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business
statistics for business and economics
Questions and Answers of
Statistics For Business And Economics
Investment advisors sometimes recommend holding gold as part of an investor’s portfolio, because the value of gold appears to be negatively related to that of the stock market. Thus, when the stock
Use the data from question 40 to construct a 95 % confidence interval forb. Is it possible for the true b to be negative?Question 40Investment advisors sometimes recommend holding gold as part of an
Briefly explain how we can use regression analysis to forecast values of y.
Explain why we often construct interval estimates of forecasts.
How is the size of the forecast interval affected when we use values of x that are much greater or much less than the mean value of x for forecasting?
Use the data given in question 31 to forecast Johnson & Johnson’s inventory turnover for 1989 and 1990. Construct a 95 % confidence interval for both of these forecasts. Use Eq. 14.21.Eq.
Use the regression estimated in question 40 to forecast the return for the gold mutual fund in 1989 and 1990. Assume that the best forecast for the return of the S&P 500 in 1989 and 1990 is the mean
Use the data and the regression given in question 19 to forecast the number of bushels of wheat that will be harvested if 250 lb of fertilizer are used. Construct a 90 % and a 99 % confidence belt
Use the regression results from questions 23 and 24 to forecast the return for Ford in January 1988, using both the standard market model and the CAPM version of the market model. Assume that the
Construct a 95 % confidence interval for the forecasts produced in question 48.Which model has the larger interval? Use Eq. 14.21.Eq. 14.21Question 48Use the regression results from questions 23 and
What is proxy error? Give some examples of proxy error in economics, accounting, and finance.
Briefly explain how proxy error of x affects the results from a standard linear regression.
Use your results from the regression given in question 65 of Chap. 13 to test the significance of b via a t-test. Also construct a 90 % confidence interval for b.Question 65 of Chap. 13Use the data
Again using your results from question 65 of Chap. 13, forecast the value of J&J’s current ratio. Assume that the best forecast of the industry’s current ratio is the mean of that ratio.
Redo questions 52 and 53, using J&J’s inventory turnover.Question 52Use your results from the regression given in question 65 of Chap. 13 to test the significance of b via a t-test. Also
Redo questions 52 and 53, using J&J’s return on assets.Question 52Use your results from the regression given in question 65 of Chap. 13 to test the significance of b via a t-test. Also
Suppose you estimate the following simple regression:(a) On the basis of the information provided, test the significance of the slope at the 99 % confidence level.(b) Construct a 99 % confidence
Suppose a researcher is interested in the relationship between the dollar volume of sales and the number of miles customers live from the store. She collects data on dollar volume of sales per
Using the information from question 58, construct a 90 % confidence interval for b.Question 58Suppose a researcher is interested in the relationship between the dollar volume of sales and the number
In finance we are sometimes interested in hedging the risk associated with future price changes by using futures contracts. A futures contract allows the buyer of the contract to buy the commodity at
Estimate a simple regression model, using the least-squares method and the information given. X 10 20 30 40 50 y 12.8 18.9 21 38 40 xy xy ye e (y - y)
Estimate a simple regression model, using the least-squares method and the information given. X 10 20 30 40 50 y 52 48 31 28 10 xy xy yee (y-y)
Evaluate the goodness of fit for the following graph: Yi = + bx; Xi
The following table summarizes the sales X and advertising expenditures Y(both in millions) for Rivera Company.(a) Estimate the regression, using X as the explanatory variable.(b) What will be the
The table shown below lists the administrative and enrollment breakdowns for the schools of each municipality in Middlesex County, New Jersey. Using total enrollment as the independent variable and
The table below shows the undergraduate GPA and quantitative scores on the GRE of 10 students. Explain the MINITAB output shown below. Student 1 2 234 3 4 5 6 7 8 9 10 GPA 4.00 2.62 3.30 3.15 3.54
You are given the following information for x and y:(a) Compute the least-squares estimates for the slope and intercept.(b) Compute the t-value for b and construct a 99 % confidence interval for b.
Use the data from question 47 to compute the sample correlation coefficient r between x and y. Use a t-test to test the significance of r.Question 47Use the data and the regression given in question
Suppose x and y are bivariately normally distributed. Use a t-test to test the significance of the sample correlation coefficient r if r = .79 and n = 12.
It is of interest to find the relationship between the monthly closing stock prices of IBM (y; unit: $10) and the closing indices of Dow Jones Industrial Average(x; unit 100).Estimate the slope of
Using the data in Problem 70, do an F-test for the significance of the regression at α = .05.Problem 70It is of interest to find the relationship between the monthly closing stock prices of IBM (y;
Using the data in Problem 70, test the hypothesis that β > 0 at α = .05.Problem 70It is of interest to find the relationship between the monthly closing stock prices of IBM (y; unit: $10) and
Using the data in Problem 70, construct a 95 % confidence interval forb. Is it possible for the true b to be negative?Problem 70It is of interest to find the relationship between the monthly closing
Suppose we expect the DJIA for 2012/1 to be 12600. Using the data in Problem 70, forecast the closing price for IBM and construct a 95 % prediction interval for it.Problem 70It is of interest to find
Find the critical values for the following standard normal distributions:(a) Two-tailed test for α = .05(b) One-tailed test for α = .05(c) Two-tailed test for α = .01(d) One-tailed test for α =
A candidate believes that more than 30 % of the citizens will vote for him. A random sample of 250 citizens was taken and 101 of them vote for the candidate.(a) State the null and alternative
A college professor wants to use a normal distribution to analyze his students’ grades. He randomly selects 200 previous grades and organizes them in the following table. The mean is 67.75 and the
A college professor has taught business statistics for the last 5 years. He used standard tests every semester. The distribution of grades during the past 5 years wasHe feels that this semester’s
A travel agency was curious about whether the service a guest receives is related to the size of the hotel. The agency surveyed 300 customers and summarized their responses in the accompanying table.
Use the following information to answer question. Four hundred and fifty economists of different ideologies were asked to forecast the prospects for the economy during the Bush administration.
Test, at the 5 % level, the hypothesis that about equal numbers of economists hold each opinion.Use the following information to answer question. Four hundred and fifty economists of different
Can you say that the opinion pattern of the liberal economists is the same as the opinion pattern of the radical economists? Do a 5 % test.Use the following information to answer question. Four
A magazine is interested in knowing whether which newspaper is read and level of education of the reader are related.Use MINITAB to determine whether newspaper read and education are related.Use the
The sales manager wants to know whether salespeople’s performance is related to their zodiac sign. Three hundred salespeople were surveyed. Their performance is summarized in the following table.Do
An advertising agency wants to know whether there is a relationship between TV shows and the age of the audience. The following data were compiled.Do the data support the hypothesis that the age of
Is the distance from the construction sites independent of the way people hear of the housing project? Do a 5 % test.Use the following information to answer question. A developer asks visitors how
Can we conclude that the effects of publicizing the project in the 3 different media (newspaper, radio, and TV) are different? Do a 5 % test.Use the following information to answer question. A
If you live 10–30 miles away from the construction site, is your sources of information pattern the same as that of the people living within 10 miles? Do a test of 5 %.Use the following information
Do the three different kinds of mutual funds attract about the same numbers of investors? Do a 5 % test.Use the following information to answer question. A company operates three mutual funds. The
Can we conclude that the 3 different kinds of mutual funds generate about the same average rate of return? Do a 5 % test, using a one-way ANOVA.Use the following information to answer question. A
Do a two-way ANOVA to determine whether the rates of return for the three kinds of mutual funds are about the same. Do a 5 % test.Use the following information to answer question. A company operates
Determine whether the stock fund is equally popular among the four different age groups. Do a 5 % test.Use the following information to answer question. A company operates three mutual funds. The
Determine whether the investment pattern of the age group 20–35 is the same as that of the age group 51–65. Do a 5 % test.Use the following information to answer question. A company operates
The placement office in a business school randomly sampled 24 graduates from three departments and recorded their starting salaries. Determine whether graduates of the 3 departments have about the
Use the data from problem 99. At the a = 0.05, use Scheffe´’s multiple comparison to test for the difference between any pair.Problem 99Money magazine (Money, March 2003) reports percentage
Calculate the standard error of the residual using the results from question 41.Question 41Use the data and results of questions 30 and 31 to calculate SSE, SSR, SST, and the coefficient of
Review the information given in question 62. What is the probability that a sample of 50 babies will have a mean weight greater than 8 lb?Question 62Suppose an obstetrician knows from past experience
Suppose the teacher in question 9 is teaching four algebra classes. She would like to predict the average course grade of all her students from only the midterm scores. Should she use inferential or
Suppose the teacher in question 10 would like to predict the average grade of all her students by using only the midterm scores from one class. Should she use inferential or descriptive
Suppose that in question 20, Weight Watchers uses a sample. Does this represent the use of inferential or descriptive statistics? How would your answer change if Weight Watchers used the
Are the statistics you found in answering question 26 inferential or descriptive statistics?Question 26Using any newspaper of your choice, find examples of statistics from the following sections: (a)
Use the data from question 10 to construct a relative frequency graph and a cumulative relative frequency graph for both EPS and DPS.Question 10Use the EPS and DPS data given in Table 2.3 in Chap. 2
Use the data of question 21 to calculate(a) Coefficient of skewness(b) Pearson coefficient
The daily rate of return for a stock (adjusted to an annual rate) is summarized in the following table. Can you show that these data do not come from a normal distribution? The mean is 0%and the
Suppose you estimate a regression of y against x and find that b = 1.3 and σb = .4 (population standard error of the regression, which is known).(a) Construct a 90 % and a 99 % confidence interval
Suppose the analyst of question 34 decides on the following regression:(a) Estimate the intercept and slope coefficients.(b) Use an F-test to test the joint significance of the slope coefficients.(c)
Use the following information to answer question. It is believed that American League pitchers should have higher earned-run averages because of the designated hitter rule. A baseball analyst
Use the following information to answer question. You are given the following return information for 3-month T-bills, the NYSE Index, Chrysler, Ford, and GM for the 3-year period from January 1985
Use the data given in question 34 to compute the change in real wages between 1986 and 1990. Are workers any better off?Question 34Suppose you are given the following information about wages and
The Students for an Affordable Education have asked you to estimate the average amount of money spent per semester on textbooks. To produce this estimate, you have decided to randomly sample 25
A local deli prepares fresh potato salad for its customers every day. The unsold salad has to be thrown away. The demand for potato salad can be classified as low (100 lb), medium (200 lb), or high
A hospital collects data on the number of emergency room patients in during a certain period. It is estimated that in an hour, the average number of emergency room patients to arrive is 1.2. If the
A real estate agent in Connecticut is interested in the mean home price in the state. A random sample of 50 homes shows a mean home price of $175,622 and a sample standard deviation of $37,221.
An auditor randomly samples 75 accounts receivable of a company and finds a sample mean of $128 with a sample standard deviation of $27. Construct a 90 % confidence interval for the mean accounts
A random sample of 300 residents of a town shows that 55 % believe the mayor is doing a good job. Construct a 95 % confidence interval for the proportion of all residents who believe the mayor is
An auditor randomly samples 50 accounts payable of a company and finds a sample mean of $1,100 with a sample standard deviation of $287. Construct a 90 % confidence interval for the mean accounts
A random sample of 250 residents of a town shows that 55% favor a bond issue to finance new school construction. Construct a 99 % confidence interval for the proportion of all residents who favor the
A random sample of 500 students at Average College finds the sample mean combined-SAT score to be 1.050 with a standard deviation of 120. Construct a 90 % confidence interval for the mean SAT score.
Use the information given in question 25 to test H0: μ = 100 versus H1: μ ≠ 100 at the .01 level of significance.Question 25You are given the information X̅ = 150, σ = 30, and n = 20. Conduct
You are given the information X̅ = 1,050, sx = 250, and n = 20. Conduct the following hypothesis test at the .10 level of significance:H0: μ = 1,100 versus H1: μ < 1,100 at the .10 level of
A sample of 100 students in a high school has a sample mean score of 550 on the math portion of the SAT. Assuming that the sample standard deviation is 75, test, at the .05 level of significance, the
Redo question 29, testing H0: μ = 500 against H1: μ > 500.Question 29A sample of 100 students in a high school has a sample mean score of 550 on the math portion of the SAT. Assuming that the
A sample of 20 students in a high school has a sample mean score of 520 on the English portion of the SAT. If the sample standard deviation is 65, test, at the .01 level of significance, the
Redo question 31, substituting the alternative hypothesis H1: μ > 500.Question 31A sample of 20 students in a high school has a sample mean score of 520 on the English portion of the SAT. If the
Suppose a random sample of 25 people at a local weight-loss center is taken and the mean weight loss is found to be 12 lb. From past history, the standard deviation is known to be 3 lb. Test the
Redo question 33, but assume that the standard deviation is not known and that 3 lb represents the sample standard deviation. Do the test at the 5 % level of significance.Question 33Suppose a random
A quality control engineer is interested in testing the mean life of a new brand of light bulbs. A sample of 100 light bulbs is taken, and the sample mean life of these light bulbs is found to be
Suppose that the quality control engineer in question 35 does not know what the standard deviation is and therefore uses the sample standard deviation. Does your answer to question 35 change? Why or
Suppose that the quality control engineer in question 35 does not know what the standard deviation is and that this time, he selects a random sample of only 25 light bulbs. Does your answer to
An auditor is interested in the mean value of a company’s accounts receivable.He randomly samples 200 accounts receivable and finds that the mean accounts receivable is $231. From past experience,
Use the information given in question 38 to test the hypothesis that the population mean accounts receivable is greater than $200 at the .05 level of significance.Question 38An auditor is interested
An investment advisor is interested in determining whether a retirement community represents a potential clientele base. Of the 2,000 residents, he randomly samples 100 individuals and finds their
An automobile manufacturer claims that a new car gets an average of 35 miles per gallon. Assume that the distribution is known to be normal with a standard deviation of 3.2 miles per gallon. A random
Use the information given in question 41, except this time assume that the standard deviation is not known and that 3.2 miles per gallon represents the sample standard deviation. Again test, at the
An aspirin manufacturer claims that its aspirin stops headaches in less than 30 min. A random sample of 100 people who use the pain killer finds that the average time it takes to stop a headache is
Bob’s SAT preparation service claims that the course it offers enables students to score an average of 600 or better on the math portion of the SAT. Suppose a random sample of 25 people taking the
An advertising company claims that 80 % of stores that use their advertisements show increased sales. A random sample of 100 stores that used the company’s advertisements reveals that 80 showed
Flip a coin 40 times and count the number of heads. Test, at the 5 % level of significance, whether the proportion of heads is .5.
A manufacturer claims that 95 % of its parts are free of defects. A random sample of 100 parts finds that 92 are free of defects. Test the manufacturer’s claim at the 1 % level of significance.
An investment advisor claims that 70 % of the stocks she recommends will increase in price. Suppose testing a random sample of 125 stocks she recommends reveals that 75 have increased in price. Test
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