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Why is it worth the effort to learn about statistics Please answer for management in general. 


How should statistical analysis and business experience interact with each other?

What is the design phase of a statistical study?

What can a statistical model help you accomplish? Which basic activity of statistics can help you choose an appropriate model for your data?

Are statistical estimates always correct? If not, what else will you need (in addition to the estimated values) in order to use them effectively?

Why is a confidence interval more useful than an estimated value?

Overseas sales dropped sharply last month, and you do not know why. Moreover, you realize that you do not even have the numbers needed in order to tell what the problem is. You call a meeting to discuss how to solve the problem. Which statistical activity is involved at this stage?

If your factories produce too much, then you will have to pay to store the extra inventory. If you produce too little, then customers will be turned away and profits will be lost. Therefore, you would like to produce exactly the right amount to avoid these costs to your company. Unfortunately, however, you do not know the correct production level. Which is the main statistical activity required to solve this problem?

Before you proceed with the analysis of a large accounting data set that has just been collected, your boss has asked you to take a close look at the data to check for problems and surprises and ensure its basic integrity. Identify the basic statistical activity you are performing.

Your company has been collecting detailed data for years on customer contacts, including store purchases, telephone inquiries, and Internet orders, and you would like to systematically use this resource to learn more about your customers and, ultimately, to improve sales. What is the name of the collection of methods that will be most useful to you in this project?

Your work group would like to estimate the size of the market for high-quality stereo components in New Orleans but cannot find any reliable data that are readily available. Which basic activity of statistics is involved initially in proceeding with this project?

You are wondering whom to interview, how many to interview, and how to process the results so that your questions can be answered at the lowest possible cost. Identify the basic activity of statistics involved here.

You have collected and explored the data on Internet information requests. Before continuing on to use the data for estimation and hypothesis testing, you want to develop a framework that identifies meaningful parameters to describe relationships in the data. What basic activity of statistics is involved here?

Your firm has been accused of discrimination. Your defense will argue in part that the imbalance is so small that it could have happened at random and that, in fact, no discrimination exists. Which basic activity of statistics is involved?

By looking carefully at graphs of data, your marketing department has identified three distinct segments of the marketplace with different needs and price levels. Which basic activity of statistics helped you to obtain this helpful information?

You are trying to determine the quality of the latest shipment of construction materials based on careful observation of a sample. Which basic activity of statistics will help you reach your goal?

You think that one of the machines may be broken, but you are not sure because even when it is working properly there are a few badly manufactured parts. When you analyze the rate at which defective parts are being produced to decide whether or not there has been an increase in the defect rate, which basic activity of statistics is involved?

Your boss has asked you to take a close look at the marketing data that just came in and would like you to report back with your overall impressions of its quality and usefulness. Which main activity of statistics will you be performing?

Using data on the characteristics of houses that sold recently in a city of interest, you would like to specify the way in which features such as the size (in square feet) and number of bedrooms relate to the sale price. You are working out an equation that asserts that the sales price is given by a formula that involves the house’s characteristics and parameters (such as the dollar value of an additional bedroom) that are estimated from the data. What main activity of statistics are you involved with?

The results of the customer survey just arrived as a spreadsheet from the firm that was hired to do the research, and you are eager to understand what can be learned from these responses. Naturally you will be producing charts and summaries in order to obtain an overall impression of this new information (the firm did not provide these …). Which main activity of statistics is most strongly related to your work?

While your longer-term goal is to better understand your customer base by seeing how their attitudes correlate with purchasing activity, you realize that (at the moment) the information you would need to do this is not available. Thus your immediate task is to figure out how to survey customers in depth to gather this information. Which of the main activities of statistics is most directly involved in your immediate task? Please give its name and the reason for your choice.

What is a data set?

What is a variable?

What is an elementary unit?

In what way do bivariate data represent more than just two separate univariate data sets?

What can be done with multivariate data?

What can be done with multivariate data?

What are the qualitative data?

Which are simpler to analyze, time-series or cross-sectional data?

Choose a firm and identify a database (in general terms) that would be important to it. Identify three different kinds of data sets contained within this database. For each of these three data sets, identify the elementary unit and indicate what might be learned from an appropriate analysis.

Classify a data set found on the Internet consisting of sales, profits, and number of employees for 100 banking firms. Be sure to provide standard information about the number of variables, who controlled the design of the data-gathering plan, and whether or not the data were recorded in a meaningful sequence.

If you think about a telephone directory as a large data set, what are the elementary units?

In order to figure out how much of the advertising budget to spend on various types of media (TV, radio, newspapers, etc.), you are looking at a data set that lists how much each of your competitors spent last year for TV, how much they spent for radio, and how much for newspaper advertising. Give a complete description of the type of data set you are looking at.

Your firm’s sales, listed each quarter for the past 5 years, should be helpful for strategic planning. 

a. Is this data set cross-sectional or time-series? 

b. Is this univariate, bivariate, or multivariate data?

Consider a listing of the bid price and the ask price for 18 different U.S. Treasury bonds at the close of trading on a particular day. 

a. Is this univariate, bivariate, or multivariate data? 

b. Is this cross-sectional or time-series data?

You are looking at the sales figures for 35 companies. 

a. Is this data set univariate, bivariate, or multivariate? 

b. Is this variable qualitative or quantitative? 

c. Is this variable ordinal, nominal, or neither?

A quality control inspector has rated each batch produced today on a scale from A through E, where A represents the best quality and E is the worst. 

a. Is this variable quantitative or qualitative? 

b. Is this variable ordinal, nominal, or neither?

One column of a large inventory spreadsheet shows the name of the company that sold you each part. 

a. Is this variable quantitative or qualitative? 

b. Is this variable ordinal, nominal, or neither?

Consider the information about selected cell phones shown in Table 2.6.5. 

a. What is an elementary unit for this data set? 

b. Is this a univariate, bivariate, or multivariate data set? 


c. Is this a cross-sectional or time-series data set? 

d. Is “Operating System” quantitative, ordinal, or nominal? 

e. Is “Price” quantitative, ordinal, or nominal? 

f. Is “Screen Size” quantitative, ordinal, or nominal?

Suppose a database includes the variable “security type” for which 1= common stock, 2 = preferred stock, 3 = bond, 4 = futures contract, and 5 = option. Is this a quantitative or qualitative variable?

The ease of assembling products is recorded using the scale 1 = very easy, 2 = easy, 3 = moderate, 4 = difficult, 5 = very difficult. Is this a quantitative, ordinal, or nominal variable?

Suppose a data set includes the variable “business organization” recorded as 1 = sole proprietor, 2 = partnership, 3 = S corporation, 4 = C corporation. Is this a quantitative or qualitative variable?

As part of your firm’s loyalty system, there is a database with information about customers who have joined, including the size of their immediate family, the number of cars they own, and their income. 

a. Based only on this information, does this database consist of information from an observational study or from an experiment? 

b. You have proposed sending free samples to customers with large families and then measuring the size of future orders. If you decide randomly for each large family whether or not they would receive free samples, would the resulting data come from an observational study or an experiment?

What is a list of numbers?

What is a number line?

When a real data set is normally distributed, should you expect the histogram to be a perfectly smooth bell-shaped curve? Why or why not?

Are all data sets normally distributed?

What is an outlier?

When is it appropriate to set aside an outlier and analyze only the rest of the data?

Suppose there is an outlier in your data. You plan to analyze the data twice: once with and once without the outlier. What result would you be most pleased with? Why?

What distribution shape is represented by the histogram in Fig. 3.8.1 of voltages measured for incoming components as part of a quality control program? 


Fig 3.8.1

What distribution shape is represented by the histogram in Fig. 3.8.2 of profit margins for consumer products? 


Figure 3.8.2


What distribution shape is represented by the histogram in Fig. 3.8.3 of volume (in thousands of units) by sales region?


Fig. 3.8.3

 

What distribution shape is represented by the histogram in Fig. 3.8.4 of hospital length of stay (in days)? 


Fig. 3.8.4

Consider the yields (as an interest rate, in percent per year) of municipal bonds, as shown in Table 3.8.1. 

a. Construct a histogram of this data set. 

b. Based on the histogram, what values appear to be typical for this group of tax-exempt bonds? 

c. Describe the shape of the distribution. 


Table 3.8.1


Consider CREF, the College Retirement Equities Fund, which manages retirement accounts for employees of nonprofit educational and research organizations. CREF manages a large and diversified portfolio in its growth stock account, somewhere around $22.5 billion. Investment in media represents 5.0% of this portfolio. Data on the market value of these CREF media investments are shown in Table 3.8.4. 


a. Construct a histogram of this data set. 

b. Based on this histogram, describe the distribution of CREF’s investment in the media sector. 

c. Describe the shape of the distribution. In particular, is it skewed or symmetric? 

d. Find the logarithm of each data value. 

e. Construct a histogram of these logarithms. 

f. Describe the distribution shape of the logarithms. In particular, is it skewed or symmetric?

Consider the compensation paid to CEOs of computer programming, data processing, and other related services firms, as shown in Table 3.8.7. 

a. Construct a histogram. 

b. Describe the distribution shape. 

There are many different and varied formats and strategies for radio stations, but one thing they all have in common is the need for an audience in order to attract advertisers. Table 3.8.8 shows the percent of listeners for radio stations in the Albuquerque area (averages for ages 12 and older, 6 am to midnight all week) as a market share in percentage points. 

a. Construct a histogram. 

b. Describe the distribution shape. 

When the Internal Revenue Service (IRS) tax code was revised in 1986, Congress granted some special exemptions to specific corporations. The U.S. government’s revenue losses due to some of these special transition rules for corporate provisions are shown in Table 3.8.11. 

a. Construct a histogram for this data set. 

b. Describe the distribution shape. 

Continuing with the revenue loss data of Table 3.8.11: 

a. Find the logarithm for each data value. Omit the two firms with zero revenue loss from your answers to this problem. 

b. Construct a histogram for this data set. 

c. Describe the distribution shape. 

d. Compare this analysis of the transformed data to your analysis of the original data in problem 19. 



Consider the percentage change in the value of the dollar with respect to Asia-Pacific currencies over approximately three quarters from the start of 2015 through mid-October (Table 3.8.13). 

a. Construct an appropriate histogram of this data set. 

b. Describe the distribution shape. 

Using the data from Table 2.7 of Chapter 2 for the 30 Dow Jones Industrial companies: 

a. Construct a histogram for percent change since January 2015. 

b. Describe the shape of the distribution.

Business firms occasionally buy back their own stock for various reasons, sometimes when they view the market price as a bargain compared to their view of its true worth. It has been observed that the market price of stock often increases around the time of the announcement of such a buyback. Consider the data on actual percent changes over 3 months in stock prices for firms announcing stock buybacks shown in Table 3.8.2. The owners of these firms would probably have preferred to wait a few more months before buying back their stock, given that the crash of 1987 occurred just 1 month later, and the stock could have been bought at a lower price (although this knowledge in hindsight was not available at the time, and this is one aspect of the risk of the stock market). 

a. Construct a histogram of this data set. 

b. Based on this histogram, what can you say to summarize typical behavior of these stock prices following a buyback announcement? 

Using the data from Table 2.8 of Chapter 2 for daily values for the Dow Jones Industrial Average: 

a. Construct a histogram for net change during September 2015. 

b. Describe the shape of the distribution. 

c. Construct a histogram for percent change during September 2015. d. Describe the shape of the distribution.

What is the summarization of a data set? Why is it important?

How should you deal with exceptions when summarizing a set of data?

What is the mode?

What are the quartiles?

What is the five-number summary?

What is a box plot? What additional detail is often included in a box plot?

Your company is trying to estimate the total size of its potential market. A survey has been designed, and data have been collected. A histogram of the data shows a small amount of skewness. Which summary measure would you recommend to the company for this purpose and why?

Some people who work at your company would like to visually compare the income distributions of people who buy various products in order to better understand customer selections. For each of 16 products, a list of incomes of representative customers (who bought that product) has been obtained. What method would you recommend?

Your firm has the following securities outstanding: common stock (market value $4,500,000; investors demand 17% annual rate of return), preferred stock (market value $1,700,000; current annual yield is 13%), and 20-year bonds (market value $2,200,000; current annual yield is 11%). Find your cost of capital.

Active consumers make up 13.6% of the market and spend an average of $16.23 per month on your product. Passive consumers make up 23.8% of the market and spend $9.85. The remaining consumers have average spending of $14.77. Find the average spending for all consumers.

Your marketing research team has identified four distinct groups of people (Type A, B, C, and D, where D represents “all others”) according to personality traits. You figure that market penetration for a new product will be highest among Type A personalities, with 38% purchasing the product within two years. Similarly, for Types B, C, and D, the market penetration will be 23%, 8%, and 3%, respectively. Assume that the personality types represent 18%, 46%, 25%, and 11%, respectively, of your target population. What overall market penetration should you expect among your target population?

A large outdoor recreational facility has three entrances. According to automatic vehicle counters, last year 11,976 vehicles entered at the first entrance, 24,205 at the second, and 7,474 at the third. A survey done at each entrance showed that the average planned length of stay was 3.5 days at the first location, 1.3 days at the second, and 6.0 days at the third. Estimate the typical planned length of stay for the entire facility on a per-vehicle basis.

Given the state taxes and populations for the East North Central States, as shown in Table 4.3.4, compute the percapita state tax burden for this entire region. 

Find the upper quartile for the following box plot. 

Consider the revenues (in $ millions) for the top 12 companies in the Fortune 500 (from http://fortune.com/ fortune500/ accessed October 20, 2015.), as shown in Table 4.3.6. 

a. Find the five-number summary. 

b. Draw a box plot. 


Your factory’s inventory level was measured 12 times last year, with the results shown below. Find the average inventory level during the year. 313, 891, 153, 387, 584, 162, 742, 684, 277, 271, 285, 845

If you had a list of the miles per gallon for various cars, which of the following is the only possibility for the 65th percentile: 65 cars, 65%, $13,860, or 27 miles per gallon? 


For the yields of municipal bonds (Table 3.8.1 in Chapter 3): 

a. Find the average yield. 

b. Find the median yield. 

c. Find the quartiles. 

d. Find the five-number summary. 

e. Draw a box plot of these yields. 

f. Identify the outliers, if any, and draw a detailed box plot. 

g. Draw the cumulative distribution function for the data set. 

h. Find the percentile value of 5.40%. 

i. Find the value of the 60th percentile. 


Table 3.9.1

Using the data from Table 3.8.2 in Chapter 3, find the average and median to summarize the typical size of the market response to stock buyback announcements. 

Using the data from Table 3.8.4 in Chapter 3, for the market values of the portfolio investments of the College Retirement Equities Growth Fund in the media sector: 

a. Find the average market value for these firms’ stock in CREF’s Growth Fund portfolio. 

b. Find the median of these market values. c. Compare the average to the median. 

d. Find the five-number summary. 

e. Draw a box plot, and comment on the distribution shape. In particular, are there any signs of skewness? 

f. Is the relationship between the average and median consistent with the distribution shape? Why or why not? 



A social group shows only movies of 100 min or less at its meetings. Consider the running times of selected films from a video library as shown in Table 4.3.10. 

a. What percentage of these movies can the group show? 

b. What is the name of the longest of these movies that could be shown? 

c. Comment on the relationship between your answer to part a and the percentile ranking of your answer to part b. 


A wine store carries 86 types of wine produced in 2007, 125 types from 2008, 73 from 2009, and 22 from 2010. Identify the types of wine as the elementary units for analysis. 

a. Find the mode of the year of production. What does this tell you? 

b. Find the average year of production and compare it to the mode. 

c. Draw a histogram of year of production. 

d. If the average selling price is $17.99 for 2007 wine, $17.74 for 2008, $18.57 for 2009, and $16.99 for 2010, find the average selling price for all of these types of wine together.

Consider the data on CEO compensation in computer programming, data processing, and other related services firms from Table 3.8.7 of Chapter 3. 

a. Draw a detailed box plot. 

b. Find the 10th percentile of compensation. 


Summarize prices of funeral services using the average and median, based on the data in Table 3.8.10 of Chapter 3. 

Using the data from Table 2.6.7 of Chapter 2 for the 30 Dow Jones Industrial companies percent changes since January 2015: 

a. Find the mean percent change. 

b. Find the median percent change. 

c. Find the five-number summary for percent change. 

d. Draw the box plot for percent change. 

e. Draw the cumulative distribution function for percent change. 

f. Find the percentile of a data value of 5% and the data value of the 80th percentile for percent change. 

Using the data from Table 2.6.8 of Chapter 2 for daily values for the Dow Jones Industrial Average: 

a. Find the mean net change. 

b. Find the median net change. 

c. Find the five-number summary for net change. 

d. Draw a box plot for net change. 

e. Find the mean percent change. 

f. Find the median percent change. 

g. Find the five-number summary for percent change. 

h. Draw a box plot for percent change. 


What is variability?

a. What is the traditional measure of variability? 

b. What other measures are also used?

a. What is the variance?

b. What are the measurement units of the variance?
c. Which is the more easily interpreted variability measure, the standard deviation or the variance? Why?
d. Once you know the standard deviation, does the variance provide any additional real information about the variability?

a. What is the coefficient of variation? 

b. What are the measurement units of the coefficient of variation?

Which variability measure is most useful for comparing variability in two different situations, adjusting for the fact that the situations have very different average sizes? Justify your choice.

Summarize the variability in admission prices for the theme parks shown in Table 5.5.6 by reporting the standard deviation, the range, and the coefficient of variation. 


Consider interest rates on accounts at a sample of local banks: 3.00%, 4.50%, 4.90%, 3.50%, 4.75%, 3.50%, 3.50%, 4.25%, 3.75%, 4.00% 

a. Find the standard deviation of these interest rates. 

b. What does this standard deviation tell you about banks in this area?

Here are weights of recently produced sinks: 20.8, 20.9, 19.5, 20.8, 20.0, 19.8, 20.1, 20.5, 19.8, 20.3, 20.0, 19.7, 20.3, 19.5, 20.2, 20.2, 19.5, 20.5 Find the usual summary measure that tells approximately how far from average these weights are.

Consider the average price of a hotel room in 21 U.S. cities (Table 5.5.8) for the first half of 2015. 

a. Find the average price of a major-city hotel room in the United States, based on this data set. 

b. Find the sample standard deviation of these prices. 

c. What does the standard deviation tell you about hotel prices in major cities in the United States? 

Your costs had been forecast as having an average of $138,000 with a standard deviation of $35,000. You have just learned that your suppliers are raising prices by 4% across the board. Now what are the average and standard deviation of your costs?

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