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Statistics For Business And Economics 4th Edition Paul Newbold - Solutions
A process produces rolls of coated paper. A sequence of twenty rolls was inspected over time and the numbers of imperfections were recorded. The results are shown in the ac- companying table.(a) Find the sample mean number of imperfections per roll. (b) Find the central line and lower and upper
The accompanying table shows numbers of nonconforming items in a sequence of twenty- live samples, each of 250 observations. SAMPLE NUMBER NUMBER NONCONFORMING 23 15 18 SAMPLE NUMBER NUMBER NONCONFORMING SAMPLE NUMBER NUMBER NONCONFORMING 10 15 18 26 11 25 19 12 17 20 28 12 16 13.21 23 14 20 15 19
The accompanying table shows proportions of nonconforming items in a sequence of twenty samples, each of 500 observations. SAMPLE NUMBER b SAMPLE NUMBER SAMPLE NUMBER P .048 8 ,052 15 .068 .062 9 .032 16 .036 056 10 038 17 030 4 .060 11 .048 18 064 .038 12 042 19 056 6. .042 13 076 20 048 7 066 14
The accompanying table shows proportions of nonconforming items in a sequence of thirty samples, each of 200 observations. SAMPLE NUMBER P SAMPLE NUMBER D SAMPLE NUMBER 1 .125 11 135 21 105 .140 12 170 22 135 .090 13 105 23 140 10 456789 085 14 095 24 085 .175 15 .130 25 145 160 16 .145 26 175 130
In the study of a part for aircraft manufacture, twenty-five samples, each of 500 observa- tions, were taken. The average of the sample proportions of nonconforming items was .016. Find the central line and lower and upper control limits for a p-chart.
In the study of an automotive component, thirty samples, each of 250 observations, were taken. The average of the sample proportions of nonconforming items was .056. Find the central line and lower and upper control limits for a p-chart.
Refer to Exercise 6. Management has determined that contents weights should be between 16 and 24 ounces. (a) Compute the interval 30 and comment on your finding. (b) Find the capability index, Cp, and discuss the result. (c) Find the Cpk index and discuss the result.
Refer to Exercise 5. Management has specified that the values of the quality characteristic for this process should lie between 130 and 170.(a) Compute the interval 30 and comment on your finding. (b) Find the capability index, Cp, and discuss the result. (c) Find the Cpk index and discuss the
[This exercise requires a computer program to carry out the analysis of variance compu tations. 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,
Having carried out the study of Exercise 54, the investigator decided to take an indepen- dent 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. SAT SCORE INCOME GROUP HIGH MODERATE LOW Very high 3.9
In the study of Exercise 58, information on the dictation system was also shown to M.B.A. 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. SOURCE OF VARIATION Between
Purchasing agents were given information about a dictation 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: $605, $495, or no price given. For coun- try of origin, there were
Consider the two-way analysis of variance setup, with L observations per cell. (a) Show that the between-groups sum of squares can be written SSG - HLR. - HKL (b) Show that the between-blocks sum of squares can be written SSB-KL-HKL (c) Show that the error sum of squares can be written SSE--L 1121
Refer to Exercise 54 and consider the observation on moderate income group and high SAT score (X = 3.5). (a) Estimate. (b) Estimate G. (c) Estimate B. (d) Estimate e-
For the two-way analysis of variance model with one observation per cell. write the obser vation from the ith group and jth block as X = + G + B + 6;Refer to Exercise 53 and consider the observation on agent B and house 1 (x = 218). (a) Estimate (b) Estimate, and interpret, G. (c) Estimate, and
Students were classified according to three parental income groups and also according to three possible score ranges in the SAT examination. One student was chosen randomly from each of the nine cross-classifications, and the grade point average of each sample member at the end of the sophomore
Three real estate agents were each asked to assess the values of five houses in a neighbor- hood. The results, in thousands of dollars, are set out in the table. Set out the analysis of variance table, and test the null hypothesis that population mean valuations are the same for the three real
Information on consumer perceptions of three brand types national, private, and generic-were obtained from a random sample of 125 consumers. The sums of squares for these perception measures are given in the accompanying table. Complete the analysis of variance table, and test the null hypothesis
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 SSG=HX.-Y (b) Show that the between-blocks sum of squares can be written 14 SSB K.-nx" A (c) Show that the total sum of squares can be written SST- (d) Show
Consider the one-way analysis of variance setup. (a) Show that the within-groups sum of squares can be written - (b) Show that the between-groups sum of squares can be written SSG-x- (c) Show that the total sum of squares can be written SST = x-P
A study was aimed at assessing work schedule satisfaction levels, on a scale from 1 (very dissatisfied) to 7 (very satisfied), of hospital employees who were either job-sharers, full- time, or part-time. For a sample of twenty-five job-sharers, the mean satisfaction level was 6.60, for a sample of
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. DISTRICT A DISTRICT B 73 85 63
Lower Michigan has had restrictions on price advertising for alcoholic beverages. However, for a period, these restrictions were lifted. Data were collected on total brewed beverage sales over three periods of time under restricted price advertising, with restric- tions lifted, and after the
In a study" to estimate the effects of smoking on absenteeism, employees were classed as continuous smokers, recent ex-smokers, long-term ex-smokers, and those who never smoked. Samples of ninety-six, thirty-four, eighty-six, and 206 members of these groups were taken. Sample mean numbers of hours
A study classified each of 134 managers into one of four groups, based on observation and an interview. The sixty-two managers in group A were categorized as having high levels of stimulation and support and average levels of public spirit. The fifty-two managers in group B had low stimulation,
In an experiment designed to assess aids to the success of interviews of subordinates car- ried out by managers, interviewers were randomly assigned to one of three interview. modes-feedback, feedback and goal setting, and control. For the feedback mode, inter- viewers had the opportunity to
In Exercise 8 of Chapter 8 we considered a study to assess the readability of financial re- port messages." The technique for assessing the effectiveness of the written message is called the cluce readability procedure. Financial reports were given to independent ran- dom samples from three groups
Carefully explain what is meant by the interaction effect in the two-way analysis of vari- ance with more than one observation per cell. Give examples of this effect in business- related problems.
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.
Having carried out the study of Exercise 25, the instructor decided to replicate the study the following year. The results obtained are shown in the table. Amalgamating these re- sults with those of Exercise 25, carry out the analysis of variance calculations and discuss your findings.
Refer to Exercise 24.Suppose that a second store for each region-can color combination is added to the study, yielding the results shown in the following table. Amalgamating these results with those of Exercise 24, carry out the analysis of variance calculations and discuss your findings. REGION
Refer to Exercise 22.Having carried out the experiment to compare mean yields per acre of four varieties of com and three brands of fertilizer, an agricultural researcher suggested. that there might be some interaction between variety and fertilizer. To check this possibil ity, another set 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
Random samples of two freshmen, two sophomores, two juniors, and two seniors each from four dormitories were asked to rate on a scale from 1 (poor) to 10 (excellent) the quality of dormitory environment for studying. The results are shown in the table. YEAR DORMITORY B C D Freshman 8 6 9 9 9
A psychologist is working with three types of aptitude tests that may be given to prospec- tive 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 in- teraction, only one
Twelve pairs were entered in the ice-dancing competition. Once again, there were nine judges, and contestants were assessed in seven subevents. The sums of squares between groups (puirs of contestants) and between blocks (judges) were found to be SSG = 60.10 and SSB 1.65 while the interaction and
Refer to Exercise
The scores given by judges to competitors in the figure skating events of the 1980 Winter Olympics were analyzed. For the ladies' figure skating competition, there were twenty- two contestants and nine judges. Each contestant was assessed by each judge in seven subevents. The scores given can thus
Suppose that in the two-way analysis of variance setup with one observation per cell, there are just two groups. Show that in this case, the F ratio for testing the equality of the group population means is precisely the square of the test statistic discussed in Section 9.6 for testing equality of
Three television pilot shows for potential situation comedy series were shown to audi- ences 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
Four brands of fertilizer were evaluated. Each brand was applied to each of six plots of land containing soils of different types. Percentage increases in corn yields were then mea- sured for the twenty-four brand-soil type combinations. The results obtained are summa- rized in the accompanying
Four real estate agents were asked to appraise the values of ten houses in a particular neighborhood. The appraisals were expressed in thousands of dollars, with the results shown in the table. SOURCE OF VARIATION SUMS OF SQUARES Between agents 268 Between houses 1.152 Error 2.352 (a) Complete the
For the data of Exercise 25, obtain sample estimates for each term on the right-hand side of Eq. (15.4.2) for the text C-multiple choice combination.
In Eq. (15.4.2) we introduced for the two-way analysis of variance the population model X-G+B+ Ey For the data of Exercise 24, obtain sample estimates for each term on the right-hand side of this equation for the East region-red can combination.
An instructor in an economics class is considering three different texts. She is also consid- ering three types of examinations multiple choice, essays, and a mix of multiple choice and essays. During the year she teaches nine sections of the course, and randomly assigns a text-examination type
A diet soda manufacturer wants to compare the effects on sales of three can colors-red, yellow, and blue. Four regions are selected for the test, and three stores are randomly cho- sen from each region, each to display one color of cans. The accompanying table shows sales (in tens of cans) at the
A company has test-marketed three new types of soup in selected stores over a period of 1 year. The table records sales achieved (in thousands of dollars) for each of the three soups in each quarter of the year. QUARTER SOUP A B C 47 57 65 63 63 76 79 67 54 52 50 49 239 (a) Set out the two-way
An agricultural experiment designed to assess differences in yields of com for four differ- ent varieties, using three different fertilizers, produced the results (in bushels per acre) shown in the table. FERTILIZER VARIETY A B C D 123 *S* 86 88 92 91 75 80 323 77 81 83 #3% 84 93 79 (a) Set out the
Independent random samples of 101 lower-class women. 112 middle-class women, and ninety-six upper-class women were asked to rate, on a scale from 1 to 7, the importance attached to brand name when purchasing paper towels. The value of the Kruskal-Wallis statistic obtained was .17. (a) What null
Based on the data of Exercise 8. perform the Kruskal-Wallis test of the null hypothesis of equal population mean scores on the C.P.A. exam for students using no tutoring service and those using services A and B.
Refer to Exercise 7. Without assuming normal population distributions, test the null hy pothesis that population mean times spent on teaching responsibilities are the same for as sistant, associate, and full professors.
Based on the data of Exercise 6. use the Kruskal-Wallis method to test the null hypothesis of equality of population mean sales growth predictions for the four regions.
Using the data of Exercise 5, carry out a nonparametric test of the null hypothesis of equality of the population mean examination scores for freshmen, sophomores, and juniors.
For the data of Exercise 4, test the null hypothesis that the population mean operating costs per mile are the same for all three types of automobile, without assuming normal population distributions.
Using the data of Exercise 3, carry out a test of the null hypothesis of equality of the three population mean numbers of parts per shipment not conforming to standards without as- suming normality of population distributions
Using the data of Exercise 2, perform a Kruskal-Wallis test of the null hypothesis that the population mean test scores are the same for students assigned to the four teaching assistants.
For the data of Exercise 1. use the Kruskal-Wallis test to test the null hypothesis that the population mean sales levels are identical for the three can colors.
Use the model for the one-way analysis of variance for the data of Exercise 9. (a) Estimate 4. (b) Estimate G, for each of the three magazines. (c) Estimatee, the error term corresponding to the third observation (11.15) for True Confessions.
For the one-way analysis of variance model, we write the jth observation from the ith group as X = + G + where is the overall mean, G, is the effect specific to the ith group, ande, is a random er- ror for the jth observation from the ith group. Consider the data of Example 15.1. (a) Estimate. (b)
In the study of Example 15.1, independent random samples of six advertisements from True Confessions, People Weekly, and Newsweek were taken. The fog indices for these ad- vertisements are given in the accompanying table. Test the null hypothesis that the popula- tion mean fog indices are the same
Two tutoring services offer crash courses in preparation for the C.P.A. exam. To check on the effectiveness of these services, fifteen students were chosen. Five students were ran- domly assigned to service A, five were assigned to service B, and the remaining five took no crash course. Their
Independent random samples of six assistant professors, four associate professors, and five full professors were asked to estimate the amount of time outside the classroom spent. on teaching responsibilities in the last week. Results, in hours, are shown in the accompa- nying table. ASSISTANT
Samples of four salespeople from each of four regions were asked to predict percenta increases in sales volume for their territories in the next twelve months. The predictio are shown in the accompanying table. WEST MIDWEST SOUTH EAST 6 (a) Set out the analysis of variance table. (b) Test the null
Random samples of seven freshmen, seven sophomores, and seven juniors taking a busine statistics class were drawn. The accompanying table shows scores on the final examination FRESHMEN SOPHOMORES JUNIORS 82 71 93 62 61 85 34 94 35 64 73 87 91 69 78 56 70 66 78 53 71 (a) Set out the analysis of
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 con- forming to standards were recorded. These numbers are listed in the table. SUPPLIER A SUPPLIER B SUPPLIER C 28 22 33 37
An instructor has a class of twenty-three 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 assis- tant to discuss difficult course
The accompanying table shows fifteen annual observations from Indonesia on total gov- emment tax revenues, other than from oil (y), national income (x), and the value added by as a percentage of gross domestic product (x2). Estimate by least squares the regression log Y, a+B, logx, + Blog + & oil
A local public utility would like to be able to predict a dwelling unit's average monthly electricity bill. The company statistician estimated by least squares the following regres sion model: where Ya+ B + Box + B+ YAverage monthly electricity bill, in dollars x Average bimonthly automobile
A market researcher is interested in the average amount of money per year spent by stu- dents on entertainment. From 30 years of annual data, the following regression was esti- mated by least squares: 3 40.93+.253x, +.546y, d-1.86 where (106) (134) y, x. Expenditure per student, in dollars, on
A stockbroker is interested in the factors influencing the rate of return on the common stock of banks. For a sample of thirty banks the following regression was estimated by least squares: y 2.3784x+15x-13x+1.67x (.39) (12) (.09) (1.97) R-317 where V Percentage rate of return on common stock of
The following regression was fitted by least squares to thirty annual observations on time series data: logy, 4.31.27 log x +.53 log x-.82 log xx where (.17) (.21) (.30) .615 d-49 y Number of business failures Rate of unemployment Short-term interest rate Value of new business orders placed (a)
The following regression was fitted by least squares to thirty-two annual observations on time series data: log 4.52 62 log X. +92 log +61 log a + .16 log a where (.28) (.38) (.21) R2-638 d-61 (12)$1 Quantity of U.S. wheat exported Price of U.S. wheat on world market Quantity of U.S. wheat
An attempt was made to construct a regression model explaining student scores in inter- mediate economics courses. The population regression model assumed was where Y=Total student score in intermediate economics courses xMathematics score on scholastic aptitude test Ny Verbal score on scholastic
The following model was fitted to data from twenty-eight less developed countries in 1987 in order to explain the market value of their debt at that time." where y=77.2 9.6v (8.0 17.2.15 + 2.2 (2.73) 1.0561 (1.0) R-84 y Secondary market price, in dollars, in 1987 of $100 of country's debt if U.S.
The following model was fitted to data on 90 United Kingdom electronics companies." y= .819 +2.11x+96x-.059x+5.87x+.00226x (1.79) (1.94) (144) (4.08) (.00115) where figures in brackets are estimated standard errors, and R-410 y - Share price x Earnings per share * Funds Bow per share x Dividends
Explain the nature of and the difficulties caused by each of the following: (a) Heteroscedasticity (b) Autocorrelated errors
Discuss the following statement: "In many practical regression problems, multicollinear- ity is so severe that it would be best to run separate simple linear regressions of the depen- dent variable on each independent variable."
In Section 14.2, we discussed the fitting of the model where y=a+ B+ B+ Buls + Y-Tax revenues as a percentage of gross national product in a country Exports as a percentage of gross national product in the country Income per capita in the country Dummy variable taking the value 1 if the country
Write brief reports, including examples, explaining the use of each of the following in specifying regression models: (a) Dummy variables. (b) Lagged dependent variables. (c) The logarithmic transformation.
Refer to Exercise 9 on money spent by students on clothing. The Durbin-Watson statistic for the fitted regression model was 1.82. Test the null hypothesis of no autocorrelated er- rors against the alternative of positive autocorrelation.
The omission of an important independent variable from a time series regression model can result in the appearance of autocorrelated errors. In Section 14.5, we estimated the model relating profit margins to net revenues for our savings and loan data. Carry out a Durbin- Watson test on the
A factory operator hypothesizes that her unit output costs (v) depend on wage rate (x). other input costs (r), overhead costs (x), and advertising expenditures L.). A series of twenty-four monthly observations were obtained, and a least squares estimate of the model yielded the following results: y
Refer to the regression, in Chapter 12, of retail sales per household on disposable income per household. (a) Calculate the Durbin-Watson d statistic. (b) Test the null hypothesis of no autocorrelation in the regression errors. (c) If necessary, reestimate the model allowing for autocorrelated
Refer to Exercise 17 on beef consumption. The Durbin-Watson statistic for the fitted re- gression model was 1.72. Test the null hypothesis of no autocorrelated errors against the alterative of positive autocorrelation.
Refer to Exercise 18 on German real imports. What can be concluded from the Durbin- Watson statistic for the fitted regression?
Refer to Exercise 53 of Chapter 13 explaining the change in the real deposit rate in India. The Durbin-Watson statistic for the fitted regression model was 1.71. Test the null hypoth- esis of no autocorrelated errors against the alternative of positive autocorrelation.
Refer to Exercise 7.Lete, denote the residuals from the fitted regression and the in- sample predicted values. The least squares regression of e on y has coefficient of deter- mination .087. What can you conclude from this finding?
Consider the regression model Ya+ B+ B ++ Bele + Show that if then Var(e) Kx, (KD) Va = K Discuss the possible relevance of this result in treating a form of heteroscedasticity.
In a regression based on thirty annual observations, U.S. farm income was related to four independent variables grain exports, federal government subsidies, population, and a dummy variable for bad weather years. The model was fitted by least squares, resulting in a Durbin-Watson statistic of 1.29.
In Exercise 38 of Chapter 13, a regression explaining the percentage of females in the la- bor force was fitted to data from fifty states. (a) Graphically check for heteroscedasticity in the regression errors. (b) Use a formal test to check for heteroscedasticity.
Refer to Exercise 4.Lete, denote the residuals from the fitted regression and , the in- sample predicted values of the dependent variable. The least squares regression of eon has coefficient of determination 032.What can you conclude from this finding?
In Chapter 12, the regression of retail sales per household on disposable income per household was estimated by least squares. The data are given in Table 12.5, and Table 12.7 shows the residuals and the predicted values of the dependent variable. (a) Graphically check for heteroscedasticity in the
Refer to Exercise 55 of Chapter 13.The independent variable ... real income per capita, was dropped from the model, and the regression of growth rate in real gross domestic product on x, average tax rate, was estimated. This yielded the fitted model y=.060-074x (.034) Comment on this result. R2-072
An economist estimates the regression model The estimates of the parameters B and B are not very large, compared with their respec tive standard errors. But the size of the coefficient of determination indicates quite a strong relationship between the dependent variable and the pair of independent
In the regression model Ya Bix Box + & the extent of any multicollinearity can be evaluated by finding the correlation between t and x, in the sample. Explain why this is so.
An economist wants to estimate a regression equation relating demand for a product (y) to its price (x) and income (x). It is to be based on 12 years of quarterly data. However, it is known that demand for this product is seasonal-that is, it is higher at certain times of the year than at others.
This problem requires a computer program to carry out the regression calculations.] The accompanying table shows German real imports (y), real private consumption (x.), and real exchange rate (x), in terms of U.S. dollars per mark, over a period of 31 years. Estimate the model log Y, a B log x +
An agricultural economist believes that the amount of beef consumed (y) in tons in a year in the United States depends on the price of beef (x) in dollars per pound, the price of pork (x) in dollars per pound, the price of chicken (x) in dollars per pound, and income per household (x) in thousands
The following model was estimated for a sample of 322 supermarkets in large metropoli- areas. tan logy 2.921.680 log.x R 19 (077) where y-Store size x=Median income in zip code area in which store is located (a) Interpret the estimated coefficient on log.x. (b) Test the null hypothesis that income
In a study of the determinants of household expenditures on vacation travel, data were ob tained from a sample of 2,246 households." The model estimated was logy where -4.054 + 1.1556 log x, 4408 log X2 R 168 (.0546) (.0490) y Expenditure on vacation travel x Total annual consumption expenditure x:
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