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Statistics For Business And Economics 4th Edition Paul Newbold - Solutions
Let 1-1 SSR R= SST denote the coefficient of determination for the sample regression line. (a) Using part (d) of Exercise 20, show that R-FE 20-99'(b) 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 b
Let the sample regression line be (i=1,2...n) and let x and y denote the sample means for the independent and dependent variables, re- spectively. (a) Show that e-y--bix,-3) (b) Using the result in part (a), show that (c) Using the result in part (a), show that (d) Show that e,= 0 (e) Using the
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 ap- proximately equal size, where
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 their eventual success. The ac- companying table records average weekly sales (in thousands of dollars) and aptitude test scores for a random
For a sample of twenty monthly observations, a financial analyst wants to regress the per- centage rate of return (Y) of the common stock of a corporation on the percentage rate of return (X) of the S. and P. 500 index. The following information is available: y 22.6 x 25.4 145.7 xy, 150.5 (a)
For a period of 11 years, the figures in the accompanying table were found for annual change in unemployment rate and annual change in mean employee absence rate due to own illness." CHANGE IN UNEMPLOYMENT YEAR RATE +1.4 +1.0 8 +2.9 9 10 -1.0 CHANGE IN MEAN EMPLOYEE ABSENCE RATE DUE TO OWN ILLNESS
1989. gains. (b) Interpret the slope of the sample regression line.
Some products or services cause more shopping difficulty than others. The table given here shows rankings of twenty-four products and services, in order of shopping difficulty as perceived by men and women. Find Spearman's rank correlation coefficient, and test the null hypothesis of no association
Refer to the data of Exercise 4.Find Spearman's rank correlation coefficient, and use it to test, against a two-sided alternative, the null hypothesis of no association in the population between this pair of random variables.
Test against a two-sided alternative the null hypothesis of equality of population variances of salary offers to males and females. 9.Refer to the data of Exercise 2.Find Spearman's rank correlation coefficient, and use it to test, against a two-sided alternative, the null hypothesis of no
Refer to Exercise 28 of Chapter
The sample correlation for sixty-eight pairs of quarterly returns on common stocks in the United States and Germany was found to be .51. Test the null hypothesis that the popula tion correlation is 0, against the alternative that it is positive.
For a random sample of 353 college faculty, the correlation between annual raises and teaching evaluations was found to be 11.Test the null hypothesis that these quantities are uncorrelated in the population against the alternative that the population correlation is positive.
In the advertising study discussed in Section 12.1. the following results were also found: N N. 5 4 7.70 141.77 1.57 98.61 4.18 95.83 4.17 96.97 3.63 179.18 6.09 196.67 1.52 163.92 1.57 125.19 3.09 275.97 10.04 154.70 4.65 171.81 3.08 289.59 6.02 151.61 2.97 200.23 1.76 105.71 4.81 147.82 98 120.49
3. A college administers for all its courses a student evaluation questionnaire. For a random sample of twelve courses, the accompanying table shows both average student ratings of the instructor (on a scale from 1 to 5), and average expected grades of the students (con a scale from A 4 to E-0).
The accompanying table shows percentage changes (x) in the Dow-Jones index over the first five trading days of each of thirteen years, and also the corresponding percentage changes (y) in the index over the whole year.(a) Calculate the sample correlation. (b) Test at the 10% significance level,
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 ten students, the scores obtained are shown in the table. Find the sample correlation between the examination and project scores. EXAMINATION 81 62 74
A sample of electric companies whose first mortgage bonds experienced a rating change by Moody's was examined." These companies were classified according to whether the change was up or down and also according to whether there was a new debt issue. The findings are shown in the accompanying table.
Two brands of lemon/lime liquid dishwashing detergents Sunlight and Palmolive were monitored for fifty-two weeks." For each week it was recorded, for each brand, whether or not manufacturer trade deals were available. The accompanying table shows the num- ber of weeks in each of four possible
Samples of Anglos and Hispanics, aged 16-24, in the same areas of the southwestern United States, were asked their weekly alcohol consumption. The accompanying table shows numbers in various categories for number of drinks per week. Test the null hypoth- esis of no association between ethnicity and
Forecasts of corporate earnings that differed from actual outcomes were examined." In these cases the percentage of insider directors on the board was recorded. Test the null hy- pothesis of no association between the direction of forecast errors and the extent of insider control of the board,
The accompanying table shows responses to the statement: "I think companies should not fire employees who test positive for drugs." Respondents were also classified according to political party affiliation." Test the null hypothesis of no association between response to this statement and party
The accompanying table shows. for independent random samples of men and women, the numbers who watch television for more or less than 2 hours per day." Test at the 10% level the null hypothesis of no relationship between a person's sex and the amount of tele- vision watched. Men Women HOURS
For a sample of seventy-six firms that switched auditors following qualified reports, it was noted whether the auditor subsequent to the switch was a "Big Eight" firm or a non-Big Eight firm, and also whether the type of report subsequent to the switch was qualified or TYPE OF AUDITOR TYPE OF
In the study in Exercise 27, a random sample of 273 firms that had received qualified opin- ions was taken. The accompanying table shows the numbers of qualified opinions received by these firms in the following year for firms that did and did not switch auditors. What can be learned from these
A study assessed the reactions of firms to qualified audit opinions. The accompanying table shows, for samples of firms that did and did not receive qualified opinions, the num- bers that switched auditors in the following year. Test at the 1% significance level the null hypothesis that the
A sample of 300 daily rates of return on shares of a common stock was obtained. The sam- ple skewness was 47 and the sample kurtosis was 3.86. Test the null hypothesis that the population distribution of daily rates of return of this stock is normal.
The number of customers arriving at a supermarket checkout counter over a period of 200 minutes was recorded, yielding the results shown in the table. The average number of cus- tomers per minute was 2.3. Test the null hypothesis that the population distribution is Poisson. NUMBER OF CUSTOMERS IN
An admissions dean has noted that historically, 75% of all applicants for a college pro- gram are from in-state, 15% are from neighboring states, and 10% are from other states. For a random sample of 100 applicants for the current year, seventy were from in-state, twenty-one were from neighboring
A sample of 201 computer salespeople was followed over a year to assess factors involved in job changes. The accompanying table classifies these people according to whether they were married or single and whether they left their jobs or stayed for the year. Test at
The accompanying table shows information on fifty-five forecasts of inflation rate." Forecasts were classified as to whether or not inflation was predicted to accelerate. It was also noted whether or not the actual outcome was for accelerated inflation. Test the null hypothesis of no association
A sample of corporate chief executive officers was asked to rate both corporate level fi- nancial performance and corporate level strategy. The results are shown in the accompa- nying table."Test at the 1% level the null hypothesis of no association between the two sets of ratings. STRATEGY Low
A sample of firms with impaired assets were classified according to whether discretionary write-downs of these assets were taken and also according to whether there was evidence of subsequent merger or acquisition activity." Using the data in the accompanying table. test the null hypothesis of no
A sample of multi-unit department stores was categorized according to size (as measured by number of employees) and whether or not there was a formal marketing plan. The table shows numbers in each category." Test at the 1% level the null hypothesis of no associa tion between size and marketing
A sample of 3,262 corporate dividend changes were investigated." These were classified as increases or decreases in dividends, and also as to whether the dividend announcement was made before or after the earnings announcement. Using the data in the accompanying table, test the null hypothesis of
A sample of 165 firms filing for bankruptcy were classified according to whether the prior audit opinion was qualified or unqualified, and also according to the time from year end to the bankruptcy filing date. The results are shown in the table. Test the null hypothesis of no association between
Suppose that in a 2 2 contingency table, the numbers observed are denoteda, b,c, d, as indicated in the following table: TOTALS a b a+b d c+d TOTALS a+c b+d See B. A. Walker and J. C. Olson, "Mean-end chains: Connecting products with self," Journal of Business Research, 22 (1991), 111-18. Used by
A sample of twenty women planning to send a "thinking of you" card and a sample of twenty women planning to send a wedding card were asked about important attributes in choosing a card. The table shows numbers mentioning pictures as an important attribute Test at the 10% level the null hypothesis
The sample skewness and kurtosis are employed to test population normality. Explain why the sample mean and sample variance would be inadequate for this purpose.
A random sample of one hundred measurements of the resistance of electronic compo- nents produced in a period of one week was taken. The sample skewness was 63 and the sample kurtosis was 3.85. Test the null hypothesis that the population distribution is normal.
A random sample of fifty students were asked to estimate how much money they spent on textbooks in a year. The sample skewness of these amounts was found to be 83 and the sample kurtosis was 3.98. Test at the 10%-level the null hypothesis that the population distribution of amounts spent is normal.
In a period of 100 minutes, there were a total of 190 arrivals at a highway toll booth. The accompanying table shows the frequency of arrivals per minute over this period. Test the null hypothesis that the population distribution is Poisson. NUMBER OF ARRIVALS IN MINUTE OBSERVED FREQUENCY 012 3 4
The number of times a machine broke down each week was observed over a period of 100 weeks, giving the results shown in the accompanying table. It was found that the average number of breakdowns per week over this period was 2.1. Test the null hypothesis that the population distribution of
A campus administrator has found that 60% of all students view courses as very useful, 20% as somewhat useful, and 20% as worthless. Of a random sample of 100 students tak- ing business courses, sixty-eight found the course in question very useful, eighteen some- what useful, and fourteen
A charity solicits donations by telephone. It has been found that 60% of all calls result in a refusal to donate, 30% result in a request for more information through the mail, with a promise to at least consider donating; and 10% generate an immediate credit card dona- tion. For a random sample of
Production records indicate that in normal operation for a certain electronic component, 93% have no faults, 5% have one fault, and 2% have more than one fault. For a random sample of 500 of these components from a week's output, 458 were found to have no faults, thirty to have one fault, and
A random sample of 502 consumers were asked about the importance of price as a factor in choosing a hospital." Sample members were asked to select "not important." "impor tant," or "very important" as an answer. Respective numbers selecting these answers were 169, 136, and 197.Test the null
A random sample of sixty-five mutual funds whose performance ranked in the top 25% of all funds in 1979 83 was selected. Their performance was observed over the next five years. In this later period, eleven of the sample funds ranked in the top 25% of all funds, seventeen in the second 25%,
A professor is planning to use a new book for a financial accounting course and is consid- ering three possibilities: Financial Accounting Made Easy, Financial Accounting Without Tears, and Financial Accounting for Profit and Pleasure. He contacted a random sample of sixty students who had already
A random sample of ten corporate analysts was asked to rate, on a scale from ( poor) to 10 (very high), the prospects for their own corporations and for the econom large in the current year. The results obtained are shown in the accompanying table. U the Wilcoxon test, discuss the proposition that
Of a random sample of 120 business school professors, forty-eight believed students' lytical skills had improved over the last decade, thirty-five believed these skills had de orated, and thirty-seven saw no discernible change. Evaluate the strength of the sam evidence suggesting that, for all
Of a random sample of 100 college students, thirty-five expected to achieve a higher dard of living than their parents, forty-three expected a lower standard of living, twenty-two expected about the same standard of living as their parents. Do these data sent strong evidence that, for the
In a random sample of sixteen exchange rate analysts, eight believed that the Japanese would be an excellent investment this year, five believed that it would be a poor inv ment, and three had no strong opinion on the question. What conclusions can be dr from these data?
In a random sample of twelve analysts, seven believed that automobile sales in the Uni States were likely to be significantly higher next year than in the present year, two lieved that sales would be significantly lower, and the others anticipated that next ye sales would be roughly the same as
Construct a realistic example of a statistical problem in the business area where you wo prefer the use of a nonparametric test to the alternative parametric test.
What does it mean to say that a test is nonparametric? What are the relative advantage such tests?
Starting salaries of M.B.A. graduates from two leading business schools were compa Independent random samples of thirty students from each school were taken, and the s starting salaries were pooled and ranked. The sum of the ranks for students from on these schools was 1.243. Test the null
The time taken in days from year-end for a random sample of 120 Australian companies with clean audit reports to release a preliminary profit report was compared with the time taken for an independent random sample of eighty-six companies whose reports had a "subject to qualification. The times
A random sample of fifty students was asked what salary the college should be prepared to pay to attract the right individual to coach the football team. An independent random sam- ple of fifty faculty members was asked the same question. The 100 salary figures were then pooled and ranked in order
A corporation interviews both marketing and finance majors for general management po- sitions. A random sample of ten marketing majors and an independent random sample of fourteen finance majors were subjected to intensive interviewing and testing by a team of the corporation's senior managers. The
A random sample of eighty owners of videocassette recorders was taken. Each sample member was asked to assess the amounts of time in a month spent watching material he or she had recorded from television broadcasts and on watching purchased or rented com- mercially recorded tapes. The eighty
A consultant is interested in the impact of the introduction of a total quality management program on job satisfaction of employees. A random sample of thirty employees was asked to assess level of satisfaction on a scale from one (very dissatisfied) to ten (very sal- isfied) three months before
A random sample of forty business majors who had just completed introductory courses in both statistics and accounting was asked to rate each in terms of level of interest, on a scale from one (very uninteresting) to ten (very interesting). The forty differences in the pairs of ratings were
Based on the material of Section 9.8, can you use the data of Exercise 71 to test the null hypothesis of equality of population variances for absolute percentage forecast errors for the two analysts?1. A random sample of twelve financial analysts was asked to predict the percentage in- creases in
Using the data of Exercise 76, test against a two-sided altemative the null hypothesis that the population standard deviation of the fog index of advertisements in Scientific American is the same as the population standard deviation of the fog index of advertise- ments in Sports Illustrated.
Independent random samples were taken of male and female clients of Small Business Development Centers." These clients were considering starting a business. Of ninety-four male clients, fifty-three actually started a business venture, as did forty-seven of sixty- eight female clients. Find and
Of a random sample of sixty-nine industrial firms, forty-seven did public relations in- house, as did forty of an independent random sample of sixty-nine consumer goods firms. Find and interpret the p-value of a test of equality of the population proportions against a two-sided alternative.
Random samples of employees in mid-sized plants where the employer provides a training program were drawn. "Of a sample of sixty-seven employees who had not completed high school, eleven had participated in a training program provided by their current employer. Of an independent random sample of
In a study aimed at finding early warning signals of business failure, a random sample of twenty-three failed retail firms showed mean returns on assets 3 years previously was .058 and sample standard deviation .055. An independent random sample of twenty-three suc- cessful retail firms showed mean
Independent random samples of cosmetic and reconstructive plastic surgery patients were asked to assess the quality of service on a scale from one (low) to seven (high)." (These patients had received breast implants.) For a sample of eighty-three cosmetic patients, the mean rating was 6.543, and
Independent random samples of insider and outsider corporate directors were asked to re- spond on a scale from one (strongly disagree) to four (strongly agree) to the statement: "The threat and actuality of takeovers of publicly held companies provide discipline for boards and managers to maximize
From the report described in Exercise 76, the fog indices for a random sample of six ad- vertisements in People Weekly were as follows: 9.50 8.60 8.59 6.50 4.79 4.29 For an independent random sample of six advertisements in Newsweek, the fog indices were as follows: 10.21 9.66 7.67 5.12 4.88 3.12
The fog index is used to measure the reading difficulty of a written text. The index is cal- culated through the following steps: (i) Find the average number of words per sentence. (ii) Find the percentage of words with three or more syllables. (iii) The fog index is then 40% of the sum of (i) and
A study was aimed at assessing the effects of the size and characteristics of groups on the generation of ideas. To assess the influence of group size, groups of four and eight mem- bers were compared. For a random sample of four 4-member groups, the mean number of ideas generated per group was
Independent random samples of insider and outsider corporate directors were asked to re- spond on a scale from one (strongly disagree) to four (strongly agree) to the statement: "The threat and actuality of takeovers of publicly held companies provide discipline for boards and managers to maximize
From the report described in Exercise 76, the fog indices for a random sample of six ad- vertisements in People Weekly were as follows: 9.50 8.60 8.59 6.50 4.79 4.29 For an independent random sample of six advertisements in Newsweek, the fog indices were as follows: 10.21 9.66 7.67 5.12 4.88 3.12
The fog index is used to measure the reading difficulty of a written text. The index is cal- culated through the following steps: (i) Find the average number of words per sentence. (ii) Find the percentage of words with three or more syllables. (iii) The fog index is then 40% of the sum of (i) and
A study was aimed at assessing the effects of the size and characteristics of groups on the generation of ideas. To assess the influence of group size, groups of four and eight mem- bers were compared. For a random sample of four 4-member groups, the mean number of ideas generated per group was
Independent random samples of bachelors and masters degree holders in accounting, whose initial job was with a "big eight" firm, and who subsequently moved to industry. were questioned. For a sample of forty-four bachelors degree holders, the mean num- ber of months before the first job change was
Independent random samples of practicing public accountants and college accounting fac- ulty were asked to respond on a scale from one (strongly disagree) to seven (strongly agree) to the statement: "Grades in advanced accounting are good indicators of students' analytical skills. For a sample of
In a study of short-term absenteeism from work of ex-smokers, a random sample of thirty-four recent ex-smokers found a mean absenteeism of 2.21 days per month and a sample standard deviation of 2.21 days per month. For an independent random sample of eighty-six long-term ex-smokers, mean
In an agricultural experiment, two expensive high-yield varieties of corn are to be tested and the yield improvements measured. The experiment is arranged so that each variety is planted in one of each of ten pairs of similar plots. The data shown in the accompanying table are the percentage yield
Of a random sample of 142 company recruiters on college campuses, thirty-nine indicated that on average they spent sixty seconds or less studying each resum. Test the null hypothesis that at most 20% of all company recruiters spend this little time studying resums.
Of a random sample of 150 business graduates, fifty agreed or strongly agreed that em- ployees are often rewarded for unethical business behavior." Test at the 5%-level the null hypothesis that at most 25% of all business graduates would be in agreement with this assertion.
In a random sample of ninety-nine National Football League games, the home team won fifty-seven games. Test the null hypothesis that the home team wins one-half of all games against the alternative that the home team wins a majority of games.
A random sample of 104 executives from large U.S. corporations was questioned on fu- ture developments in the business environment." Of those sample members, fifty indi- cated some measure of agreement with the statement: "Firms will concentrate their efforts more on cash flow than on profits."
Of a random sample of 545 accountants engaged in preparing city operating budgets for use in planning and control, 117 indicated that estimates of cash flow were the most diffi- cult element of the budget to derive." (a) Test at the 5%-level the null hypothesis that at least 25% of all accountants
Supporters claim that a new windmill can generate an average of at least 800 kilowatts of power per day. Daily power generation for the windmill is assumed to be normally distrib- uted with a standard deviation of 120 kilowatts. A random sample of 100 days is taken to test this claim against the
An insurance company employs agents on a commission basis. It claims that in their first year, agents will eam a mean commission of at least $40,000 and that the population stan- dard deviation is no more than $6,000. A random sample of nine agents found, for com- mission in the first year. x=333
When operating normally, a manufacturing process produces tablets for which the mean weight of the active ingredient is 5 grams, and the standard deviation is .025 gram. For a random sample of twelve tablets, the following weights of active ingredient (in grams) were found: 5.01 4.96 5.00 5.00 5.03
A process produces cable for the local telephone company. When the process is operating correctly, cable diameter follows a normal distribution with mean 1.6 inches and standard deviation .05 inch. A random sample of sixteen pieces of cable found diameters with mean 1.615 inches and sample standard
State whether each of the following is true or false. (a) The significance level of a test is the probability that the null hypothesis is false. (b) A Type I error occurs when a true null hypothesis is rejected. (c) A null hypothesis is rejected at the .025 level, but is accepted at the .01 level.
A random sample of ten students found the following figures, in hours, for time spent studying in the week before final exams. 28 57 42 35 61 39 55 46 49 38 Assume that the population distribution is normal. (a) Find the sample mean and standard deviation. (b) Test at the 5% significance level the
Carefully explain what is meant by the p-value of a test, and discuss the use of this con- cept in hypothesis testing.
A statistician tests the null hypothesis that the proportion of men favoring a tax reform proposal is the same as the proportion of women. Based on sample data, the null hypothe- sis is rejected at the 5% significance level. Does this imply that the probability is at least .95 that the null
Explain carefully the distinction between each of the following pairs of terms: (a) Null and alternative hypotheses (b) Simple and composite hypotheses (c) One-sided and two-sided alternatives (d) Type I and Type II errors (e) Significance level and power
A wine producer claims that the proportion of its customers who cannot distinguish its product from frozen grape juice is at most .10. The producer decides to test this null hypothesis against the alternative that the true proportion is more than .10. The decision. rule adopted is to reject the
A fast-food chain tests cach day that the average weight of its "two-pounders" is at least 32 ounces. The alternative hypothesis is that the average weight is less than 32 ounces, in- dicating that new processing procedures are needed. The weights of two-pounders can be assumed to be normally
Refer to Exercise 24.Find the probability of accepting the null hypothesis with a 10% level test if in fact 60% of all audit partners agree that cash flow from operations is a valid measure of profitability.
Find the probability of rejecting the null hypothesis with a 5% level test it in fact 20% of all U.S. adults would disagree with the statement.
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