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Statistics For Business And Economics 4th Edition Paul Newbold - Solutions
Refer to Exercise
Refer to Example 9.6. Find the power of a 10% level test if in fact 45% of supermarket shoppers are able to state the correct price of an item immediately after putting it into the curt
Refer to Exercise 5. Find the probability of a 1%-level test accepting the null hypothesis when the true mean response is 3.95.
Refer to Exercise 3(a). Find the probability of a 5%-level test rejecting the null hypothesis when the true mean impurity concentration is 3.10%.
Refer to Exercise 2. Find the power of a 10%-level test when the true mean lifetime of bat- teries is 49 hours.
In Example 9.8, we tested the hypothesis that the mean numbers of ideas generated were the same for groups with and without a moderator. This test was based on the assumption that the two population variances were equal. Test this assumption against the alternative that the population variance is
In Exercise 36, it was assumed that population variances were equal for first-year sales of textbooks with plain and expensive cover designs. Test this assumption against a two- sided alternative.
In Exercise 34, it was assumed that population variances for assessments of the chance of material fraud were the same for auditors using a red flags questionnaire as for auditors not using this questionnaire. Test this assumption against a two-sided alterative hypothesis.
It is hypothesized that the market share of a corporation should vary more in an industry with active price competition than in one with duopoly and tacit collusion. In a study of the steam turbine generator industry." it was found that in 4 years of active price competition.the variance of General
It is hypothesized that the more expert a group of people examining a corporation's linan- cial report, the more variable will be their predictions about its future. Independent ran- dom samples, each of thirty individuals, from groups of different levels of expertise were chosen." The
Of a random sample of 1,200 people in the United States, 480 had a positive attitude to- ward lawyers. Of an independent random sample of 1,000 Canadians, 790 had a positive attitude toward lawyers. Test at the 1% significance level the null hypothesis that the pop- ulation proportions are equal,
Independent random samples of consumers were asked about satisfaction with their vehicles in two slightly different ways." The options available for answer were the sarne in the two cases. When asked how satisfied they were with their vehicles, 138 of 240 sample members opted for "very satisfied."
Of a random sample of 381 investment-grade corporate bonds. 191 had sinking funds. Of an independent random sample of 166 speculative-grade corporate bonds, 145 had sinking funds. Test against a two-sided alternative the null hypothesis that the two population proportions are equal.
Employees of a supermarket chain, facing a shutdown, were surveyed on a prospective employee ownership plan. Some employees pledged $5,000 to this plan, putting up $200 immediately, while others indicated that they did not intend to pledge. Of a random sam ple of 175 pledgers, seventy-eight had
Residential phone users were surveyed one year after access to carriers other than ATT became available for long-distance service." Of a random sample of 368 ATT users, ninety-two said they were attempting to learn more about their options, as did thirty-seven of an independent random sample of 116
In 1980, a random sample of 1.556 people were asked to respond to the statement: "Capitalism must be altered before any significant improvements in human welfare can be realized." Of these sample members, 38.4% agreed with the statement. When the same statement was presented to a random sample of
A publisher is interested in the effects on sales of college texts of expensive three-color cover designs. The publisher is planning to bring out twenty texts in the business area and randomly chooses ten of them to have expensive cover designs. The remaining ten are produced with plain covers. For
Initial public offerings prospectuses were examined." In a random sample of seventy prospectuses in which earnings forecasts were disclosed, the mean debt-to-equity ratio prior to the offering issue was 3.97, and the sample standard deviation was 6. 14.For an in- dependent random sample of
Auditors are greatly concerned by the possibility of fraud, and its detection. It was conjec- tured that auditors might be helped in the evaluation of the chances of fraud by a "red flags questionnaire"; that is, a list of potential symptoms of fraud to be assessed. To evaluate this possibility,
A political science professor is interested in comparing the characteristics of students who do and do not vote in national elections. For a random sample of 114 students who claimed to have voted in the last presidential election, she found a mean grade point average of 2.71 and standard deviation
For a random sample of 125 Japanese 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 Japanese corporate managers, the mean number of job changes was .21 and the sam- ple standard deviation was .53. Test the
The MATWES procedure was designed to measure attitudes toward women as managers. High scores indicate negative attitudes and low scores indicate positive attitudes. Independent random samples were taken of 151 male M.B.A. students and 108 female M.B.A. students. For the former group, the sample
In a study comparing state-chartered and federally chartered credit unions, a sample of 145 matched pairs of credit unious was formed. Each pair contained one state-chartered and one federally chartered credit union. The pairings were made in such a way that the two members were as similar as
Of a random sample of 172 minority small business owners, 118 said that personal sav ings was the most important source of initial financing." Test the null hypothesis that per sonal savings is the most important source of initial financing for 75% of minority small business owners against the
A random sample of fifty chief executive officers of small companies was asked about ex- pectations in job interviews. Of these sample members, twenty-eight agreed that the inter- viewer usually expects the interviewee to have learned as much as possible about the com pany beforehand. Test the null
Of a random sample of 199 audit partners in U.S. accounting firms. 104 indicated some measure of agreement with the statement: "Cash flow from operations is a valid measure of profitability. Test at the 10% significance level against a two-sided alternative the null hypothesis that one-half of the
In a random sample of 160 business school graduates, seventy-two sample members indi- cated some measure of agreement with the statement: "A reputation for ethical conduct is less important for a manager's chances for promotion than a reputation for making money for the firm. Test the null
In a random sample of 998 adults in the U.S., 17.3% of sample members indicated some measure of disagreement with the statement: "Capitalism is more than an economic sys- tem-it is a complex of institutions, attitudes and culture." Test at the 5% level the nuil hypothesis that at least 25% of all
Of a sample of 361 owners of retail service and business firms which had gone into bank- ruptcy, 105 reported having no professional assistance prior to opening the business." Test the null hypothesis that at most 25% of all members of this population had no profes- sional assistance before opening
An instructor has decided to introduce a greater component of independent study into an intermediate macroeconomics course, as a way of motivating students to work indepen- dently and think more carefully about the course material. A colleague cautions that a pos- sible consequence may be increased
A company produces electric devices operated by a thermostatic control. The standard de- viation of the temperature at which these controls actually operate should not exceed 2.0 Fahrenheit. For a random sample of twenty of these controls, the sample standard devia-tion of operating temperatures
One way to evaluate the effectiveness of a teaching assistant is to examine the scores achieved by his or her students in an examination at the end of the course. Obviously, the mean score is of interest. However, the variance also contains useful information--some teachers have a style that works
Plastic sheets produced by a machine are periodically monitored for possible fluctuations in thickness. If the true variance in thicknesses exceeds 2.25 square millimeters, there is cause for concem about product quality. Thickness measurements for a random sample of ten sheets produced in a
At the insistence of a government inspector, a new safety device is installed in an assembly- line operation. After the installation of this device, a random sample of eight days output gave the following results for numbers of finished components produced: 618 660 638 625 571 598 639 582
In contract negotiations, a company claims that a new incentive scheme has resulted in average weekly earnings of at least $400 for all production workers. A union representa tive takes a random sample of fifteen workers and finds that their weekly earnings have an average of $381.35 and a standard
A beer distributor claims that a new display, featuring a life-size picture of a well-known athlete, will increase product sales in supermarkets by an average of 50 cases in a week. For a random sample of twenty supermarkets, the average sales increase was 41.3 cases and the sample standard
A statistics instructor is interested in the ability of students to assess the difficulty of a test they have taken. This test was taken by a large group of students, and the average score was 78.5. A random sample of eight students was asked to predict this average score. Their predictions were:
A process that produces bottles of shampoo, when operating correctly, produces bottles whose contents weigh, on average, 20 ounces. A random sample of nine bottles from a single production run yielded the following contents weights (in ounces): 21.4 19.7 19.7 20.6 20.8 20.1 19.7 20.3 20.9 Assuming
A company selling franchises advertises that operators obtain, on average during the first year, a yield of 10% on their initial investments. A random sample of ten of these fran chises produced the following yields for the first year of operation: 6.1 9.2 IL5 8.6 12.1 3.9 8.4 10.1 9.4 8.9 Assuming
On the basis of a random sample, the null hypothesis is tested against the alternative H:p> the 5% significance level. is contained in the 95% confidence interval for and the null hypothesis is accepted at (a) Does this necessarily imply that (b) Does this necessarily imply that if the observed
In Exercise 64, we found a confidence interval for the proportion of American consumers who believe they own an American-made television set. How many sample observations would be needed to be sure that a 95% confidence interval for the population proportion extends no more than .05 on each side of
Samples of Small Business Center clients considering starting a business were questioned. Of a random sample of 94 males, 50 received assistance in business planning. Of an inde pendent random sample of 68 females, 40 received assistance in business planning. Find a 99% confidence interval for the
Of a random sample of 69 Canadian industrial firms, 43 did market research in-house. Of an independent random sample of 69 Canadian consumer goods firms. 30 did market re- search in-house." Find a 95% confidence interval for the difference between the popula- tion proportions of these two types of
Of a random sample of 569 males in introductory college accounting classes. 90 dropped the class. Of an independent random sample of $17 females in these classes, 85 dropped the class. Find a 90% confidence interval for the difference in the population proportions of males and females who drop
Of a random sample of 151 marketing executives in consumer goods manufacturing, 76.0% said that brand identification held by incumbents was an important or extremely important harrier to entering a new market. Based on this information a statistician com puted, for the population proportion with
Of a random sample of 87 firms with employee stock ownership plans, 54 said that the pri- mary motivation for setting up such a plan was tax-related." (a) Find a 90% confidence interval for the population proportion of all such firms with this primary motivation. (b) Without doing the calculations,
Of a random sample of 113 American consumers, 57 claimed to own an American-made television set." (a) Find a 95% confidence interval for the population proportion of all American con- sumers who would make this claim. (b) Without doing the calculations, state whether a 90% confidence interval for
Of a random sample of 177 people who claimed to be able to correctly identify the official credit card sponsor of the 1988 Calgary Winter Olympic Games, 106 correctly nominated. Visa. Find a 90% confidence interval for the population proportion of those making this claim who could in fact do so.
In a random sample of 1,158 newly promoted executives, 47.9% rated a statistics course as very important or somewhat important as part of the preparation for a career in general management." (a) Find a 99% confidence interval for the population proportion of all newly promoted executives holding
In order to estimate the mean value of the purchases of card holders in a month, a credit card company takes a random sample of twelve monthly statements and obtains the fol- lowing amounts in dollars: 1 Assuming that the population distribution is normal, find a 90% confidence interval for the
(a) Explain the relevance of the central limit theorem to interval estimation for a popula- tion mean (b) In Section 8.7, we discussed two different procedures for finding confidence intervals for the difference between population means. Explain why two different procedures are needed, and provide
Suppose that time spent, in hours, by students studying for a test has a normal distribution. A random sample of six students found the following results for hours spent studying (a) Find the sample mean and sample variance. 24.0 (b) Find a 99% confidence interval for the population mean. (c) Find
A random sample of sixteen tires of a particular brand found a sample mean of 32.0 thou- sand miles for lifetime, and a sample standard deviation of 6.4 thousand miles. Assume that the population distribution is normal. (a) Find a 90% confidence interval for the population mean, in thousands of
The numbers of requests for seats on a particular airline flight for midweek days can be as- sumed to be normally distributed. A random sample of eighty-one observations on num- bers of requests for this flight was taken. The sample mean number of requests for seats was 112, and the sample standard
A random sample of 595 packaging professionals was asked to assess on a scale from one (completely unethical) to seven (completely ethical) the practice of packaging a store brand to closely resemble a national brand. The sample mean response was 3.38 and the sample standard deviation was 1.80. (a)
A brewing company knows that the quantities of beer in its cans have a normal distribu- tion with standard deviation .2 ounce. (a) A random sample of twenty-five cans was taken, and using the sample results, a statis- tician found a confidence interval for the population mean ranging from 11.98
Based on independent random samples from the two populations, an investigator found a 95% confidence interval for the difference between mean fuel consumption for X-cars and for Y-cars, running from 6 to 1.9 miles per gallon. Does this imply that the probability is .95 that the true difference in
An investigator wants to compare two population proportions and intends to take indepen- dent random samples of the same size from each population. She wants to be sure that a 90% confidence interval for the difference between the two population proportions ex- tends no further than 05 on each side
A politician wants to estimate the proportion of constituents favoring a controversial piece of proposed legislation. Suppose that a 99% confidence interval that extends at most .05 on each side of the sample proportion is required. How many sample observations are needed?
A research group wants to estimate the proportion of consumers who claim, all else equal, that they would purchase a domestically made product rather than a foreign competitor. It is required that a 95% confidence interval for the population proportion extends at most 04 on either side of the
Using the information in Exercise 3, find the number of sample observations required for a 99% confidence interval for the population mean amount of impurities to extend 5 gram on each side of the sample mean.
Using the information in Exercise 2, find the sample size needed so that a 90% confidence interval for the population mean weight of bricks extends an amount .01 on each side of the sample mean
Using the information in Exercise 1, find the number of sample observations necessary to obtain a 95% confidence interval for the population mean grade point average extending .05 point on each side of the sample mean.
A random sample of 100 men contained sixty-one in favor of a state constitutional amend- ment to retard the rate of growth of property taxes. An independent random sample of 100 women contained fifty-four in favor of this amendment. The confidence interval 04
Of a random sample of 154 physicians, 59.0% viewed hospital advertising as a poor or very poor idea. Of an independent random sample of 310 consumers, 24.2% had this view. Find a 95% confidence interval for the difference between the two population pro- portions with this view of hospital
Of a random sample of 1.203 business students in 1979, 20.2% said that teaching as a ca- reer was very unappealing. Of an independent random sample of 1.203 business students in 1989, 13.2% had this reaction to teaching as a carcer." Find a 99% confidence interval for the difference between the
Of a random sample of 112 large retailers, 70 used regression as a method of forecasting. Of an independent random sample of 135 small retailers, 65 used regression as a method of forecasting. Find a 95% confidence interval for the difference between the two popu- lation proportions.
Students in an introductory economics class are assigned to quiz sections conducted by teaching assistants. For one teaching assistant, the twenty-one students in the quiz section obtained a mean score of 72.1 on the final examination, and a standard deviation of 11.3. For a second teaching
A company sends a random sample of twelve of its salespeople to a course designed to in- crease their motivation and hence, presumably. their effectiveness. In the following year. these people generated sales with an average value of $435.000 and a sample standard de- viation of $56,000. During the
A researcher intends to estimate the effect of a drug on the scores of human subjects per- forming a task of psychomotor coordination. The members of a random sample of nine subjects were given the drug prior to testing. Their mean score was 9.78, and the sample variance was 17.64. An independent
For a random sample of 190 firms that revalued their fixed assets, the mean ratio of debt to tangible assets was 517 and the sample standard deviation was 148. For an independent random sample of 417 firms that did not revalue their fixed assets," the mean ratio of debt to tangible assets was 489
Recent business graduates currently employed in full-time positions were surveyed. Family backgrounds were self-classified as relatively high or low socioeconomic status." For a random sample of 138 high socioeconomic status recent business graduates, mean total compensation was $36,558 and the
In a survey of practicing certified public accountants on women in the accounting profes sion, sample members were asked to respond on a scale from one (strongly disagree) to five (strongly agree) to the statement: "Women are equally acceptable to clients as are men to perform work on engagements."
For a random sample of forty accounting students in a class using group learning tech- niques, the mean examination score was 322.12. and the sample standard deviation was 54.53. For an independent random sample of sixty-one students in the same course but in a class not using group learning
A manufacturer bonds a plastic coating to a metal surface. A random sample of nine ob servations on the thicknesses of this coating is taken from a week's output. The sample thicknesses (in millimeters) were as follows: Assuming that the population distribution is normal, find a 90% confidence
A manufacturer is concerned about the variability of the levels of impurity contained in consignments of raw material from a supplier. A random sample of fifteen consignments showed a standard deviation of 2.36% in the concentration of impurity levels. Assume a normal population distribution. (a)
A psychologist wants to estimate the variance of employee test scores. A random sample of eighteen scores had sample standard deviation 10.4. Find a 90% confidence interval for the population variance. What assumption, if any, have you made in calculating this inter- val estimate?
Given the same sample information, it is possible (in principle) to obtain narrower confi- dence intervals, of the same probability content, for the population variance than those found in this section. Explain graphically why this is so.
The confidence intervals for the population variance described in this section are not cen- tered on the sample variance. Explain graphically why this is so.
Using the data of Exercise 13, find a 95% confidence interval for the population standard deviation of all test scores of the group of students.
Using the data of Exercise 12, find a 90% confidence interval for the population standard deviation of weight losses for patients of the clinic's weight reduction program.
Using the data of Exercise 11.find an 80% confidence interval for the population variance of the speeds of all automobiles travelling over this stretch of highway.
A random sample of fifteen financial analysts' forecasts of next year's earnings per share for General Motors Corporation was taken. The sample standard deviation was 5.880. Find a 95% confidence interval for the variance of predicted earnings per share for all analysts.
Of a random sample of 198 marketing students, 98 rated a case of resum inflation as un- ethical. Based on this information, a statistician computed for the population proportion a confidence interval running from 445 to 545. What is the probability content of this interval?
A random sample was taken of 96 foreign manufacturers, with direct investment in the United States, who use independent U.S. industrial distributors. Of these sample members, 32 said the distributors were rarely or never capable of performing the advice and techni- cal support function." Find an
Of a random sample of 95 small manufacturing firms, 29 indicated improvements in qual- ity as the most important action taken to revitalize products or improve competitive performance." (a) Find a 99% confidence interval for the population proportion. (b) Without doing the calculations, state
Of a random sample of 134 auditors employed by major auditing firms, 82 said that, on re- ceiving new audit business, they always enquired of the predecessor auditor the reason for the change of auditors." Find a 95% confidence interval for the population proportion.
Of a random sample of 323 union members, 47.9% agreed or strongly agreed with the statement: "Union workers should refuse to work when a nonunion worker is sent to the job. Based on this information, a statistician calculated, for the percentage of all union members with this view, a confidence
A random sample was taken of 189 National Basketball Association games in which the score was not tied after one quarter. In 132 of these games, the team leading after one quarter won the game." (a) Find a 90% confidence interval for the population proportion of all occasions on which the team
In October 1992, ownership of the San Francisco Giants baseball team was considering a sale of the franchise that would lead to a move to St. Petersburg, Florida. A random sam- ple of 610 San Francisco Bay Area taxpayers, carried out by The San Francisco Examiner, contained 50.7% who would be
A car rental company is interested in the amount of time its vehicles are out of operation for repair work. A random sample of nine cars showed that over the past year, the numbers of days each had been inoperative were 19 16 10 21 22 8 17 19 14 Stating any assumptions you need to make, find a 90%
A manufacturer of electronic games is considering their installation in campus bars. In a pilot study of the potential profitability of this enterprise, games were placed for one week in ten randomly chosen college bars. Denoting by x, weekly profits in dollars, the follow- ing sample results were
A business school placement officer wants to estimate the mean annual salaries of the school's former students 5 years after graduation. A random sample of twenty-five such graduates found a sample mean of $42.740 and a sample standard deviation of $4,780. Assuming that the population distribution
A population has a normal distribution with unknown mean and unknown variance. Based on the material of Section 8.4, it is possible, given a random sample of two observations, to find confidence intervals for the population mean. However, this is not possible for a sample of one observation.
Scores obtained by a large group of students taking a test are known to be normally dis- tributed. A random sample of twenty-five test scores yielded the following statistics: x-1,508 (a) Find the sample mean and variance. x-95,628 (b) Find a 90% confidence interval for the population mean.
A clinic offers a weight reduction program. A review of its records found the following weight losses, in pounds, for a random sample of ten of its patients at the conclusion of the program. 18.2 20.3 25.9 6.3 11.8 15.4 16.8 19.5 12.3 17.2 Assume the population distribution is normal. (a) Find a
There is concern about the speed of automobiles traveling over a particular stretch of high- way. For a random sample of seven automobiles, radar indicated the following speeds, in miles per hour: 79 73 68 77 86 71 69 (a) Find the sample mean and variance. (b) Assuming a normal population
A retail clothing store is interested in the expenditures on clothes of college students in the first month of the school year. For a random sample of nine students, the mean expendi- ture was $157.82, and the sample standard deviation was $38.89. Assuming that the pop- ulation distribution is
A random sample, X., X....X.. of observations is taken from a population with mean and variance of o. Consider the following estimator of 2 n(n + 1) (X,+2X+3X, + +nX) (a) Show that is an unbiased estimator of p. (b) Find the efficiency of relative to X, the sample mean. Hint: n(n + 1) 2 and IM
A random sample of ten X-cars achieved the following fuel consumption figures, in miles per gallon:An independent random sample of twelve Y-cars achieved the following results: (a) Use an unbiased estimation procedure to obtain a point estimate of the difference in population mean fuel consumption
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