ĐĎॹá>ţ˙ fhţ˙˙˙e˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙ěĽÁ7 đż˝4bjbjUU …7|7|˝/˙˙˙˙˙˙lćććććććdě„„„„ těXD       ÚÜÜÜ=ÔíÔÁ$œ ź!xĺ-ć     ĺ ćć      ć ć Ú  Ú N nććn  §W§ÔŔě˜„ nnl(0Xn4" 4"n JX˘JććććŮ1. The cost of housing for elderly persons who rent as a percentage of income is distributed as listed below. Beneath the national percentages are the observed frequencies for a random sample of 300 elderly renters from a the Jacksonville area. At the 0.025 level, could the distribution of housing costs as a percentage of income for the elderly persons in this area be the same as for the nation as a whole? National Local Sample 20% to 30% to < 20% under 30% under 40% $ 40% National Local Sample 13.0% 26 25.6% 67 20.3% 68 41.1% 139 100% n = 300 2. The following data are the number of persons who were waiting in line at a fast food counter at 100 randomly selected times during the week. At the 0.05 level, test whether the population of these values could be Poisson distributed. x = Number Number of of persons Observations 0 24 1 24 2 18 3 20 4 10 5 4 100 3. A lottery researcher collecting data for an article on his state lottery system, has found the 200 digits most recently selected to be distributed as shown below. Based on this information, and using the 0.10 level of significance, can he conclude that the digits have not been drawn from a discrete uniform distribution? Digit Frequency 0 1 2 3 4 5 6 7 8 9 17 18 24 25 19 16 14 23 24 20 200 4. The following table describes types of collisions versus driving environments for a random sample of two-vehicle accidents that occurred in a given region last year. At the 0.01 level of significance, can we conclude that the type of collision is independent of whether the accident took place in a rural versus an urban setting? Type of Collision Angle Rear-end Other Driving Urban 40 30 72 142 Environment Rural 6 12 15 33 46 42 87 175 5. The following contingency table lists the number of financial institutions in various size categories in selected states. At the 0.01 level of significance, do these data indicate that no relationship exists between the size of a institution and the state in which it is located? Assets (millions of dollars) Under 100 to 300 to 500 to 1000 100 <300 <500 <1000 or over Texas 123 94 21 22 19 279 California 79 54 18 15 40 206 Florida 59 43 8 11 27 148 261 191 47 48 86 633 6. What is the purpose of the one-way ANOVA? 7. A one-way ANOVA has been conducted for an experiment in which there are three treatments and each treatment group consists of 10 persons. The results include the sum of squares terms shown below. Based on this information, construct the ANOVA table of summary findings and use the 0.025 level of significance in testing whether all of the treatment effects could be zero. SSTR = 252.1 SSE = 761.1 8. Students in a large section of a biology class have been randomly assigned to one of two graduate students for the laboratory portion of the class. A random sample of final examination scores has been selected from students supervised by each graduate student, with the following results: Grad student A: 78 78 71 89 80 93 73 76 Grad student B: 74 81 65 73 80 63 71 64 50 80 a. What are the null and alternative hypotheses for this test? b. Use ANOVA and the 0.01 level of significance in testing the null hypotheses identified in part (a). c. From the F distribution tables. What is the most accurate statement that can be made about the p-value for this test? 9. For a two-way ANOVA in which factor A operates on 3 levels and factor B operates on 4 levels, there are 2 replications within each cell. Given the following sum of squares terms, construct the appropriate table of ANOVA summary findings and use the 0.05 level in examining the null and alternative hypotheses associated with the experiment. SSA = 89.58 SSB = 30.17 SSAB = 973.08 SSE = 29.00 10. Given the following data for a two-way ANOVA, identify the sets of null and alternative hypotheses, then use the 0.05 level in testing each null hypothesis. Factor B 1 2 3 1 13 19 19 2 10 15 17 Factor A 15 22 16 15 19 17 11. Determine the least squares regression line for the following data values, then find the estimated values of y for x = 6 and x = 9. x: 2 3 8 10 y: 20 12 7 3 12. The following data represent x = boat sales and y = boat trailer sales from 1991 through 1996. Year Boat Sales (Thousands) Boat Trailer Sales (Thousands) 1991 594.5 190.0 1992 499.5 160.0 1993 570.7 184.0 1994 657.7 200.0 1995 636.8 192.0 1996 660.0 194.0 a. Determine the least squares regression line and interpret its slope. b. Estimate, for a year during which 620,000 boats are sold, the number of boat trailers that would be sold. c. What reasons might explain why the number of boat trailers sold per year is less than the number of boats sold per year? 13. For the 1989 National Football League season, ratings for the leading passers in the National Conference were as shown below. Also shown for each quarterback is the percentage of passes that were interceptions, along with the percentage of passes that were touchdowns. Rating TD% Int % Montana, S.F. 112.4 6.7% 2.1% Everett, L.A. 90.6 5.6 3.3 Rypien, Wash. 88.1 4.6 2.7 Hebert, N.O. 82.7 4.2 4.2 Majkowski, G.B. 82.3 4.5 3.3 Simms, N.Y. 77.6 3.5 3.5 Miller, Atl. 76.1 3.0 1.9 Cunningham, Phila. 75.5 3.9 2.8 Wilson, Minn. 70.5 2.5 3.3 Hogeboom, Phoe. 69.5 3.8 5.2 Testaverde, T.B. 68.9 4.2 4.6 Tomczak, Chi. 68.2 5.2 5.2 Gagliano, Det. 61.2 2.6 5.2 Aikman, Dall. 55.9 3.1 6.2 a. Determine the least squares regression line for estimating the passer rating based on the percentage of passes that were touchdowns. b. A quarterback says 5.0% of his passes will be touchdowns next year. Assuming this to be true, estimate his rating for the coming season. c. Determine the standard error of estimate. 14. The ratings below are based on collision claim experience and theft frequency for 12 makes of small, two-door cars. Higher numbers reflect higher claims and more frequent thefts, respectively. Collision: 103 97 105 115 127 104 106 139 110 96 84 105 Theft: 103 113 81 68 90 79 97 425 82 81 59 167 a. Determine the least squares regression line for predicting the rate of collision claims on the basis of theft frequency rating. b. Calculate and interpret the values of r and r2. c. If a new model were to have a theft rating of 110, what would be the predicted rating for collision claims? 15. In a proxy statement to stockholders, First Alabama Bancshares, Inc. included the following age and share-ownership data for members of the board of directors. Thousands of Thousands of Thousands of Age Shares Held Age Shares Held Age Shares Held 53 7.9 62 121.1 66 18.8 60 66.4 63 35.3 57 3.1 69 29.7 55 2.8 54 96.5 49 60.5 57 74.4 64 47.0 67 10.4 71 11.1 56 31.1 68 28.7 66 9.1 46 86.9 70 19.1 a. Determine the least squares regression line predicting stock ownership on the basis of age. b. Determine and interpret the coefficients of correlation and determination. c. If a board member were 64 years of age, what would be the predicted number of shares owned? 16. For the regression analysis of the data in number 15. a. Use the 0.05 level in testing whether the population coefficient of correlation could be zero. b. Use the 0.10 level in testing whether the population regression equation could have a slope of zero. c. Construct the 90% confidence interval for the slope of the population regression equation. Discuss the interval in terms of the results of part (b). 17. The owner of a large chain of health spas has selected eight of her smaller clubs for a test in which she varies the size of the newspaper ad and the amount of the initiation fee discount to see how this might affect the number of prospective members who visit each club during the following week. The results are shown on the below. New Ad Column- Discount Club Visitors, y Inches, x1 Amount, x2 1 23 4 $100 2 30 7 20 3 20 3 40 4 26 6 25 5 20 2 50 6 18 5 30 7 17 4 25 8 31 8 80 a. Use MyStat to determine the least squares multiple regression equation. b. Interpret the y-intercept and partial regression coefficients. c. What is the estimated number of new visitors to a club if the size of the ad is 5 column-inches and a $75 discount is offered? 18. The multiple regression equation, EQ \O(y,^) = 10 + 3x1 - 2x2 + 14x3, has been fitted to a set of 18 data points. The sum of the squared differences between observed and predicted values of y has been calculated as SSE = 200.0. The sum of squared differences between y values and the mean of y is SST = 900. What is the multiple standard error of estimate? 19. For a given regression analysis, the sum-of-squares terms have been calculated as SST = 342.5, SSR = 200.0, and SSE = 142.5. Determine the value of R2 and interpret its meaning. 20. Interested in the possible relationship between the size of his tip versus the size of the check and the number of diners in the party, a food server has recorded the following for a sample of 8 checks: Observation Number y = Tip x1 = Check x2 = Diners 1 $7.5 $40 2 2 0.5 15 1 3 2.0 30 3 4 3.5 25 4 5 9.5 50 4 6 2.5 20 5 7 3.5 35 5 8 1.0 10 2 a. Using MyStat, determine the multiple regression equation. Interpret the partial regression coefficients. b. What is the estimated tip amount for 3 diners who have a $40 check? c. Determine the 95% prediction interval for the tip left by a dining party like the one in part (b). d. Determine the 95% confidence interval for the mean tip left by all dining parties like the one in part (b). e. Determine the 95% confidence interval for the partial regression coefficients, ˛1 and ˛2. f. Interpret the significance tests in the computer printout. 21. The estimated trend value of community water consumption is 400,000 gallons for a given month. Assuming that the cyclical component is 120% of normal, with the seasonal and irregular components 70% and 110% of normal, respectively, use the multiplicative time series model in determining the quantity of water consumed during the month. 22. Fit a linear trend equation to the following data describing average hourly earnings in the metal-cutting machine tools industry.1 What is the trend estimate for 1994? Year: 1985 1986 1987 1988 Average hourly earnings: $12.42 $12.78 $12.90 $13.05 23. A management consulting firm consists of three partners, whose number of clients and average fee per client were as shown below for 1988 through 1990: Number of Average Billing Clients Served per Client A B C A B C 1988 8 10 3 $2,500 $15,000 $65,000 1989 10 8 4 $1,500 $20,000 $50,000 1990 15 12 2 $3,000 $10,000 $80,000 a. Using 1988 as the base period, what is the simple aggregate price index for clients served in 1989? In 1990? b. Using 1988 as the base period, what is the simple aggregate quantity index for the number of clients served in 1989? In 1990? 24. U.S. brick shipments from 1977 through 1988 are represented by the following index numbers. Convert the index numbers so that the base period will be 1984 instead of 1980. 1977 142.6 1983 101.6 1978 141.0 1984 114.8 1979 126.2 1985 111.5 1980 100.0 1986 121.3 1981 83.6 1987 119.7 1982 83.6 1988 116.4 25. The following table summarizes the unit sales and prices for Norman=s Nuts from 1987 through 1990: Pounds Sold Price per Pound Cashews Hot Mix Macadamia Nuts Cashews Hot Mix Macadamia Nuts 1987 1240 140 40 $7.50 $4.00 $14.00 1988 1310 200 400 $8.00 $6.00 $16.00 1989 1400 160 520 $9.50 $7.50 $19.50 1990 1950 850 840 $11.00 $8.00 $23.00 Using 1987 as the base period, construct a. A Paasche price index for each year. b. A Laspeyres price index for each year. c. A fixed-weight aggregate price index for each year. 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