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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

Use the data given in question 57 to calculate r and R2. Also use your regression results to estimate the graduating GPA for someone who scores 620 on the SAT.Question 57The Department of Accounting
What is the relationship between the correlation coefficient r and the coefficient of determination R2?
What type of correlation (positive, negative, or zero) would you expect from the following pairs of variables?(a) A company’s earnings per share and its dividends per share(b) A company’s
Suppose you are interested in finding the relationship between bond prices and interest rates. You run a regression of bond prices against the prime lending rate and find that the slope of the
Look at the following graph and identify the explained error, the unexplained error, and the total error. y y i = a + bx; X
Briefly explain what the slope of a regression line tells us.
Explain the difference between the coefficient of determination and the adjusted coefficient of determination. Which do you believe provides a better measure of the goodness of fit of a regression?
Use the data and results from question 21 to calculate the standard error of the residuals.Question 21You are given the following information on the heights and weights of 5 people: Weight (pounds)
Look at the scatter diagram given in question 32. Would you expect a regression on that data to produce a high or a low coefficient of determination?Question 32In order to determine whether a company
Two hundred and ten people were asked which TV news programs they usually watch. The answers are compiled in the following table. Can you say that the three networks have audiences of about the same
Do workbooks make a difference in students’ performance? A statistics instructor uses her class as a sample. Do the results suggest that the grade patterns of those who own a workbook and of those
An election was held in a big city whose population is 50 % white, 40 % black, and 10 % Hispanic. Among the elected, 40 council members are white, 30 are black, and 10 are Hispanic. Do we have enough
The president of a local bank suspects that his employees care only about the big customers. He randomly sampled 325 loans made during the last year and asked the borrowers their opinion of the
A gambler wants to know whether the dice used in a casino are fair. If the dice are fair, the probabilities of seeing 1, 2,. . ., 6 are all 1/6 .. The gambler recorded the outcomes of 600 rolls of
A magazine wants to study the relationship between people’s education and the medium they are exposed to the most. Questionnaires were sent to 100 people of different educational backgrounds. The
On November 18, 1980, the Wall Street Journal published a Gallup survey of the opinions of 782 chief executives of US corporations. The 782 chief executives represent samples of 282 fromlarge firms,
Money magazine (Money, March 2003) reports percentage returns and expense ratios for top bond funds under four categories: US government (G), high-yield corporate (H), tax exempt (T), world bond
The rates of returns data from year 2000 to 2009 in Table 4.15 is listed below:At the α = 0.05, can we conclude that the two stocks and the general market generate about the same average rate of
A study by the New York/New Jersey Port Authority on the effects of train ticket prices on the number of passengers produced the following results:(a) Which variable should be the independent
Discuss the standard assumptions for linear regression analysis.
A Department of Agriculture research team has investigated the relationship between the wheat harvest and the amount of fertilizer used.(a) Plot the data.(b) Use the method of least squares to
As vice president in charge of marketing, Bob Seller is interested in the relationship between dollars spent on advertising and the number of widgets his company sells. He has collected the following
Financial economists are often interested in measuring the relationship between the return on an individual stock and the return on the S&P 500.This model is usually referred to as the market
Explain whether you would expect a positive relationship, a negative relationship, or no relationship to exist for the following pairs of data. If you think there is a relationship, identify the
Mary Jones, a professor of statistics, has collected the following sample of hours spent studying for her course and grades received on the midterm exam.(a) Plot the data.(b) Use the method of least
An English professor has estimated the following relationship between English SAT scores (x) and score in the freshman English course (y).where standard deviations are shown in parentheses. The
Elmore Truesdale, vice president in charge of strategic pricing, is trying to find the relationship between the price of widgets and the quantity of widgets sold.Mr. Truesdale has collected the
The following table gives data on personal consumption C and disposable income Yd in the United States. Use the MINITAB or SAS program to answer the following.(a) Plot the data, using C as the
The following table shows the annual rates of return for several assets and the rate of inflation.(a) Use the method of least squares to estimate the relationship between the rate of return on common
Briefly explain the difference between a dependent variable and an independent variable in regression analysis.
What is causality? What is correlation? What is the relationship among casualty, correlation, and regression analysis?
Explain the difference between a population and a subpopulation.
The market model equation in finance is(a) What is the independent variable?(b) What is the dependent variable?(c) What are the regression coefficients? where Rji Rm.t Rjt = aj + BjRm,t + ej, t
What is a scatter diagram? Briefly explain the concept of a regression line in the context of a scatter diagram.
Suppose you collect data on household consumption and income in the United States and estimate the regression equation C–500 + .8 Y, where C = consumption and K = income.(a) Plot the relationship
Suppose you estimate the regression equation y = 5 + .6x(a) What is the dependent variable?(b) What is the independent variable?(c) What is the intercept?(d) What is the slope?
What is a sample? What is a population? Briefly explain how a sample can be used to estimate population parameters.
Briefly explain what we mean by the method of least squares.
You are given the following information on the heights and weights of 5 people:(a) If you are interested in finding the relationship between height and weight, which variable should be the dependent
The consumption function can be estimated by regressing private consumption on GNP. Use the data given in Table 2.2 and the MINITAB or SAS program to estimate the consumption function.Table 2.2
Use the data given in question 21 and the results you got there to plot the regression line. Calculate the estimated values of y and the error from the regression.Question 21You are given the
What do we mean when we say that estimates of a and b determined by the least-squares method are BLUE?
Do you think opinion pattern and year in school are related? Do a 5 % test.Use the following information to answer question. A survey was sent to 400 students to solicit their opinions about a new
Do you think the three different opinions receive about the same amount of support among first-year students? Do a 5 % test.Use the following information to answer question. A survey was sent to 400
Do you think the three different opinions have about the same number of responses? Do a 5 % test.Use the following information to answer question. A survey was sent to 400 students to solicit their
Use the following information to answer question. A survey was sent to 400 students to solicit their opinions about a new rule for using the student centers. Here are the results:Do you think there
An insurance company is interested in knowing the relationship between traffic accident claims arid the type of cars that policyholders drive. The numbers of accidents per 1,000 automobiles during
The accompanying table shows highway patrol data on the numbers of speeding tickets given in the last 3 months. Do the data show that all 3 months have about the same number of tickets? Do a 5 %
In a recent survey, people were asked whether they are happy with the current income tax structure. Do the results that follow support the hypothesis that how people feel about the tax structure
In a poll, people were asked their opinions about the death penalty. The breakdown of the responses is given in the accompanying table. Do the data show that educational level and opinion are
Do the data support the hypothesis that April, May, and June have the same amount of sales? Do a 5 % test, using one-way ANOVA.Use the following information to answer question. A company puts vending
Do a one-way ANOVA to see whether you can argue that the three different locations have different amounts of sales. Use 5 %.Use the following information to answer question. A company puts vending
Use the following information to answer question. A company puts vending machines in different locations. The numbers of sodas sold (in thousands) in the last 3 months are presented in the following
Hannah, a wine dealer, believes that the taste of wine depends on the year the wine was bottled. Do the data she collected from a recent wine-tasting contest support her belief? Do a 5 % test.
The manager in a department store believes that whether a customer pays by cash, charge, or check depends on the amount of money spent. Do the following data support what the manager believes? Do a 5
The demand for different types of automobiles should be related to their owners’ needs. A manager in a local auto dealership randomly pulls samples from the dealership’s customer files. Do the
An advertising agent believes that different types of programs attract audiences of different age groups. She collects the following data to study her claim.Determine, at α = 5 %, whether you can
A consumer rights organization wanted to check out different diet plans. It recruited 33 volunteers and sent them to four different programs. After the first 2 weeks, the weight losses, in pounds,
The dean of the business school wants to find out whether the instructors in four departments are grading students similarly. The following data are compiled.Do you think the grade distribution
A Consumer Protection Coalition decides to study the delay times, in minutes, for four different airlines: A, B, C, and D.It is believed that the average delay times of the 4 airlines are about
The delay times of 200 delayed flights were compiled in the following frequency distribution. The mean is about 45 and the standard deviation is 20. Do the data follow a normal distribution? Do a 5 %
The numbers of missing pieces of luggage are compiled in the following table.Do the data. follow a Poisson distribution? Do a 5 % test. Number of missing Pieces of luggage 0 1 23 3 More than 3 Number
A financial analyst is interested in conducting an extensive study of credit card debt. He wants to know whether the income of cardholders is related to the size of the debt. He compiles the data in
A bank manager is interested in the amount of cash being withdrawn each Friday. He collects data on the last 90 Fridays and compiles them in the accompanying table. The mean is 340 and the standard
Are African–Americans’ opinions equally split among the three categories? Do a 5 % test.Use the following information to answer question. A questionnaire was sent to 200 students on the campus,
The makeup of the student body is 75 % white, 15 % African–American, and 10 % Asian–American. If the samples are randomly selected, the samples’ ethnic distribution should be similar to the
Are ethnic background and opinion on this issue related? Do a 5 % test.Use the following information to answer question. A questionnaire was sent to 200 students on the campus, asking them to
There are many books to help people learn to use computer software packages.An instructor checked these books and found that they are all of similar quality.He picked four books and used them in his
It is believed that the quality of a certain product is related to the time of day the product is produced. The following table summarizes the results of tests on some random samples produced in a
A magazine wants to know the relationship between people’s voting behavior and their level of income. Questionnaires were sent to 200 voters, and FCE responses are summarized here. Do the data
Use the following information to answer question. A questionnaire was sent to 200 students on the campus, asking them to indicate their ethnic background and give their opinion about race relations
Briefly explain what we mean by a direct and by an inverse relationship.
The accompanying scatter diagram shows the numbers of hours several students studied and their midterm scores.(a) Which is the dependent variable and which the independent variable?(b) Is there a
Suppose you are a safety consultant for the Department of Transportation. You are interested in the relationship between the number of miles a trucker drives per year and the number of accidents he
Use the method of least squares to estimate the intercept and slope of the regression line for the data given in question 27.Question 27Suppose you are a safety consultant for the Department of
Use the data from question 27 and your results from question 28 to estimate the number of accidents for each trucker. Also calculate the errors from the regression line.Question 27Suppose you are a
Suppose a labor economist at the Department of Labor estimates the following relationship between years of experience and earnings of accountants. Earnings = 22,000+ 3,200(years of experience)
Now suppose the actual earnings of the 5 accountants in question 30 are as follows. Calculate the error from the regression.Question 30Suppose a labor economist at the Department of Labor estimates
In order to determine whether a company should encourage its employees to live close to work, an efficiency expert collects data on the number of latenesses per month and the number of miles an
The manager of the Tow Time Auto Club would like to know the relationship between the age of a car and the number of service calls per year. He collects the following information:(a) Draw a scatter
Explain what we mean by the goodness of fit for a regression. Give two measures we can use to assess the goodness of fit.
Use the results from question 33 to predict the number of service calls for a car that is 3 years old and for one that is 6 years old.Question 33The manager of the Tow Time Auto Club would like to
Suppose you have the following information about number of dollars spent on advertising, X, and amount of car sales, Y: Cov(X,Y) = 500, Var(X) = 250, Var(Y) = 1,000, mean of X = 1,000, and mean of Y
Use the information given in question 36 to find the correlation between advertising dollars and sales.Question 36Suppose you have the following information about number of dollars spent on
Briefly define total deviation, unexplained deviation, and explained deviation.
Use the data and results from question 21 to calculate SSE, SSR, SST, and the coefficient of determination. Interpret what the coefficient tells us.Question 21You are given the following information
Suppose you collect data for IBM’s sales and dollars spent on advertising and then compute the following statistics:(a) Compute the correlation coefficient between advertising dollars and sales.(b)
A grocery store sells an average of 478 loaves of bread each week. Sales (X) are normally distributed with a standard deviation of 17.(a) If a random sample of size n = 1 (week) is drawn, what is the
A random variable s measures the daily balances in customers’ savings accounts. It is normally distributed, with a mean of μs – $108 and a standard deviation of $15.(a) If a random sample of
On average, a book distributor fills orders for 1,000 books per day. If daily orders are normally distributed and the standard deviation is 100, what is the probability that a 5-day average will be
A company makes a pastry called a chocco. During the manufacturing process, the individual choccos are placed in a baking oven. The time it takes to bake them is normally distributed around a mean of
In a large group of corporate executives, 20 % have no college education, 10 % have exactly 2 years of college, 20 % have exactly 4 years, and 50 % have 6 years. A sample size of 2 (with replacement)
Out of 10 pay telephones located in a municipal building, two phones are to bepicked at random, with replacement, for a study of phone use. The actual usageof the phones on a particular day is shown
To demonstrate the central limit theorem, draw 100 samples of size 5 from a random-number table and calculate the sample mean for each of the 100 samples. Construct a frequency distribution of sample
The accompanying probability density function is a uniform distributionshowing that a certain delicate new medical device will fail between 0 and10 years after it is implanted in the human body. The
The daily catch of a small tuna-fishing fleet averages 130 t. The fleet’s logbook shows that the weight of the catch varies from day to day and this variation is measured by the standard deviation
A type of cathode ray tube has a mean life of 10,000 h and a variance of 3,600. If we take samples of 25 tubes each and for each sample we find the mean life, between what limits (symmetric with
The population of times measured by 3-min egg timers is normally distributed with μ = 3 min and σ = .2 min. We test samples of 25 timers. Find the time that would be exceeded by 95 % of the sample
A light bulb manufacturer claims that 90 % of the bulbs it produces meet tough new standards imposed by the consumer protection agency. You just received a shipment containing 400 bulbs from this
At the beginning of every decade, the US government conducts a census. Why does it take a census? What are the advantages of a census over a sample?

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