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business
business statistics for contemporary

Questions and Answers of Business Statistics For Contemporary

The United Nations’ World Happiness Report aims to demonstrate the role of variables other than income in shaping peoples’ happiness. Let us consider the role of GDP, our income measure.
A prestigious national news service has gathered information on a number of nationally ranked private colleges; these data are contained in the data file Private Colleges. You have been asked to
A prestigious national news service has gathered information on a number of nationally ranked private colleges; these data are contained in the data file Private Colleges. You have been asked to
A prestigious national news service has gathered information on a number of nationally ranked private colleges; these data are contained in the data file Private Colleges. You have been asked to
A prestigious national news service has gathered information on a number of nationally ranked private colleges; these data are contained in the data file Private Colleges. You have been asked to
A prestigious national news service has gathered information on a number of nationally ranked private colleges; these data are contained in the data file Private Colleges. You have been asked to
The OECD Better Life Initiative focuses on measuring statistics that can capture aspects of life that matter most to people and that help to shape the quality of their lives. In this exercise, using
Casper Jensen, director of energy affairs at the Ministry of Economic Affairs, wants to know whether mindset or taxes are the better instrument to stimulate the adoption of renewable energy resources
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
The fertility rates of many countries in the West have been decreasing in the recent decades. The Ministry of Labor and Social Policies, Italy, has asked you to analyze whether structural economic
The fertility rates of many countries in the West have been decreasing in the recent decades. The Ministry of Labor and Social Policies, Italy, has asked you to analyze whether cyclical economic
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
Yeast grows faster at a higher temperature. If a regression of the amount of yeast growth is estimated using the temperature, the slope of the estimated regression line will certainly be positive.
A researcher believes that the time spent on physical exercise per week (Y) correlates to the age of a person(X). For a random sample of 23 individuals, the sample regression line.y = 15.02 - 0.29x
Based on a sample of 18 observations, the population regression model yi = b0 + b1xi + ei was estimated. The least squares estimates obtained were as follows:b0 = 5 and b1 = 2.2 The total and error
Based on a sample of 45 observations, the population regression model yi = b0 + b1xi + ei was estimated. The least squares estimates obtained were as follows:b0 = 60 and b1 = 15 The regression and
For a sample of 175 car loan applications received by a bank, the sample regression line y = 2,580 + 0.4385x was obtained. Here, y = affordable car price (€ 000)x = loan applicant salary (€
For 10 employees from a firm in the United Kingdom, the following table shows their overtime earnings (y) and the number of hours worked overtime (x) in a month:x 73 22 65 80 35 54 26 46 71 16 y 566
A study was conducted to evaluate price as a predictor of the supply of eggs (in €) in Belgium. For a sample of 61 daily observations, the estimated linear regression yn = 3.84 - 0.204x was
Based on a sample on n observations, 1x1, y12, 1x2, y22,c, 1xn, yn2, the sample regression of y on x is calculated. Show that the sample regression line passes through the point 1x = x, y = y2, where
For a sample of 72 senior citizens, the correlation between the age growth and height reduction was found to be -0.611. Test the null hypothesis that the population correlation is 0 against the
For a random sample of 350 industries, the sample correlation between the proportion of an industry’s employee turnover rate and economic growth rate was found to be 0.8729. Test, against a
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.
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
Frank Anscombe, senior research executive, has asked you to analyze the following four linear models using data contained in the data file Anscombe:Y1 = b0 + b1X1 Y2 = b0 + b1X2 Y3 = b0 + b1X3 Y4 =
In the commodity price file of the World Bank, two different types of coffee are enclosed: Arabica and Robusta. Their price progressions differ, but the differences are not significant. There is also
Your friend is an experienced investor in the stock market. She plans to expand to the commodity market and invest in precious metals. She needs your advice to decide which among gold, platinum, and
You are asked to assist the purchasing agent of a trade business in designing a purchase policy for metals based on the price fluctuations in the global market. Using the data file World Bank
The World Bank collects data on commodity markets, thereby allowing the estimation of the beta of individual commodities relative to an index. Using the data file World Bank Commodity Prices, find
As part of a process to build a new banking portfolio, you have been asked to determine the beta coefficients for two Dutch banking and financial services companies, ING and Rabobank. Data for this
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
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
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
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
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 a study of 33 countries, the sample correlation between an index of political turmoil and the infant mortality rate was 0.28. At the 0.05 level, test the null hypothesis of no correlation between
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
Using a 0.10 level of significance, test the null hypothesisgiven the following.a. A sample correlation of 0.46 for a random sample of size n = 25.b. A sample correlation of 0.52 for a random sample
Given the following pairs of 1x, y2 observations, compute the sample correlation.a. 12, 52, 15, 82, 13, 72, 11, 22, 18, 152b. 17, 52, 110, 82, 18, 72, 16, 22, 113, 152c. 112, 42, 115, 62, 116, 52,
You are asked to look into the impact of population growth on the growth rate of GDP per capita.The data for this study are in the data file Renewable Energy. As a first step, you estimate the
In order to tackle climate change, many countries are increasingly adopting renewable sources of energy. You have been asked to investigate whether energy taxes are a useful instrument to stimulate
The data file Trading Stocks shows percentage changes (xi) in a stock market over the first five trading days of each of 11 years and also the corresponding percentage changes (yi) in the index over
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
For a sample of 50 monthly observations the regression of the percentage return on an investment (y)against the percentage change in the consumer price index (x) was estimated. The sample regression
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
Denote by r the sample correlation between a pair of random variables.a. Show thatb. Using the result in parta, show that 1-72 n-2 SST
Estimate a linear regression model for the monthly rents of student rooms in Amsterdam on room size in square meters, using the data file Amsterdam Rents. Test, against a two-sided alternative, the
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
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
A sample of 10 blue-collar employees at a production plant was taken. Each employee was asked to assess their job satisfaction (x) on a scale of 1 to 10. In addition, the numbers of days absent (y)
Given a simple regression analysis, suppose that we have obtained a fitted regression modelFind the 95% confidence interval and 95% prediction interval for the point where x = 17. and also = 8 +
Given a simple regression analysis, suppose that we have obtained a fitted regression model yn i = 22 + 8xi and alsoFind the 95% confidence interval and 95% prediction interval for the point where x
Given a simple regression analysis, suppose that we have obtained a fitted regression modelFind the 95% confidence interval and 95% prediction interval for the point where x = 11. and also i = 14 +
Given a simple regression analysis, suppose that we have obtained a fitted regression modelFind the 90% confidence interval and 90% prediction interval for the point where x = 12. and also Se = = 11
Estimate a linear regression model for the monthly rents of student rooms in Amsterdam on room size, using the data file Amsterdam Rents.a. Use an unbiased estimation procedure to obtain a point
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
In order to tackle climate change, many countries are increasingly adopting renewable sources of energy. You have been asked to investigate whether attitudes toward the environment are important in
A local wholesaler is interested in assessing the effect of the price of a premium bars of on the quantity sold. The results in the accompanying table on price, in pounds, and sales, in bars, were
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
Use a simple regression model to test the hypothesis H0 : b1 = 0 versus H1 : b1 ? 0 with a = 0.05, given the following regression statistics.a. The sample size is 35, SST = 100,000, and the
Given the simple regression model Y = b0 + b1X and the regression results that follow, test the null hypothesis that the slope coefficient is 0 versus the alternative hypothesis of greater than zero
In a study it was shown that for a sample of 353 college faculty, the correlation was 0.11 between annual raises and teaching evaluations. What would be the coefficient of determination of a
Find the proportion of the sample variability in the monthly rent of student rooms, explained by their linear dependence on room size, based on the data in the data file Amsterdam Rents.
Find and interpret the coefficient of determination for the regression of the percentage change in the stock market index in a year based on the percentage change in the index over the first five
Find and interpret the coefficient of determination for the regression of DVD system sales on price, using the following data.Sales 420 380 350 400 440 380 450 420 Price 98 194 244 207 89 261 149 198
Letdenote the coefficient of determination for the sample regression line.a. Using part d of the previous exercise, show thatb. Using the result in parta, show that the coefficient of determination
Let the sample regression line be yi = b0 + b1xi + ei = yn i + ei 1i = 1, 2,c, n2 and let x and y denote the sample means for the independent and dependent variables, respectively.a. Show that ei =
Compute SSR, SSE, se 2, and the coefficient of determination, given the following statistics computed from a random sample of pairs of X and Y observations. n a. (y) = 130,000; R = 0.50; n = 50 i=1 n
Student accommodation comes in a wide variety of sizes and prices. The data file Amsterdam Rents shows the size (x, in m2) of a random sample of 38 student rooms available for rent. It also shows the
Refer to the following data, which contains the percentage change (X) in a stock market index over the first five trading days of the year and percentage change (Y) in the index over the whole
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
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
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
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
Compute the coefficients for a least squares regression equation and write the equation, given the following sample statistics.a. x = 10, y = 50, SX = 80, SY = 75, RXY = 0.4, n = 60b. x = 60, y = 50,
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
Suppose that we obtained an estimated equation for the regression of weekly sales of palm pilots and the price charged during the week. Interpret the constant b0 for the product brand manager.
Explain the difference between the residual ei and the model error ei.
What is the difference between a population linear model and an estimated linear regression model?
An agent for a real estate company in a large European city collected data, as shown in the following table, on the sizes (x in square feet) and monthly rents (y in euros)of a sample of eight
As the new market manger for Blue Crunchies breakfast cereal, you are asked to estimate the demand for next month using regression analysis. Two months ago the target market had 20,000 families and
A critically important aspect of customer service at a supermarket is the waiting time at the checkout. Refer to the data file Supermarket, which contains total number of customers in the store (x)
Given the regression equation Y = 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
Given the regression equation Y = 43 + 10Xa. What is the change in Y when X changes by +8?b. What is the change in Y when X changes by -6?c. What is the predicted value of Y when X = 11?d. What is
Given the regression equation Y = -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
Given the regression equation Y = 56 - 3Xa. What is the change in Y when X changes by +4?b. What is the change in Y when X changes by -7?c. What is the predicted value of Y when X = 10?d. What is the
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
Simoné Berk, president of Food Unlimited, has asked you to study the relationship between market price(euros) and the amount of rice (kg) supplied by her competitor, Good Food, Inc. Simoné supplies
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
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, Y 10 100 8 120 5 200 4 200 10 90 7 110 6 150a. Prepare
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 80 7 60 8 70 9 40 10 0a. Prepare a scatter
Complete the following for the 1x, y2 pairs of data points (3,1), (4,5), (5,4), (7, 6), and (9, 8).a. Prepare a scatter plot of these data points.b. Compute b1.c. Compute b0.d. What is the equation
We will now understand the effects of another home condition: does the student have books at home to help with their school work? Using a random sample of 500 observations from the PISA database, to
Let us now investigate the effects of another home condition: does the student have access to the Internet at home? Using a random sample of 500 observations from the PISA database, to be found in
Let us now investigate another home condition:can the student use educational software at home?Using a random sample of 500 observations from the PISA database, to be found in the data file PISA
Let us look at another home condition in this exercise:does the student have a computer for school work at home? Using a random sample of 500 observations from the PISA database, to be found in the
In this exercise, let us look at a third home condition that might affect the reading and mathematics scores of 15-year-old students: does the student have a quiet place to study at home? Using a
In this exercise, we will be looking at another home condition that might affect the mathematics and readings scores of 15-year-old students: does the student have a room of their own at home? Using
Another one of equity’s dimensions in the PISA studies is home conditions/facilities available to the student is also a factor. Does the education system succeed in adequately compensating for
Equity is a major theme in the PISA studies of the mathematics and reading performance scores of 15-year-olds around the world. Equity has several dimensions, one of which is gender equity. Using a

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