Economics \ Statistics 205

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1. value: 2.50 points (Use Excel) A recent survey by Genworth Financial Inc., a financial-services company, concludes that the cost of long-term care in the United States varies significantly, depending on where an individual lives (The Wall Street Journal, May 16, 2009). An economist collects data from the five states with the highest annual costs (Alaska, Massachusetts, New Jersey, Rhode Island, and Connecticut) in order to determine if his sample data are consistent with the survey's conclusions. The economist provides the following portion of an ANOVA table. Use Table 4: a. Complete the ANOVA table. Assume that long-term care costs are normally distributed. (Leave no cells blank - be certain to enter "0" wherever required. Round your answers except "df" to 2 decimal places.) MS F p-value Fcrit at 5% ANOVA Source of Variation Between Groups Within Groups SS 635.0542 df 4 253.2192 20 Total 888.2734 24 b. Specify the competing hypotheses to test whether some differences exist in the mean long-term care costs in these five states. Ho PAlaska = Massachusetts = PNew Jersey = PRhode Island = P Connecticut. Ha; Not all population means are equal. Ho: PAlaska SP Massachusetts SH New Jersey - PRhode Island SPConnecticut. HA; Not all population means are equal. Ho: PAlaskaMassachusetts - PNew Jersey ? PRhode Island Connecticut. Hai Not all population means are equal. c. At the 5% significance level, can we conclude that mean costs differ? Yes, since the p-value is less than a. Yes, since the p-value is not less than a. No, since the p-value is less than a. No, since the p-value is not less than a. OC 3. value: 2.50 points (Round all intermediate calculations to at least 4 decimal places.) The following statistics are computed by sampling from three normal populations whose variances are equal: Use Table 2 and Table 5. X1 = 22.6, n1 = 6; X2 = 30.1, n2 = 8; X3 = 34.0, n3 = 5; MSE = 28.7 a. Use Fisher's LSD test to determine which population means differ at 95% confidence intervals. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Population Mean Differences P1 P2 Confidence Interval [ [ ] ] Can we conclude that the population means differ? (Click to select) (Click to select) 4 (Click to select) 4 1-M3 9 23 [ ] b. Repeat the analysis with Tukey's HSD approach. (If the exact value for nt - c is not found in the table, use the value which is closer. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Population Mean Differences 1 - 2 Confidence Interval ] ] Can we conclude that the population means differ? (Click to select) (Click to select) (Click to select) 13 12 - 3 [ c. Which of these two approaches would you use to determine whether differences exist between the population means? Tukey's HSD Fisher's LSD 4. value: 2.50 points (Round all intermediate calculations to at least 4 decimal places.) Do energy bills vary dramatically depending on where you live in the United States? Suppose 25 households from four regions in the United States are sampled. The values for the average annual energy bill are shown below and are consistent with those found by The Department of Energy (Money, June 2009). Use Table 5. Region Average annual Energy bill West $1,491 Northeast $2,319 Midwest $1,768 South $1,758 A portion of the ANOVA calculations are below: ANOVA Source of Variation Between Groups Within Groups SS 7531769 3492385 df 3 96 MS ? ? F ? p-value 7.13E-24 Total 11024154 99 a. Complete the ANOVA table. (Round your answers to 2 decimal places.) df MS F ANOVA Source of Variation Between Groups Within Groups SS 7531769 p-value 7.13E-24 3 3492385 96 Total 11024154 99 5. value: 2.50 points (Round all intermediate calculations to at least 4 decimal places.) The following observations were obtained when conducting a two-way ANOVA experiment with no interaction. Use Table 4 Click here for the Excel Data File Factor B 1 2 3 Xi for Factor A 1 3 8 12 7.667 Factor A 2 3 4 3 10 9 16 14 10.000 8.667 4 5 8. 13 8.667 Xj for Factor B 3.750 8.750 13.750 X = 8.750 a. Calculate SST, SSA, SSB, and SSE. (Round your answers to 2 decimal places.) ,SST SSA SSB SSE b. Calculate MSA, MSB, and MSE. (Round your answers to 2 decimal places.) MSA MSB MSE 2 2 10 9 9 13 11 XI = 10.1250 si = 2.4107 11 9 10 10 11 8 *2 = 9.7500 sź = 1.0714 I = 9.5000 10 9 8 7 8. 9 x3 = 8.6250 să = 0.8393 a. Construct an ANOVA table. Assume production rates are normally distributed. (Round SS, MS, and F to 2 decimal places and p-value to 4 decimal places.) df MS F ANOVA Source of Variation Between Groups Within Groups SS. 9.75 p-value 0.072058 2 4.875 2.989051 34.25 21 1.630952 Total 44 23 b. Specify the competing hypotheses to test whether there are some differences in the mean production rates across the three assembly lines. Ho: PRazor = Blazer = H Tracer. Ha: Not all population means are equal. Ho: Prazor s Blazers Tracer. Ha: Not all population means are equal Ho: PRazor Blazer Tracer. Ha: Not all population means are equal. C-1. At the 5% significance level, what is the conclusion of the test? A conclude that the mean buggies/hour differs for Do not reject Ho, we cannot some production lines. C-2. What about the 10% significance level? can conclude that the mean buggies/hour differs for Reject HO 4 Ho, we some production lines. 2. value: 2.50 points (Round all intermediate calculations to at least 4 decimal places.) Wenton Powersports produces dune buggies. They have three assembly lines, "Razor,” “Blazer," and "Tracer," named after the particular dune buggy models produced on those lines. Each assembly line was originally designed using the same target production rate. However, over the years, various changes have been made to the lines. Accordingly, management wishes to determine whether the assembly lines are still operating at the same average hourly production rate. Production data (in dune buggies/hour) for the last eight hours are as follows. Razor 11 10 8 10 9 9 13 11 X1 = 10.1250 si = 2.4107 Blazer 10 9 11 9 10 10 11 8 *2 = 9.7500 sź = 1.0714 X = 9.5000 Tracer 9 9 10 9 8 7 8 9 X3 = 8.6250 s3 = 0.8393 a. Construct an ANOVA table. Assume production rates are normally distributed. (Round SS, MS, and F to 2 decimal places and p-value to 4 decimal places.) df MS ANOVA Source of Variation Between Groups Within Groups SS 9.75 F 2.989051 p-value 0.072058 2 4.875 34.25 21 1.630952 44 Total 23 6. value: 2.50 points (Round all intermediate calculations to at least 4 decimal places.) The following output summarizes a portion of the results for a two-way analysis of variance experiment with no interaction. Factor A consists of four different kinds of organic fertilizers, factor B consists of three different kinds of soil acidity levels, and the variable measured is the height (in inches) of a plant at the end of four weeks. a. Find the missing values in the ANOVA table. (Round your answer to 2 decimal places.) ANOVA Source of Variation Rows df SS 0.13 MS MSB = F FFactor B = FFactor A = p-value 0.8182 F crit @ 5% 5.143 2 Columns 44.25 3 MSA = 0.0001 4.757 Error 1.88 6 MSE = Total 46.26 11 b. At the 5% significance level, can you conclude that average growth of the plant differs by organic fertilizer? Yes, since the p-value for Factor A is less than a. Yes, since the p-value for Factor A is greater than a. No, since the p-value for Factor A is less than a. No, since the p-value for Factor A is greater than a. c. At the 5% significance level, can you conclude that the average growth of the plant differs by acidity level? Yes, since the p-value for Factor B is less than a. Yes, since the p-value for Factor B is greater than a. No, since the p-value for Factor B is less than a. No, since the p-value for Factor B is greater than a. 4. value: 2.50 points (Round all intermediate calculations to at least 4 decimal places.) Do energy bills vary dramatically depending on where you live in the United States? Suppose 25 households from four regions in the United States are sampled. The values for the average annual energy bill are shown below and are consistent with those found by The Department of Energy (Money, June 2009). Use Table 5. Region Average annual Energy bill West $1,491 Northeast $2,319 Midwest $1,768 South $1,758 A portion of the ANOVA calculations are below: ANOVA Source of Variation Between Groups Within Groups SS 7531769 3492385 df 3 96 MS ? ? F ? p-value 7.13E-24 Total 11024154 99 a. Complete the ANOVA table. (Round your answers to 2 decimal places.) df MS F ANOVA Source of Variation Between Groups Within Groups SS 7531769 p-value 7.13E-24 3 3492385 96 Total 11024154 99 3. value: 2.50 points (Round all intermediate calculations to at least 4 decimal places.) The following statistics are computed by sampling from three normal populations whose variances are equal: Use Table 2 and Table 5. X1 = 22.6, n1 = 6; X2 = 30.1, n2 = 8; X3 = 34.0, n3 = 5; MSE = 28.7 a. Use Fisher's LSD test to determine which population means differ at 95% confidence intervals. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Population Mean Differences P1 P2 Confidence Interval [ [ ] ] Can we conclude that the population means differ? (Click to select) (Click to select) 4 (Click to select) 4 1-M3 9 23 [ ] b. Repeat the analysis with Tukey's HSD approach. (If the exact value for nt - c is not found in the table, use the value which is closer. Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Population Mean Differences 1 - 2 Confidence Interval ] ] Can we conclude that the population means differ? (Click to select) (Click to select) (Click to select) 13 12 - 3 [ c. Which of these two approaches would you use to determine whether differences exist between the population means? Tukey's HSD Fisher's LSD 5. value: 2.50 points (Round all intermediate calculations to at least 4 decimal places.) The following observations were obtained when conducting a two-way ANOVA experiment with no interaction. Use Table 4 Click here for the Excel Data File Factor B 1 2 3 Xi for Factor A 1 3 8 12 7.667 Factor A 2 3 4 3 10 9 16 14 10.000 8.667 4 5 8. 13 8.667 Xj for Factor B 3.750 8.750 13.750 X = 8.750 a. Calculate SST, SSA, SSB, and SSE. (Round your answers to 2 decimal places.) ,SST SSA SSB SSE b. Calculate MSA, MSB, and MSE. (Round your answers to 2 decimal places.) MSA MSB MSE
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