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Statistics For Business And Economics 8th Edition Paul Newbold, William Carlson, Betty Thorne - Solutions

The president of Amalgamated Retailers International, Samiha Peterson, has asked for your assistance in studying the market penetration for the company's new cell phone. You are asked to study two markets and determine if the difference in market share remains the same. Historically, in market 1 in
National education officials are concerned that there may be a large number of low-income students who are eligible for free lunches in their schools. They also believe that the percentage of students eligible for free lunches is larger in rural areas.As part of a larger research study you have
You are the product manager for brand 4 in a large food company. The company president has complained that a competing brand, called brand 2, has higher average sales. The data services group has stored the latest product sales (saleb2 and saleb4) and price data (apriceb2 and apriceb4) in a file
Joe Ortega is the product manager for Ole ice cream. You have been asked to determine if Ole ice cream has greater sales than Carl's ice cream, which is a strong competitor. The data file Ole contains weekly sales and price data for the competing brands over the year in three different supermarket
Mary Peterson is in charge of preparing blended flour for exotic bread making. The process is to take two different types of flour and mix them together in order to achieve high-quality breads. For one of the products, flour A and flour B are mixed together. The package of flour A comes from a
An agency offers preparation courses for a graduate school admissions test to students. As part of an experiment to evaluate the merits of the course, 12 students were chosen and divided into 6 pairs in such a way that the members of any pair had similar academic records. Before taking the test,
A study was conducted to determine if there was a difference in humor content in British and American trade magazine advertisements. In an independent random sample of 270 American trade magazine advertisements, 56 were humorous. An independent random sample of 203 British trade magazine
Individuals have their HEI measured on two different days with the first and second day indicated by the variable daycode. A number of researchers argue that individuals will have a higher-quality diet for the second interview because they will adjust their diet after the first interview. You are
Previous research has suggested that immigrants in the United States have a stronger interest in good diet compared to the rest of the population. If true, this behavior could result from a desire for overall life improvement, historical experience from their previous country, or some other complex
There is an increasing interest in healthier lifestyles, especially among the younger population. This is exhibited in the increased interest in exercise and a variety of emphases on eating foods that contribute to a higher-quality diet. You have been asked to determine if people who are physically
Various research studies and personal lifestyle advisers argue that increased social interaction is important for a higher quality of life. You have been asked to determine if people who are single (variable single = 1) have a healthier diet than those who are married or living with a partner.
Throughout society there are various claims of behavioral differences between men and women on many different characteristics. You have been asked to conduct a comparative study of diet quality between men and women. The variable female is coded 1 for females and 0 for males. Perform an appropriate
A recent radio commentator argued that his experience indicated that women believed that purchasing higher-cost food would improve their lifestyle. Is there evidence to conclude that women have a lower daily food cost compared to men (daily-cost)? Use an appropriate test to determine the answer.
The food stamp program has been part of a longterm public policy to ensure that lower-income families will be provided with adequate nutrition at lower cost. Some people argue that providing food income supplements will merely encourage lower-income people to purchase more expensive food, without
Excess body weight is, of course, related to diet, but, in turn, what we eat depends on who we are in terms of culture and our entire life experience. Does the immigrant population have a lower percentage of people that are overweight compared to the remainder of the population? Provide strong
You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as µ1 and process 2 has a mean defined as µ2. The null and alternative hypotheses are as follows:H0: µ1 - µ1 = 0H1: µ1 – µ2 > 0Use a
You have been asked to determine if two different production processes have different mean numbers of units produced per hour. Process 1 has a mean defined as µ1 and process 2 has a mean defined as µ2. The null and alternative hypotheses are as follows:H0: µ1 – µ2 ≤0H1: µ1 - µ2 > 0The
A screening procedure was designed to measure attitudes toward minorities as managers. High scores indicate negative attitudes and low scores indicate positive attitudes. Independent random samples were taken of 151 male financial analysts and 108 female financial analysts. For the former group the
For a random sample of 125 British entrepreneurs, the mean number of job changes was 1.91 and the sample standard deviation was 1.32. For an independent random sample of 86 British corporate managers, the mean number of job changes was 0.21 and the sample standard deviation was 0.53. Test the null
Complete the following for the (x, y) pairs of data points (1, 5), (3, 7), (4, 6), (5, 8), and (7, 9).a. Prepare a scatter plot of these data points.b. Compute b1.c. Compute b0.d. What is the equation of the regression line?
Given the regression equationY = 100 + 21Xa. What is the change in Y when X changes by +5?b. What is the change in Y when X changes by -7?c. What is the predicted value of Y when X = 14?d. What is the predicted value of Y when X = 27?e. Does this equation prove that a change in X causes a change in
In recent news commentaries, it has been argued that the quality of family life has decayed in recent years. Arguments include statements that families do not share meals together. Because of busy schedules, families just go out to eat because there is limited time for food preparation. What is the
In recent news commentaries, it has been argued that the quality of family life has decayed in recent years. Arguments include statements that families do not share meals together. Because of busy schedules, families just go out to eat because there is limited time for food preparation. In
In Example 11.1 a linear regression model was developed. Use that model to answer the following.a. Interpret the coefficient b1 = 2.545 for the plant manager.b. How many tables would be produced on average with 19 workers?c. Suppose you were asked to estimate the number of tables produced if only
Consider the sales prediction model developed for Northern Household Goods in Example 11.2.a. Estimate per capita sales if the mean disposable income is $56,000.b. Interpret the coefficients b0 and b1 for Northern's management.c. You have been asked to estimate per capita sales if mean disposable
What is the difference between a population linear model and an estimated linear regression model?
Explain the difference between the residual ei and the model error εi.
A regression model of total grocery sales on disposable income was estimated using data from small, isolated towns in the western United States. Prepare a list of factors that might contribute to the random error term.
Compute the coefficients for a least squares regression equation and write the equation, given the following sample statistics.a. x-bar = 50, y-bar = 100, sx = 25, sy = 75, rxy = 0.6, n = 60b. x-bar = 60, y-bar = 210, sx = 35, sy = 65, rxy = 0.7, n = 60c. x-bar = 20, y-bar = 100, sx = 60, sy = 78,
A company sets different prices for a particular DVD system in eight different regions of the country. The accompanying table shows the numbers of units sold and the corresponding prices (in dollars). a. Graph these data, and estimate the linear regression of sales on price. b. What effect would
The following data give X, the price charged per piece of plywood, and Y, the quantity sold (in thousands).Price per Piece, X Thousands of Pieces Sold, Y$6 ................807 ................608 ................709 ................4010 ................. 0a. Prepare a scatter plot of these data
For a sample of 20 monthly observations, a financial analyst wants to regress the percentage rate of return (Y) of the common stock of a corporation on the percentage rate of return (X) of the Standard & Poor€™s 500 index. The following information is available:a. Estimate the linear
A corporation administers an aptitude test to all new sales representatives. Management is interested in the extent to which this test is able to predict sales representatives€™ eventual success. The accompanying table records average weekly sales (in thousands of dollars) and aptitude test
It was hypothesized that the number of bottles of an imported premium beer sold per evening in the restaurants of a city depends linearly on the average costs of meals in the restaurants. The following results were obtained for a sample of n = 17 restaurants of approximately equal size wherey =
Refer to the data file Dow Jones, which contains percentage change (X) in the Dow Jones index over the first five trading days of the year and percentage change (Y) in the index over the whole year. a. Estimate the linear regression of Y on X. b. Provide interpretations of the intercept and slope
On Friday, November 13, 1989, prices on the New York Stock Exchange fell steeply; the Standard & Poor’s 500-share index was down 6.1% on that day. The data file New York Stock Exchange Gains and Losses shows the percentage losses (y) of the 25 largest mutual funds on November 13, 1989. Also
Compute SSR, SSE, s2e, and the coefficient of determination, given the following statistics computed from a random sample of pairs of X and Y observations.
Let the sample regression line beyi = b0 + b1xi + ei = y`i + ei (i = 1, 2, c, .., n)and let x and y denote the sample means for the independent and dependent variables, respectively.a. Show thatei = yi €“ y-bar €“ b(xi €“ x-bar)b. Using the result in part a, show thatc. Using the result
LetR2 = SSR / SSTdenote the coefficient of determination for the sample regression line.a. Using part d of the previous exercise, show thatb. Using the result in part a, show that the coefficient of determination is equal to the square of the sample correlation between X and Y. c. Let b1 be the
Find and interpret the coefficient of determination for the regression of DVD system sales on price, using the following data.
Find and interpret the coefficient of determination for the regression of the percentage change in the Dow Jones index in a year based on the percentage change in the index over the first five trading days of the year. Compare your answer with the sample correlation found for these data. Use the
A random sample of data for 7 days of operation produced the following (price, quantity) data values:Price per Gallon of Paint, X Quantity Sold, Y10 .................1008 ...................1205 ...................2004 ...................20010 ................. 907 ...................1106
Find the proportion of the sample variability in mutual fund percentage losses on November 13, 1989, explained by their linear dependence on 1989 percentage gains through November 12, based on the data in the data file New York Stock Exchange Gains and Losses.
Given the simple regression modelY = β0 + β1XAnd the regression results that follow, test the null hypothesis that the slope coefficient is 0 versus the alternative hypothesis of greater than zero using probability of Type I error equal to 0.05, and determine the two-sided 95% and 99% confidence
Use a simple regression model to test the hypothesisH0 : β1 = 0versusH0 : β1 ≠ 0with α = 0.05, given the following regression statistics.a. The sample size is 35, SST = 100,000, and the correlation between X and Y is 0.46.b. The sample size is 61, SST = 123,000, and the correlation between X
Mumbai Electronics is planning to extend its marketing region from the western United States to include the midwestern states. In order to predict its sales in this new region, the company has asked you to develop a linear regression of DVD system sales on price, using the following data supplied
A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed. The
You have been asked to determine the effect of per capita disposable income on retail sales using cross-section data by state. The data are contained in the data file Economic Activity. Estimate the appropriate regression equation and determine the 95% confidence interval for the expected change in
Estimate the regression equation for the percentage change in the Dow Jones index in a year on the percentage change in the index over the first five trading days of the year. Use the data file Dow Jones.a. Use an unbiased estimation procedure to find a point estimate of the variance of the error
Estimate a linear regression model for mutual fund losses on November 13, 1989, using the data file New York Stock Exchange Gains and Losses.a. Use an unbiased estimation procedure to obtain a point estimate of the variance of the error terms in the population regression.b. Use an unbiased
Given a simple regression analysis, suppose that we have obtained a fitted regression modely`i = 12 + 5xiand alsoFind the 95% confidence interval and 95% prediction interval for the point where x = 13.
A large consumer goods company has been studying the effect of advertising on total profits. As part of this study, data on advertising expenditures and total sales were collected for a five-month period and are as follows:110, 1002 115, 2002 17, 802112, 1202 114, 1502The first number is
Given a simple regression analysis, suppose that we have obtained a fitted regression modely`i = 14 + 7xiand alsoFind the 95% confidence interval and 95% prediction interval for the point where x = 11.
Given a simple regression analysis, suppose that we have obtained a fitted regression modely`i = 22 + 8xiand alsoFind the 95% confidence interval and 95% prediction interval for the point where x = 17.
Given a simple regression analysis, suppose that we have obtained a fitted regression modely`i = 8 + 10xiand alsoFind the 95% confidence interval and 95% prediction interval for the point where x = 17.
A sample of 25 blue-collar employees at a production plant was taken. Each employee was asked to assess his or her own job satisfaction (x) on a scale of 1 to 10. In addition, the numbers of days absent (y) from work during the last year were found for these employees. The sample regressiony`i =
Doctors are interested in the relationship between the dosage of a medicine and the time required for a patient's recovery. The following table shows, for a sample of 10 patients, dosage levels (in grams) and recovery times (in hours). These patients have similar characteristics except for medicine
For a sample of 20 monthly observations, a financial analyst wants to regress the percentage rate of return (Y) of the common stock of a corporation on the percentage rate of return (X) of the Standard & Poor's 500 index. The following information is available:a. Test the null hypothesis that
Estimate a linear regression model for mutual fund losses on November 13, 1989, on previous gains in 1989, using the data file New York Stock Exchange Gains and Losses. Test, against a two-sided alternative, the null hypothesis that mutual fund losses on Friday, November 13, 1989, did not depend
Denote by r the sample correlation between a pair of random variables.a. Show thatb. Using the result in part a, show that
It was hypothesized that the number of bottles of craft beer sold per evening in the restaurants of a city depends linearly on the average costs of meals in the restaurants. The following results were obtained for a sample ofn = 17 restaurants, of approximately equal size, wherey = number of
For a sample of 74 monthly observations the regression of the percentage return on gold (y) against the percentage change in the consumer price index (x) was estimated. The sample regression line, obtained through least squares, was as follows:y = -0.003 + 1.11xThe estimated standard deviation of
Abdul Hassan, president of Floor Coverings Unlimited, has asked you to study the relationship between market price and the tons of rugs supplied by his competitor, Best Floor, Inc. He supplies you with the following observations of price per ton and number of tons, obtained from his secret
A liquor wholesaler is interested in assessing the effect of the price of a premium scotch whiskey on the quantity sold. The results in the accompanying table on price, in dollars, and sales, in cases, were obtained from a sample of 8 weeks of sales records.Test, at the 5% level against the
The data file Dow Jones shows percentage changes (xi) in the Dow Jones index over the first five trading days of each of 13 years and also the corresponding percentage changes (yi) in the index over the whole year. If the Dow Jones index increases by 1.0% in the first five trading days of a year,
You have been asked to study the relationship between mean health care costs and mean disposable income using the state level data contained in the data file Economic Activity. Estimate the regression of health and personal expenditures on disposable income. Compute the 95% prediction interval and
An economic policy research organization has asked you to study the relationship between disposable income and unemployment level. The data for this study are contained in the data file Economic Activity. As a first step you estimate the regression model for the relationship between unemployment
Given the following pairs of (x, y) observations, compute the sample correlation.a. (2, 5), (5, 8), (3, 7), (1, 2), (8, 15)b. (7, 5), (10, 8), (8, 7), (6, 2), (13, 15)c. (12, 4), (15, 6), (16, 5), (21, 8), (14, 6)d. (2, 8), (5, 12), (3, 14), (1, 9), (8, 22)
Test the null hypothesisH0 : p = 0versusH0 : p ≠ 0given the following.a. A sample correlation of 0.35 for a random sample of size n = 40b. A sample correlation of 0.50 for a random sample of size n = 60c. A sample correlation of 0.62 for a random sample of size n = 45d. A sample correlation of
An instructor in a statistics course set a final examination and also required the students to do a data analysis project. For a random sample of 10 students, the scores obtained are shown in the table. Find the sample correlation between the examination and project scores.
In the study of 49 countries discussed in Example 11.4, the sample correlation between the experts' political riskiness score and the infant mortality rate in these countries was 0.75. Test the null hypothesis of no correlation between these quantities against the alternative of positive
For a random sample of 353 high school teachers, the correlation between annual raises and teaching evaluations was found to be 0.11. Test the null hypothesis that these quantities are uncorrelated in the population against the alternative that the population correlation is positive.
The sample correlation for 68 pairs of annual returns on common stocks in country A and country B was found to be 0.51. Test the null hypothesis that the population correlation is 0 against the alternative that it is positive.
A random sample of 12 college baseball players participated in a special weight-training program in an attempt to improve their batting averages. The program lasted for 20 weeks immediately prior to the start of the baseball season. The average number of hours per week and the change in their
The accompanying table and the data file Dow Jones show percentage changes (xi) in the Dow Jones index over the first five trading days of each of 13 years and also the corresponding percentage changes (yi) in the index over the whole year.a. Calculate the sample correlation.b. Test, at the 10%
A college administers a student evaluation questionnaire for all its courses. For a random sample of 12 courses, the accompanying table and the data file Student Evaluation show both the average student ratings of the instructor (on a scale of 1 to 5), and the average expected grades of the
In an advertising study the researchers wanted to determine if there was a relationship between the per capita cost and the per capita revenue. The following variables were measured for a random sample of advertising programs:xi = Cost of Advertisement, ÷ Number of Inquiries Receivedyi = Revenue
As part of a process to build a new automotive portfolio, you have been asked to determine the beta coefficients for AB Volvo and General Motors. Data for this task are contained in the data file Return on Stock Price 60 Months. Compare the required return on the two stocks to compensate for the
In this exercise you are asked to determine the beta coefficient for Senior Housing Properties Trust. Data for this task are contained in the data file Return on Stock Price 60 Months. Interpret this coefficient.
An investor is considering the possibility of including TCF Financial in her portfolio. Data for this task are contained in the data file Return on Stock Price 60 Months. Compare the mean and variance of the monthly return with the S & P 500 mean and variance. Then, estimate the beta
Allied Financial is considering the possibility of adding one or more computer industry stocks to its portfolio. You are asked to consider the possibility of Seagate, Microsoft, and Tata Information systems. Data for this task are contained in the data file Return on Stock Price 60 Months. Compare
Charlie Ching has asked you to analyze the possibility of including Seneca Foods and Safeco in his portfolio. Data for this task are contained in the data file Return on Stock Price 60 Months. Compute the beta coefficients for the stock price growth for each stock. Then construct a portfolio that
Frank Anscombe, senior research executive, has asked you to analyze the following four linear models using data contained in the data file Anscombe: Y1 = β0 + β1X1 Y2 = β0 + β1X2 Y3 = β0 + β1X3 Y4 = β0 + β1X4 Use your computer package to obtain a linear regression estimate for each model.
Josie Foster, president of Public Research, Inc., has asked for your assistance in a study of the occurrence of crimes in different states before and after a large federal government expenditure to reduce crime. As part of this study she wants to know if the crime rate for selected crimes after the
Given the regression equationY = 100 + 10Xa. What is the change in Y when X changes by +3?b. What is the change in Y when X changes by -4?c. What is the predicted value of Y when X = 12?d. What is the predicted value of Y when X = 23?e. Does this equation prove that a change in X causes a change in
For a random sample of 53 building supply stores in a chain, the correlation between annual sales per square meter of floor space and annual rent per square meter of floor space was found to be 0.37. Test the null hypothesis that these two quantities are uncorrelated in the population against the
For a random sample of 526 firms, the sample correlation between the proportion of a firm's officers who are directors and a risk-adjusted measure of return on the firm's stock was found to be 0.1398. Test, against a two-sided alternative, the null hypothesis that the population correlation is 0.
For a sample of 66 months, the correlation between the returns on Canadian and Singapore 10-year bonds was found to be 0.293. Test the null hypothesis that the population correlation is 0 against the alternative that it is positive.
Based on a sample on n observations, (x1, y1), (x2, y2), .. ,(xn, yn), the sample regression of y on x is calculated. Show that the sample regression line passes through the point (x = x-bar, y = y-bar), where x and y are the sample means.
An attempt was made to evaluate the inflation rate as a predictor of the spot rate in the German treasury bill market. For a sample of 79 quarterly observations, the estimated linear regression y` = 0.0027 + 0.7916xwas obtained, wherey = actual change in the spot ratex = change in the spot rate
The following table shows, for eight vintages of select wine, purchases per buyer (y) and the wine buyer€™s rating in a year (x):a. Estimate the regression of purchases per buyer on the buyer€™s rating.b. Interpret the slope of the estimated regression line.c. Find and interpret the
For a sample of 306 students in a basic business statistics course, the sample regression liney = 58.813 + 0.2875xwas obtained. Here,y = final student score at the end of the coursex = score on a diagnostic statistics test givenat the beginning of the course The coefficient of determination was
Based on a sample of 30 observations, the population regression modelyi = Î²0 + Î²1xi + Îµiwas estimated. The least squares estimates obtained were as follows:b0 = 10.1 and b1 = 8.4The regression and error sums of squares were as follows:SSR = 128 and SSE = 286a. Find and interpret the
Based on a sample of 25 observations, the population regression modelyi = β0 + β1x1 + εiwas estimated. The least squares estimates obtained were as follows:b0 = 15.6 and b1 = 1.3The total and error sums of squares were as follows:SST = 268 and SSE = 204a. Find and interpret the coefficient of
An analyst believes that the only important determinant of banks' returns on assets (Y) is the ratio of loans to deposits (X). For a random sample of 20 banks, the sample regression liney = 0.97 + 0.47xwas obtained with coefficient of determination 0.720.a. Find the sample correlation between
Given the regression equationY = -50 + 12Xa. What is the change in Y when X changes by +3?b. What is the change in Y when X changes by -4?c. What is the predicted value of Y when X = 12?d. What is the predicted value of Y when X = 23?e. Does this equation prove that a change in X causes a change in
A college's economics department is attempting to determine if verbal or mathematical proficiency is more important for predicting academic success in the study of economics. The department faculty have decided to use the grade point average (GPA) in economics courses for graduates as a measure of
The administrator of the National Highway Traffic Safety Administration (NHTSA) wants to know if the different types of vehicles in a state have a relationship to the highway death rate in the state. She has asked you to perform several regression analyses to determine if average vehicle weight,
The Department of Transportation wishes to know if states with a larger percentage of urban population have higher rates of automobile and pickup crash deaths. In addition, it wants to know if either the average speed on rural roads or the percentage of rural roads that are surfaced is related to
An economist wishes to predict the market value of owner-occupied homes in small midwestern cities. She has collected a set of data from 45 small cities for a 2-year period and wants you to use these as the data source for the analysis. The data are stored in the file Citydatr. She wants you to

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