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Statistics For Business And Economics 8th Edition Paul Newbold, William Carlson, Betty Thorne - Solutions

An instructor in an economics class is considering three different texts. He is also considering three types of examinations-multiple choice, essay, and a mix of multiple choice and essay questions. During the year he teaches nine sections of the course and randomly assigns a text-examination type
Four real estate agents were asked to appraise the values of 10 houses in a particular neighborhood. The appraisals were expressed in thousands of dollars, with the results shown in the following table.Source of Variation Sum of SquaresBetween agents ......... 268Between houses
Four brands of fertilizer were evaluated. Each brand was applied to each six plots of land containing soils of different types. Percentage increases in corn yields were then measured for the 24 brand-soil-type combinations.The results obtained are summarized in the accompanying table.Source of
Three television pilots for potential situation-comedy series were shown to audiences in four regions of the country-the East, the South, the Midwest, and the West Coast. Based on audience reactions, a score (on a scale from 0 to 100) was obtained for each show. The sums of squares between groups
A manufacturer of cereal is considering three alternative box colors-red, yellow, and blue. To check whether such a consideration has any effect on sales, 16 stores of approximately equal size are chosen. Red boxes are sent to 6 of these stores, yellow boxes to 5 others, and blue boxes to the
Suppose that, in the two-way analysis of variance setup with one observation per cell, there are just two groups. Show in this case that the F ratio for testing the equality of the group population means is precisely the square of the test-statistic discussed in Section 10.1 for testing equality of
Consider an experiment with treatment factors A and B, with factor A having four levels and factor B having three levels. The results of the experiment are summarized in the following analysis of variance table.Compute the mean squares and test the null hypotheses of no effect from either treatment
Consider an experiment with treatment factors A and B, with factor A having five levels and factor B having six levels. The results of the experiment are summarized in the following analysis of variance table:Compute the mean squares and test the null hypotheses of no effect from either treatment
Consider an experiment with treatment factors A and B, with factor A having three levels and factor B having seven levels. The results of the experiment are summarized in the following analysis of variance table:Compute the mean squares and test the null hypotheses of no effect from either
Suppose that scores given by judges to competitors in the ski-jumping events of the Winter Olympics were analyzed. For the men's ski-jumping competition, suppose there were 22 contestants and 9 judges. Each judge in seven subevents assessed each contestant. The scores given can, thus, be treated in
Refer to Exercise 15.44. Twelve pairs were entered in the ice-dancing competition. Once again, there were 9 judges, and contestants were assessed in seven subevents. The sums of squares between groups (pairs of contestants) and between blocks (judges) were found to beIn exercise Source of
A psychologist is working with three types of aptitude tests that may be given to prospective management trainees. In deciding how to structure the testing process, an important issue is the possibility of interaction between test takers and test type. If there were no interaction, only one type of
Random samples of two freshmen, two sophomores, two juniors, and two seniors each from four dormitories were asked to rate, on a scale of 1 (poor) to 10 (excellent), the quality of the dormitory environment for studying. The results are shown in the following table:a. Set up the analysis of
In some experiments with several observations per cell the analyst is prepared to assume that there is no interaction between groups and blocks. Any apparent interaction found is then attributed to random error. When such an assumption is made, the analysis is carried out in the usual way, except
Refer to Exercise 15.31. Having carried out the experiment to compare mean yields per acre of four varieties of corn and three brands of fertilizer, an agricultural researcher suggested that there might be some interaction between variety and fertilizer. To check this possibility, another set of
An instructor has a class of 23 students. At the beginning of the semester, each student is randomly assigned to one of four teaching assistants€”Smiley, Haydon, Alleline, or Bland. The students are encouraged to meet with their assigned teaching assistant to discuss difficult course material.
Refer to Exercise 15.33. Suppose that a second store for each region-can color combination is added to the study, yielding the results shown in the following table. Combining these results with those of Exercise 15.33, carry out the analysis of variance calculations and discuss your findings.
Having carried out the study of Exercise 15.34, the instructor decided to replicate the study the following year. The results obtained are shown in the table.Combining these results with those of Exercise 15.34, carry out the analysis of variance calculations and discuss your findings.
Carefully distinguish between the one-way analysis of variance framework and the two-way analysis of variance framework. Give examples different from those discussed in the text and exercises of business problems for which each might be appropriate.
Carefully explain what is meant by the interaction effect in the two-way analysis of variance with more than one observation per cell. Give examples of this effect in business-related problems.
Consider a study to assess the readability of financial report messages. The effectiveness of the written message is assessed using a standard procedure. Financial reports were given to independent random samples from three groups-certified public accountants, chartered financial analysts, and
In an experiment designed to assess aids to the success of interviews of graduate students carried out by faculty mentors, interviewers were randomly assigned to one of three interview modes-feedback, feedback and goal setting, and control. For the feedback mode interviewers had the opportunity to
A study classified each of 134 lawyers into one of four groups based on observation and an interview. The 62 lawyers in group A were categorized as having high levels of stimulation and support and average levels of public spirit. The 52 lawyers in group B had low stimulation, average support, and
In a study to estimate the effects of smoking on routine health risk, employees were classified as continuous smokers, recent ex-smokers, long-term ex-smokers, and those who never smoked. Samples of 96, 34, 86, and 206 members of these groups were taken. Sample mean numbers of mean health risk
Michigan has had restrictions on price advertising for wine. However, for a period these restrictions were lifted. Data were collected on total wine sales over three periods of time-under restricted price advertising, with restrictions lifted, and after the re-imposition of restrictions. The
Independent random samples of the selling prices of houses in four districts were taken. The selling prices (in thousands of dollars) are shown in the accompanying table. Test the null hypothesis that population mean selling prices are the same in all four districts.
Three suppliers provide parts in shipments of 500 units. Random samples of six shipments from each of the three suppliers were carefully checked, and the numbers of parts not conforming to standards were recorded. These numbers are listed in the following table:a. Prepare the analysis of variance
For the data of Exercise 15.59, use the Kruskal-Wallis test to test the null hypothesis that the population mean selling prices of houses are the same in the four districts.In exercise
A study was aimed at assessing the class-schedule satisfaction levels, on a scale of 1 (very dissatisfied) to 7 (very satisfied), of nontenured faculty who were job-sharers, full time, or part-time. For a sample of 25 job-sharers, the mean satisfaction level was 6.60; for a sample of 24 full-time
Consider the one-way analysis of variance setup.a. Show that the within-groups sum of squares can be written as follows:b. Show that the between-groups sum of squares can be written as follows:c. Show that the total sum of squares can be written as follows:
Consider the two-way analysis of variance setup, with one observation per cell.a. Show that the between-groups sum of squares can be written as follows:b. Show that the between-blocks sum of squares can be written as follows:c. Show that the total sum of squares can be written as follows:d. Show
Information on consumer satisfactions of three price groupings for beer-high, medium, and low-were obtained from a random sample of 125 consumers. The sums of squares for these satisfaction measures are given in the accompanying table. Complete the analysis of variance table, and test the null
Three real estate agents were each asked to assess the values of five houses in a neighborhood. The results, in thousands of dollars, are given in the table. Prepare the analysis of variance table, and test the null hypothesis that population mean valuations are the same for the three real estate
Students were classified according to three parental income groups and also according to three possible score ranges on the SAT examination. One student was chosen randomly from each of the nine cross-classifications, and the grade point averages of those sample members at the end of the sophomore
For the two-way analysis of variance model with one observation per cell, write the observation from the ith group and jth block asXij = µ + Gi + Bj + eijRefer to Exercise 15.65 and consider the observation on agent B and house (x21 = 218).a. Estimate µ.b. Estimate and interpret G2.c. Estimate
Refer to Exercise 15.66 and consider the observation on moderate-income group and high SAT score (x21 = 218).a. Estimate µ.b. Estimate and interpret G2.c. Estimate and interpret B2.d. Estimate ε22.
Consider the two-way analysis of variance setup, with µ observations per cell.a. Show that the between-groups sum of squares can be written as follows:b. Show that the between-blocks sum of squares can be written as follows:c. Show that the error sum of squares can be written as follows:d. Show
A corporation is trying to decide which of three makes of automobile to order for its fleet-domestic, Japanese, or European. Five cars of each type were ordered, and, after 10,000 miles of driving, the operating cost per mile of each was assessed. The accompanying results in cents per mile were
Purchasing agents were given information about a cellular phone system and asked to assess its quality. The information given was identical except for two factors-price and country of origin. For price there were three possibilities: $150, $80, and no price given. For country of origin there were
In the study of Exercise 15.70, information on the cellular phone system was also shown to MBA students. Part of the analysis of variance table for their quality assessments is shown here. Complete the analysis of variance table and provide a full analysis of these data.
Having carried out the study of Exercise 15.66, the investigator decided to take a second independent random sample of one student from each of the nine income-SAT score categories. The grade point averages found are given in the accompanying table.a. Prepare the analysis of variance table.b. Test
An experiment was carried out to test the effects on yields of five varieties of corn and five types of fertilizer. For each variety-fertilizer combination, six plots were used and the yields recorded, with the results shown in the following table:a. Test the null hypothesis that the population
Random samples of seven freshmen, seven sophomores, and seven juniors taking a business statistics class were drawn. The accompanying table shows scores on the final examination.a. Prepare the analysis of variance table.b. Test the null hypothesis that the three population mean scores are equal.c.
Samples of four salespeople from each of four regions were asked to predict percentage increases in sales volume for their territories in the next 12 months. The predictions are shown in the accompanying table.a. Prepare the analysis of variance table.b. Test the null hypothesis that the four
The data file Housing Starts shows private housing units started per thousand of population in the United States over a period of 24 years. Use a computer to prepare a time plot of this series and comment on the components of the series revealed by this plot.
a. Show that the centered s-point moving average series of Section 16.2 can be written as follows:b. Show thatDiscuss the computational advantages of this formula in the seasonal adjustment of monthly time series.
The data file Inventory Sales shows the inventory sales ratio for manufacturing and trade in the United States over a period of 12 years. Use the method of simple exponential smoothing to obtain forecasts of the inventory-sales ratio over the next 4 years. Use a smoothing constant of α = 0.6.
The data file Gold Price shows the year-end price of gold (in dollars) over 14 consecutive years. Use the method of simple exponential smoothing, with a smoothing constant of α = 0.7, to obtain forecasts of the price of gold in the next 5 years.
The data file Housing Starts shows private housing units started per thousand of population in the United States over a period of 24 years. Using the data, employ the method of simple exponential smoothing with smoothing constant a = 0.5 to predict housing starts in the next 3 years.
The data file Earnings per Share shows earnings per share of a corporation over a period of 18 years.a. Using smoothing constants a = 0.8, 0.6, 0.4, and 0.2, find forecasts based on simple exponential smoothing.b. Which of the forecasts would you choose to use?
Comment on the following statement: We know that all business and economic time series 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, this
The data file Industrial Production Canada shows an index of industrial production for Canada over a period of 15 years. Use the Holt-Winters procedure with smoothing constants α = 0.7 and β = 0.5 to obtain forecasts over the next 5 years.
The data file Hourly Earnings shows manufacturing hourly earnings in the United States over 24 months. Use the Holt-Winters procedure with smoothing constants α = 0.7 and β = 0.6 to obtain forecasts for the next 3 months.
The data file Earnings per Share shows earnings per share of a corporation over a period of 28 years. Use a computer to prepare a time plot of this series and comment on the components of the series revealed by this plot.
The data file Food Prices shows an index of food prices, seasonally adjusted, over a period of 14 months in the United States. Use the Holt-Winters method with smoothing constants α = 0.5 and β = 0.5 to obtain forecasts for the next 3 months.
The data file Profit Margins shows percentages of profit margins of a corporation over a period of 11 years. Obtain forecasts for the next 2 years, using the Holt-Winters method with smoothing constants α = 0.4 and β = 0.4.
The data file Quarterly Earnings shows quarterly sales of a corporation over a period of 6 years. Use the Holt-Winters seasonal method to obtain forecasts of sales up to eight quarters ahead. Employ smoothing constants α = 0.4, β = 0.5, and γ = 0.6. Graph the data and the forecasts.
The data file Quarterly Sales shows quarterly sales of a corporation over a period of 6 years. Use the Holt-Winters seasonal method to obtain forecasts of sales up to eight quarters ahead. Employ smoothing constants α = 0.5, β = 0.6, and γ = 0.7. Graph the data and the forecasts.
Using the data in the data file Earnings per Share, estimate a first-order autoregressive model for the earnings per share. Use the fitted model to obtain forecasts for the next 4 days.
The data file Trading Volume 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.
Using the data file Housing Starts, estimate autoregressive models of orders 1 through 4. Use the method of this section to test the hypothesis that the order of the autoregression is p – 1 against the alternative that the order is p, with a significance level of 10%. Select one of these models,
From the data file Earnings per Share on corporate earnings per share, fit autoregressive models of orders 1 through 4. Use the procedure of this section to test the hypothesis that the order of the autoregression is p - 1 against the alternative that the true order is p, with a 10% significance
In Figure, 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 alternative of autoregression of order p at the 5% significance level. Repeat this procedure, but
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 as follows: xt = 202 + 1.10xt-1 – 0.48xt-2 + 0.17xt-3 + εt For 1993, 1994, and 1995, sales were 867, 923, and 951, respectively. Calculate
The data file Fargo Electronics Earnings shows quarterly sales of a corporation over a period of 6 years.a. Draw a time plot of this series and discuss its features.b. Use the seasonal-index method to seasonally adjust this series. Graph the seasonally adjusted series and discuss its features.
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 as follows:xt = xt-1 + εtShow that, if this model is appropriate, forecasts of xn+h, standing at time n, are given byx`n+h = xn
Refer to the data file Hourly Earnings, showing earnings over 24 months. Denote the observations xt (t = 1, 2, .., 24). Now, form the series of first differences:zt = xt – xt-1 (t = 2, 3, c, 24)Fit autoregressive models of orders 1-4 to the series zt.Using the approach of this section for testing
Explain the statement that a time series can be viewed as being made up of a number of components. Provide examples of business and economic time series for which you would expect particular components to be important.
The data file Quarterly Earnings 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 seasonal component?b. Use the seasonal index method to obtain a seasonally adjusted series.
The data file Product Sales shows 24 annual observations on sales of a product. Use simple exponential smoothing with smoothing constant α = 0.5 to obtain forecasts of sales for the next 3 years.
Refer to the data file Quarterly Earnings. Use the Holt-Winters seasonal method with smoothing constants α = 0.6, β = 0.6, and γ = 0.8 to obtain forecasts of this earnings-per-share series for the next four quarters.
Using the data file Product Sales, estimate autoregressive models of orders 1-4 for product sales. Using the procedure of Section 16.4 for testing the hypothesis that the autoregressive order is p - 1 against the alternative that the order is p, with a significance level of 10%, choose one of these
The data file Fargo Electronics Sales shows quarterly sales of a corporation over a period of 6 years.a. Draw a time plot of this series and discuss its features.b. Use the seasonal-index method to seasonally adjust this series. Graph the seasonally adjusted series and discuss its features.
Using the data in the file Macro2010, develop and autoregressive model for the prime interest rate. First, use the data for the period 1980, first quarter, through 2000, fourth quarter, to forecast for the quarters in years 2001-2003. Then use the data from 1980, first quarter, through 2007, fourth
Using the data in the file Macro2010 develop an autoregressive model for the Personal Consumption Expenditures. First, use the data for the period 1980, first quarter, through 2000, fourth quarter, to forecast for the quarters in years 2001-2003. Then use the data from 1980, first quarter, through
Using the data in the file Macro2010 develop an autoregressive model for fixed investment. First, use the data for the period 1965, first quarter, through 2000, fourth quarter, to forecast for the quarters in years 2001-2003. Then use the data from 1965, first quarter, through 2007, fourth quarter,
Using the data in the file Macro2010, develop an autoregressive model for imports. First, use the data for the period 1970, first quarter, through 2000, fourth quarter, to forecast for the quarters in years 2001-2003. Then use the data from 1970, first quarter, through 2007, fourth quarter, to
The data file Gold Price shows the year-end price of gold (in dollars) over 14 consecutive years. Compute a simple, centered 3-point moving average series for the gold price data. Plot the smoothed series and discuss the resulting graph.
The data file Housing Starts shows private housing units started per thousand of population in the United States over a period of 24 years. Compute a simple, centered 5-point moving average series for the housing starts data. Draw a time plot of the smoothed series and comment on your results.
The data file Earnings per Share shows earnings per share of a corporation over a period of 28 years. Compute a simple, centered 7-point moving average series for the corporate earnings data. Based on a time plot of the smoothed series, what can be said about its regular components?
Letbe a simple, centered (2m + 1)-point moving average. Show that How might this result be used in the efficient computation of series of centered moving averages?
The data file Acme LLC Earnings per Share shows earnings per share of a corporation over a period of 7 years.a. Draw a time plot of these data. Does your graph suggest the presence of a strong seasonal component in this earnings series?b. Using the seasonal index method, obtain a seasonally
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, 90, and 90 households, respectively, from these three districts. Sample members were asked
Refer to Exercise 17.2. 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 allocationb. Optimum allocation, assuming the stratum population standard deviations are the same as the
Refer to the data of Exercise 17.3. If a total sample of 160 households is to be taken, determine how many of these should be from subdivision 1 under each of the following schemes.a. Proportional allocationb. Optimum allocation, assuming the stratum population standard deviations are the same as
Refer to the data of Exercise 17.4. 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 allocationb. Optimum allocation, assuming the stratum population standard deviations are the same
Refer to the data of Exercise 17.6. 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 allocationb. Optimum allocation, assuming the stratum population standard deviations are the
Refer to the data of Example 17.2. If a total sample of 100 colleges is to be taken, determine how many of these should be 4-year schools under each of the following schemes.a. Proportional allocationb. Optimum allocation, assuming the stratum population standard deviations are the same as the
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, respectively. On the basis of past experience, it is estimated that the standard deviations of values in these strata will be
Mean household income must be estimated for a town that can be divided into three districts. 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 in
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 65 precincts. A simple random sample of 10 precincts was selected, and every household in each sampled precinct was questioned. The following
A union executive wants to estimate the mean value of bonus payments made to a corporation's clerical employees in the first month of a new plan. This corporation has 52 subdivisions, and a simple random sample of 8 of these is taken. Information is then obtained from the payroll records of every
In the survey of Exercise 17.17, 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 television.b. Find a 90% confidence interval for this
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 40 assistant professors, 40 associate professors, and 50 full professors
In the survey of Exercise 17.18, 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 following table:a. Find a point estimate of the proportion of all clerical employees satisfied with
A city is divided into 50 geographic subdivisions. An estimate was required of the proportion 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 service
A bank holds 720 delinquent mortgages in residential properties. It required an estimate of the mean current appraised value of these properties. Initially, a random sample of 20 was appraised, and a sample standard deviation of $37,600 was found. If the bank requires a 90% confidence interval for
A college has 3,200 undergraduate students and 800 graduate students. Researchers are interested in the amount of money spent in a year on textbooks by these students. Initially, simple random samples of 30 undergraduate students and 30 graduate students were taken. The sample standard deviations
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 10 cars of each type is selected.The sample standard deviations for repair costs are $105 for compact cars, $162

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