was fit to the data.a)b)c)
Tell what each of the following residual plots indicates about the appropriateness of the linear model that was fit to the data.a)b) c)
An analyst at a large credit card bank is looking at the relationship between customers’ charges to the bank’s card in two successive months. He selects 150 customers at random, regresses charges
An actuary at a mid-sized insurance company is examining the sales performance of the company’s sales force. She has data on the average size of the policy ($) written in two consecutive years by
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?
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,
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,
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)
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
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
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
A business student needs cash, so he decides to sell his car. The car is a valuable BMW 850CSi that was only made over the course of a few years in the 1990s. He would like to sell it on his own,
Use the advertised prices for BMW 850s 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)
The Worldwide Cost of Living Survey City Rankings determine the cost of living in the most expensive cities in the world as an index. This index scales New York City as 100 and expresses the cost of
The demand for lobster has grown steadily for several decades. The Maine lobster fishery is carefully controlled to protect the lobster population from over-fishing. The number of fishing licenses
Concern over the weather associated with El Nino has increased interest in the possibility that the climate on Earth is getting warmer. The most common theory relates an increase in atmospheric
The table shows the number of live births per 1000 women aged 15-44 years in the United States, starting in 1965. (National Center for Health Statistics, www.cdc.gov/nchs/)a) Make a scatterplot and
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
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
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 j'-values
Philanthropic organizations often rely on contributions from individuals to finance the work that they do, and a national veterans€™ organization is no exception. The Paralyzed Veterans of
Fuel efficiency Both drivers and auto companies are motivated to raise the fuel efficiency of cars. Recent information posted by the U.S. government proposes some simple ways to increase fuel
Indicate which of the following represent independent events. Explain briefly. a) The gender of customers using an ATM machine. b) The last digit of the social security numbers of students in a
Using the table from Exercise 8,a) What is the probability that a randomly selected Black multigenerational family is a 2 Adult Generation family?b) What is the probability that a randomly selected
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)
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
Summit Projects provides marketing services and website management for many companies that specialize in outdoor products and services (www.summitprojects.com). To understand customer Web behavior,
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
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
U.S. Customs and Border Protection have been testing automated kiosks that may be able to detect lies. One measurement used (among several) is involuntary eye movements. Using this method alone,
Respond to the following questions: a) A casino claims that its roulette wheel is truly random. What should that claim mean? b) A reporter on Market Place says that there is a 50% chance that the

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