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Statistics For Business And Economics 4th Edition Paul Newbold - Solutions

You have been asked to design and carry out a survey in your city on the effectiveness of a radio advertising campaign aimed at promoting a new movie. (a) Outline how you would proceed. (b) Discuss the possibilities for nonsampling errors and means for minimizing their im- portance. (c) To what
A corporation has a fleet of 480 company cars--100 compact, 180 midsize, and 200 full- size. To estimate the overall mean annual repair costs for these cars, a preliminary random sample of ten cars of each type is selected. The sample standard deviations for repair costs were $105 for compacts,
A college has 3,200 undergraduate students and 800 graduate students. Interest is in the amount of money spent in a year on textbooks by these students. Initially, simple random samples of thirty undergraduate students and thirty graduate students were taken. The sample standard deviations for
A city is divided into fifty geographical subdivisions. It was required to estimate the pro- portion of households in the city interested in a new lawn care service. A random sample of three subdivisions contained 611, 521, and 734 households, respectively. The numbers expressing interest in the
In the survey of Exercise 48, the clerical employees in the eight sampled subdivisions were asked if they were satisfied with the operation of the bonus plan. The results obtained are listed in the table. SUBDIVISION NUMBER SATISFIED 1 2 3 4 5 6 7 8 24 25 21 35 44 30 34 (a) Find a point estimate of
In the survey of Exercise 47, the households were asked if they had cable television. The numbers having cable are given in the accompanying table.(a) Find a point estimate of the proportion of all households in the city having cable tele- vision. (b) Find a 90% confidence interval for this
A union executive wants to estimate the mean value of bonus payments made to a corpo- ration's clerical employees in the first month of a new plan. This corporation has fifty-two subdivisions, and a simple random sample of eight of these is taken. Information is then obtained from the payroll
A market research organization wants to estimate the mean amounts of time in a week that television sets are in use in households in a city that contains sixty-five precincts. A simple random sample of ten precincts was selected, and every household in each sampled precinct was questioned. The
Mean household income must be estimated for a town that can be divided into three dis- tricts. The relevant information is shown in the table.If a 95% confidence interval for the population mean, extending $500 on each side of the sample estimate, is required, determine how many sample observations
An auditor wants to estimate the mean value of a corporation's accounts receivable. The population is divided into four strata, containing 500, 400, 300, and 200 accounts, respec- tively. On the basis of past experience, it is estimated that the standard deviations of val- ues in these strata will
An instructor of a class of 417 students is considering the possibility of a take-home final examination. She wants to take a random sample of class members to estimate the propor tion who prefer this form of examination. If it is required that a 90% confidence interval for the population
A country club wants to poll a random sample of its 320 members to estimate the propor- tion likely to attend an early-season function. The number of sample observations should be sufficiently large to ensure that a 99% confidence interval for the population proportion ex- tends at most .05 on each
A department store has an inventory of 1,420 different products. To estimate the total dollar value of this inventory, an auditor intends to take a simple random sample of products. Based on last year's records, the population standard deviation is estimated to be $160. It is required that a 90%
The mean amount of the 812 mortgages taken out in a city in the past year must be esti mated. Based on previous experience, a real estate broker knows that the population stan- dard deviation is likely to be about $20,000. If a 95% confidence interval for the popula tion mean is to extend $2,000 on
Refer to the data of Example 18.5. If a total sample of 100 colleges is to be taken, deter mine how many of these should be 4-year schools under each of the following schemes: (a) Proportional allocation. (b) Optimum allocation, assuming the stratum population standard deviations are the same as
Refer to the data of Exercise 32.If a total sample of 135 accounts receivable is to be taken, determine how many of these should be from division 1 under each of the following schemes: (a) Proportional allocation. (b) Optimum allocation, assuming the stratum population standard deviations are the
Refer to the data of Exercise 30.If a total sample of 100 students is to be taken, determine how many of these should be freshmen and sophomores under each of the following schemes: (a) Proportional allocation. (b) Optimum allocation, assuming the stratum population standard deviations are the same
Refer to the data of Exercise 29.If a total sample of 160 households is to be taken, deter- mine how many of these should be from subdivision I under each of the following schemes: (a) Prope tional allocation. (b) Optimum allocation, assuming the stratum population standard deviations are the same
Refer to Exercise 28.If a total sample of 130 faculty members is to be taken, determine how many of these should be full professors under each of the following schemes: (a) Proportional allocation. (b) Optimum allocation, assuming the stratum population standard deviations are the same as the
A college has 152 assistant professors, 127 associate professors, and 208 full professors. A journalist with the student newspaper was interested in whether faculty members were ac- tually in their offices during posted office hours. She decided to investigate samples of forty assistant professors,
A consulting company has developed a short course on modern business forecasting meth- ods for corporate executives. The first course was attended by 150 executives. From the information they supplied, it was concluded that the technical skills of 100 course mem- bers were more than adequate to
Of the 1,395 colleges in the United States, 364 have 2-year programs and 1,031 are 4-year schools. In a random sample of forty 2-year schools, it was found that the text Statistics Can Be Fun, by A. N. Optimist was used in ten of the schools. In an independent random sample of sixty 4-year schools,
A company has three divisions, and auditors are attempting to estimate the total amounts of the company's accounts receivable. Random samples of these accounts were taken for each of the three divisions, yielding the results shown in the table.(a) Using an unbiased estimation procedure, find a
Refer to Exercise 28.1 (a) Find a 90% confidence interval for the total amount of time spent in meetings by all full professors in this college in the semester. (b) Find a 90% confidence interval for the total amount of time spent in meetings by all faculty members in this college in the semester.
In a stratified random sample of students on a small campus, sample members were asked to rate, on a scale from 1 (poor) to 5 (excellent), opportunities for extracurricular activi- ties. The results are shown in the accompanying table.(a) Find a 95% confidence interval for the mean rating that
A local bus company is planning a new route to serve four housing subdivisions. Random samples of households are taken from each subdivision and sample members are asked to rate on a scale from 1 (strongly opposed) to 5 (strongly in favor) their reaction to the pro- posed service. The results are
A college has 152 assistant professors. 127 associate professors, and 208 full professors. The college administration is investigating the amount of time these faculty members. spend in meetings in a semester. Random samples of forty assistant professors, forty asso ciate professors, and fifty full
A small town contains a total of 1,800 households. The town is divided into three districts. containing 820, 540, and 440 households, respectively. A stratified random sample of 300 households contains 120, ninety, and ninety households, respectively, from these districts. Sample members were asked
A class has 420 students. The final examination is optional--taking it can raise, but not lower, a student's grade. Of a random sample of eighty students, thirty-one indicated that they would take the final examination. Find a 90% confidence interval for the total number of students in this class
In a college dormitory, 257 of the residents are freshmen. Of a random sample of 120 of them, thirty-seven indicated strong interest in living in the dormitory next year. Find a 95% confidence interval for the proportion of freshmen in this dormitory with a strong in- terest in living there next
A business school dean is contemplating a change in the requirements for graduation. At present, business majors are required to take one science course, chosen from a list of possible courses. The proposal is that this be replaced by the requirement that a course in ecology be taken. The business
A simple random sample of 400 from a total 1,395 colleges in the United States contained 39 colleges that use the text Statistics Made Difficult and Boring by J. T. Ripper. Find a 95% confidence interval for the proportion of all colleges using Ripper's text.
A senior manager, responsible for a group of 120 junior executives, is interested in the to- tal amount of time per week spent by these people in internal meetings. A random sample of thirty-five of these executives was asked to keep diary records during the next week. When the results were
Using the data of Exercise 16, find a 90% confidence interval for the total amount of time taken in answering these 125 calls,
Using the data of Exercise 15, find a 95% confidence interval for the total amount of these. 820 accounts receivable.
Using the data of Exercise 14, find a 99% confidence interval for the total number of hours overtime billed by junior accountants in the firm during the week of interest.
Show that our estimate of the variance of the sample mean can be written When N, it follows that 0.Explain why such a conclusion is to be expected.
State whether each of the following statements is true or false: (a) For a given number of population members and a given sample variance, the larger the number of sample members, the wider is a 95% confidence interval for the popula- tion mean. (b) For a given number of population members and a
On a particular day, a consumer advice bureau received 125 calls. For a random sample of forty of these calls, it was found that mean time taken in providing the requested advice was 7.28 minutes, and the sample standard deviation was 5.32 minutes. Find a 99% confi- dence interval for the mean time
An auditor, examining a total of 820 accounts receivable of a corporation, took a random sample of sixty of them. The sample mean was $127.43, and the sample standard devia- tion was $43.27. (a) Using an unbiased estimation procedure, find an estimate of the population mean. (b) Using an unbiased
Take a random sample of fifty pages from this book and estimate the proportion of all pages that contain Figures.
A campus has 12,723 students. From a complete list of these students you want to draw a random sample of 100.Explain how you would use a table of random numbers to do this.
Obtain from your local newspaper a list of all houses advertised for sale in your city. Using the random numbers in Table 4 of the Appendix, draw a simple random sample of fifteen advertisements, and find the sample mean of the advertised prices.
Consult today's Wall Street Journal to obtain a list of all stocks traded on the New York Stock Exchange. Using the random numbers of Table 4 of the Appendix, draw a simple random sample of twenty of these stocks. For your sample, find the mean percentage in- crease in price over the past week.
One approach to nonresponse of a particular kind is the recall method. A survey of house- holds is conducted by having interviewers call on a Thursday evening. Households where no one was home are called again the following Thursday evening. This process can be continued so that households that
For the study of Exercise 5.discuss the potential for nonsampling errors and nonresponse. Indicate how you would go about minimizing these problems.
Refer to the study of Exercise 3.(a) Discuss likely sources of nonsampling errors, and indicate how these could be mini- mized. (b) Would you expect nonresponse to be a serious problem in carrying out this study? If so, how might the problem be alleviated?
Refer to the study of Exercise 2.(a) Within the sampling framework you have designed, do you see the potential for non- sampling errors? If so, what steps would you take to minimize their magnitude? (b) Is nonresponse likely to be a serious issue in this study? If so, what might be done about it?
Insurance company executives, aware of substantial increases in certain types of insurance premiums in the last few years, have become concerned about the public image of their in- dustry and the possibility of political repercussions. It has been decided to mount a public relations campaign to
A financial services corporation is considering the possibility of introducing three new types of mutual funds. It is believed that at least initially, most support for these is likely to come from its current customers. The corporation would like to assess the degree of interest these customers
The manager of a campus clothing store is considering introducing some additional brand name items, and wants to assess possible student demand for them. You have been asked to design a survey to elicit this information. Discuss, in detail, how you would proceed.
A campus administrator is interested in the views of students living in dormitories on cam- pus on various aspects of the services provided. You have been approached to carry out a survey. Suggest how you might proceed, following the six steps outlined in Section 18.1.
Suppose that you want to conduct a study to determine the views of business majors on your campus as to whether statistics should be a required course. Discuss the steps that you would take in setting up this study, the problems you might expect to encounter, and tech- niques you might employ to
A second-order autoregressive model was fitted to quarterly data on the ratio of consumer installment debt to personal income in the United States." The estimated model was X, 0.021 +1.74X,--.74X-2+ a The last two observations of this time series were X-13.217 X.-13.147 Obtain forecasts of XXX and
[This exercise requires a computer program to carry out the multiple regression calcula- tions] Using the data of Exercise 52, estimate autoregressive models of orders I through 4 for product sales. Using the procedure of Section 17.9 for testing that the autoregressive order is (p-1) against the
Refer to Exercise 53.Use the Holt-Winters seasonal method, with smoothing constants A 4. B 4, and C-2, to obtain forecasts of this carnings-per-share series for the next 4 quarters.
Refer to Exercise 54.Use the Holt-Winters method, with smoothing constants A =.3 and B=4, to obtain forecasts of the price index for the next 4 months.
The accompanying table shows fifteen monthly values on the price index of a commodity.
The table shows quarterly earnings per share of a corporation over 7 years.(a) Draw a time plot of these data. Does this graph suggest the presence of a strong sea- sonal component? (b) Use the seasonal index method to obtain a seasonally adjusted series.
The following table shows 24 annual observations on sales of a product.(a) Use the large-sample variant of the runs test to test this series for randomness. (b) Draw a time plot of the data and discuss the characteristics of the series shown by this graph. (c) Compute the series of simple centered
The accompanying table shows an index of U.S. industrial production over 14 years. (a) Test this series for randomness using the runs test. (b) Draw a time plot of these data, and discuss the features revealed by the graph. (c) Compute the series of simple centered 3-point moving averages. Graph
A manager in charge of inventory control requires sales forecasts for several products, on a monthly basis, over the next 6 months. This manager has available monthly sales records over the past 4 years for each of these products. He decides to use, as forecasts for each of the next 6 months, the
In many business applications, forecasts for future values of time series, such as sales and eamings, are made exclusively on the basis of past information on the time series in question. What features of time series behavior are exploited in the production of such forecasts?
A library purchases both books and journals. The accompanying table shows the average prices (in dollars) paid for each and the quantities purchased over a period of 6 years. Use year 1.as base. (a) Find the unweighted aggregate index of prices. (b) Find the Laspeyres price index. (c) Find the
Refer to Exercise 30, which shows monthly hourly earnings in manufacturing. (a) Obtain an index with month I as base. (b) Obtain an index with month 15 as base.
[This exercise requires a computer program to carry out the multiple regression calcula tions.] Refer to the data of Exercise 30, showing earnings over 24 months. Denote the ob servations X. (1, 2,.... 24). Now, form the series of first differences (12.3.....24) Fit autoregressive models of orders
Sometimes it is desirable to extend the model of Exercise 42 to allow for the possibility that the expected change from period to period is not 0. This augmented model, known as the random walk with drift, is written X = y +X+a Show that if this model is appropriate, forecasts of X..., standing at
For many time series, particularly prices in speculative markets, the random walk model has been found to give a good representation of actual data. This model is written X = X-+a Show that if this model is appropriate, forecasts of X... standing at time n. are given by x...= x. (1,2,3...)
For a certain product, it was found that annual sales volume could be well described by a third-order autoregressive model. The estimated model obtained was X, 202 +1.10X-48X, +.17X+a For 1993, 1994, and 1995, sales were 867, 923, and 951, respectively. Calculate sales forecasts for the years 1996
In Section 17.9, Eqs. (17.9.4)-(17.9.7), fitted autoregressive models of orders 1 through 4. are given for annual sales data. We then selected a model by testing the null hypothesis of autoregression of order (p-1) against the alterative of autoregression of order p, at the 10% significance level.
[This exercise requires a computer program to carry out the multiple regression calcula tions.] Refer to the data of Exercise 25 on corporate earnings per share. Fit autoregressive models of orders 1, 2, and 3. Use the procedure of Section 17.9 to test the hypothesis that the order of the
This exercise requires a computer program to carry out the multiple regression calcula- tions. From the data of Exercise 12 on corporate earnings per share. fit autoregressive models of orders I through 4. Use the procedure of Section 17.9 for testing that the order of the autoregression is (p 11
This exercise requires a computer program to carry out the multiple regression calcula tions.] Using the data of Exercise 11 on housing starts, estimate autoregressive models of orders through 4. Use the method of Section 17.9 for testing that the order of the autore- gression is (p-1) against the
The accompanying table shows the volume of transactions (in hundreds of thousands) in shares of a corporation over a period of 12 weeks. Using these data, estimate a first-order autoregressive model, and use the fitted model to obtain forecasts of volume for the next 3 weeks. WEEK VOLUME WEEK
Using the data of Table 17.9, estimate a first-order autoregressive model for the index of volume of shares traded. Use the fitted model to obtain forecasts for the next 4 days.
Use the Holt-Winters seasonal method to obtain forecasts of sales up to eight quarters abead, based on the data of Exercise 14.Employ smoothing constants A C 3. Graph the data and the forecasts. 5,B-4, and
Use the Holt-Winters seasonal method to obtain forecasts of sales up to eight quarters ahead, based on the data of Exercise 13.Employ smoothing constants A6, B5, and C 4. Graph the data and the forecasts.
The table shows an index of industrial production for Canada over a period of 15 years. Use the Holt-Winters procedure, with smoothing constants A-3 and B 5, to obtain forecasts over the next 5 years.
Comment on the following statement: "We know that all business and economic time se- ries exhibit variability through time. Yet if simple exponential smoothing is used, the same forecast results for all future values of the time series. Since we know that all future values will not be the same,
Suppose that in the simple exponential smoothing method, the smoothing constant ar is set equal to 1. What forecasts will result?
(a) If forecasts are based on simple exponential smoothing, with X, denoting the smoothed value of the series at timef, show that the error made in forecasting X.. standing at time (-1), can be written (b) Hence, show that we can write e = X-X X, X, -ae, from which we see that the most recent
The accompanying table shows earnings per share of a corporation over a period of 18 years.(a) Using smoothing constants a = 2, 4, 6, and .8, find forecasts based on simple expo- nential smoothing. (b) Which of the forecasts would you choose to use?
Use the method of simple exponential smoothing, with a smoothing constant of a = .3. 10 obtain forecasts of the price of gold in the next 5 years, based on the data of Exercise 10.24. Using the data of Exercise II, employ the method of simple exponential smoothing, with smoothing constant a .5. to
Based on the data of Exercise 8, use the method of simple exponential smoothing to obtain forecasts of inventory-sales ratio over the next 4 years. Use a smoothing constant of a 4, Graph the observed time series and the forecasts.
The accompanying table shows monthly product sales over a period of 3 years. Use the seasonal index method to obtain a seasonally adjusted series. EXERCISES
(a) Show that the centered s-point moving average series of Section 17.6 can be written X-2X++X+ 1) + X- (b) Show that XX 25 X-X Discuss the computational advantages of this formula in the seasonal adjustment of monthly time series.
The accompanying table shows earnings per share of a corporation over a period of 7 years. YEAR QUARTER 2 3 4 362 .370 .621 384 389 .389 .639 431 ,411 448 .712 .584 620 620 .891 570 540 690 870 .680 .780 440 .800 .780 .690 400 1.030 940 (a) Draw a time plot of these data. Does your graph suggest
Let X,*= Ex... 2m+1 be a simple centered (2m+1)-point moving average. Show that X-X- 2m+1 How might this result be used in the efficient computation of series of centered moving averages?
Compute a simple centered 7-point moving average series for the corporate earnings data of Exercise 12.Based on a time plot of the smoothed series, what can be said about its reg- ular components?
Compute simple centered 5-point moving averages for the housing starts data of Exercise 11.Draw a time plot of the smoothed series and comment on your results.
Plot the smoothed series and discuss the resulting graph.
Compute a simple centered 3-point moving average series for the gold price data of Exercise
The table shows earnings per share of a corporation over a period of 28 years.
The accompanying table shows private housing units started per thousand of population in the United States over a period of 24 years. YEAR STARTS YEAR STARTS YEAR STARTS 8.5 13 9.9 21 7.8 8.0 14 11.3 5.7 7.6 15 9.7 5.9 16 6.3 Z 4.7 4.6 (a) Use the large-sample variant of the runs test to test this
The table shows the year-end price of gold (in dollars) over 14 consecutive years. Use the runs test to test this series for randomness. YEAR PRICE (5) YEAR PRICE (5) YEAR PRICE ($) 135 6 399 166 7 450 227 8 385 533 9 308 1234 11 405 486 410 14 369 591 10 329
The accompanying table shows sample observations for a sequence of sixteen samples. each of four observations, on a quality characteristic of a product.(a) Find the sixteen sample means and sample standard deviations. (b) Find the overall mean of the sample observations. (c) Find the average sample
A department store customer complaints department has recorded the number of com- plaints received over a period of eighteen weeks. The results are shown in the accompany- ing table. WEEK COMPLAINTS WEEK COMPLAINTS WEEK COMPLAINTS 15 7 201 13 20 8 11 14 15 17 9 15 15 9 19 10 15 16 16 5 14 19 17 17
The accompanying table shows proportions of nonconforming items in a sequence of twenty samples, each of 500 observations. SAMPLE NUMBER " SAMPLE NUMBER SAMPLE NUMBER P .078 080 15 094 062 9 068 16 066 .048 10 076 17 070 086 "1 064 18 088 .092 12 .068 19 .062 074 13 1058 20 .054 .076 141 082 (a)
A process manufactures raisin scones. Periodically, a scone is inspected and the number of raisins it contains is counted. The accompanying table shows results for fifteen scones. SCONE RAISINS SCONE RAISINS SCONE RAISINS 12345 15221 18 16 15 7 13 12 8 18 13 10 14 9 14 14 7 17 10 12 15 8 (a) Find
A newspaper reader has very carefully read her local paper for twenty weeks. For each Wednesday's edition she has counted the number of typographical and/or spelling errors. The results are shown in the accompanying table. WEEK ERRORS WEEK ERRORS WEEK ERRORS 12345ST 2 4 11 6 298953 12 8 21 15 19 9

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