Use the following information to answer the next four (4) multiple choice questions. Altobene, Inc.'s R&D department recently conducted a test of three different brake systems to determine if there is a difference in the average stopping distance among the different systems. In the test, 21 identical mid-sized cars were obtained from one of the major domestic carmakers. Seven (7) cars were fitted with Brake A, seven (7) with Brake B, and seven (7) with Brake C. The number of feet required to bring the test cars to a full stop was recorded. 1. Which of the following is the appropriate null and alternative hypotheses about the stopping distance among the different systems? a. Ho: MATHBE HC HA: All of the population mean stopping distances are different from each other b. Ho: MA= Mga HC HA: At least one population mean stopping distances is different from the others C. Ho: MAHBA HC HA: At least one population mean stopping distance is equal to another population mean stopping distance d. Ho: MAHBE HC Ha: Exactly one population mean stopping distance is greater than the other two population mean stopping distances 2. An ANOVA for the Stopping Distance Effect in Question 1 has been conducted with the partial results shown in the table below. Complete the ANOVA table. Sum of Degrees of Squares | Freedom F-Calculated Source Between Groups (Brakes) Within Groups Mean Square 1314 XXXXXXXXXXXXX Total 5299 20 3. What is the critical value of the test statistic for the brake stopping distance ANOVA if the hypothesis of interest is tested at the a = 0.01 level of significance? a. 6.013 C. 4.938 b. d. 5.092 3.127 4. Based on the ANOVA analysis, what conclusion would you make regarding the effect the braking system has on average stopping distance? a. Reject Ho, there is significant evidence to conclude there is a brake effect. b. Do not reject Ho, there is significant evidence to conclude there is a brake effect. C. Reject Ho, there is insignificant evidence to conclude there is a brake effect. d. Do not reject Ho, there is insignificant evidence to conclude there is a brake effect. 6. A randomized block ANOVA analysis is performed to examine whether the color of an energy drink (e.g., red, green, blue, purple) has an effect on the sales of the energy drink. Because the type of store (e.g., convenience, grocery, and discount) where the drink is sold could have an effect on sales the analyst decided to control for store differences by blocking on stores (the analyst believes the stores could be a nuisance in the analysis). Three blocks were used in the analysis. The results of the hypothesis tests for whether blocking is effective or not resulted in an F calculated of 1.76 which had a p-value of 0.206. If the analyst wants to control for the probability of a Type 1 Error to be no more than 0.025 (a=0.025), then the analyst would a. Reject the null hypothesis and conclude that there is a store effect (blocking was effective) b. Not reject the null hypothesis and conclude that there is no store effect (blocking was not effective) C. Reject the null hypothesis and conclude that there is no effect due to stores (blocking was not necessary) d. Not reject the null hypothesis and conclude that there is a store effect (blocking was necessary) 7. A machine is set to produce a product whose diameter is 35 cm. The company is concerned about the variation in the diameter of the product because if there is significant variation in the standard deviation of the diameter then the product must be thrown away. A random sample of 19 items is selected and sample standard deviation of the diameter is computed. The sample results are shown below: Sample Size = 19 Sample Standard Deviation = S = 0.004 Using the sample data provided, you want to construct a 95% confidence interval estimate for the true population variance, 02, for the product's diameter. In order to do so you must first determine the appropriate values from the x distribution for computing the confidence interval. The upper and lower tail critical values of the xdistribution that are used to construct the 95% confidence interval for this problem would be: a. x = 8.9065 b. x2 = 8.2307 c. x = 10.1170 d. XZ = 10.8649 xi = 32.8523 xi = 31.5264 x = 30.1435 x = 28.8693 8. A quick service restaurant wants drive through service times to have a variance that does not exceed 2 minutes. A random sample of 200 customers was taken and a formal hypothesis test conducted to determine if the restaurant was within its service time variance target. The correct specification of the hypotheses of interest would be a. Ho: 02= 2 vs. Ha: 02 2 b. Ho: 0= 2 vs. Ha: 0 # 2 C. Ho: 02= 22 vs. Ha: 02 22 d. Ho: 0252 vs. Ha: 02 > 2 e. Ho: 02 > 2 vs. Ha: 02 4 9. To estimate the standard deviation in the diameter of parts produced by a machine a random sample of 15 parts was selected and the sample standard deviation of the sample was computed to be 0.02 inches. Using the sampled data, the 90 percent confidence interval estimate for the true standard deviation in the diameter of parts produced by this machine would be a. 0.0154 0.052 vs. Ha : 02 0.0522 C. Ho: o 20.052 vs. Ha : 0 F critical = 2.901, reject the null hypothesis and conclude that there is a difference in video stores. b. Because F calculated = 26.7 > F critical = 3.287, reject the null hypothesis and conclude that there is a difference in video stores. C Because F calculated = 26.7 is > Fcritical = 3.287, do not reject the null hypothesis and conclude that there is not a difference in video stores. d. No decision can be made as to whether there is a difference in video stores without conducting a post-test comparison of all possible contrasts. 13. Suppose in the video store ANOVA problem above, a post-test comparison is conducted to determine where differences exist between all possible contrasts (all pairs) of video stores. For this question focus only on the contrast between Video Store A and Video Store D. If Fisher's Least Significant Difference is computed to be 293 then what conclusion would you make concerning whether there is a significant difference between Video Store A and Video Store D? a. No conclusion can be reached unless a pooled t-test is conducted. b. Because the absolute difference in sample means between Video Store A and Video Store Dis greater than Fisher's Least Significant Difference, we conclude the cash sales for the two video stores is equal. c Because the absolute difference in sample means between Video Store A and Video Store Dis greater than Fisher's Least Significant Difference, we conclude the average cash sales for the two video stores is different. The confidence interval for the difference between the two video stores would need to include the value of 0 (zero) for us to conclude that the average cash sales for the two video stores is different. Use the following information to answer the next four (4) multiple choice questions. Altobene, Inc.'s R&D department recently conducted a test of three different brake systems to determine if there is a difference in the average stopping distance among the different systems. In the test, 21 identical mid-sized cars were obtained from one of the major domestic carmakers. Seven (7) cars were fitted with Brake A, seven (7) with Brake B, and seven (7) with Brake C. The number of feet required to bring the test cars to a full stop was recorded. 1. Which of the following is the appropriate null and alternative hypotheses about the stopping distance among the different systems? a. Ho: MATHBE HC HA: All of the population mean stopping distances are different from each other b. Ho: MA= Mga HC HA: At least one population mean stopping distances is different from the others C. Ho: MAHBA HC HA: At least one population mean stopping distance is equal to another population mean stopping distance d. Ho: MAHBE HC Ha: Exactly one population mean stopping distance is greater than the other two population mean stopping distances 2. An ANOVA for the Stopping Distance Effect in Question 1 has been conducted with the partial results shown in the table below. Complete the ANOVA table. Sum of Degrees of Squares | Freedom F-Calculated Source Between Groups (Brakes) Within Groups Mean Square 1314 XXXXXXXXXXXXX Total 5299 20 3. What is the critical value of the test statistic for the brake stopping distance ANOVA if the hypothesis of interest is tested at the a = 0.01 level of significance? a. 6.013 C. 4.938 b. d. 5.092 3.127 4. Based on the ANOVA analysis, what conclusion would you make regarding the effect the braking system has on average stopping distance? a. Reject Ho, there is significant evidence to conclude there is a brake effect. b. Do not reject Ho, there is significant evidence to conclude there is a brake effect. C. Reject Ho, there is insignificant evidence to conclude there is a brake effect. d. Do not reject Ho, there is insignificant evidence to conclude there is a brake effect. 6. A randomized block ANOVA analysis is performed to examine whether the color of an energy drink (e.g., red, green, blue, purple) has an effect on the sales of the energy drink. Because the type of store (e.g., convenience, grocery, and discount) where the drink is sold could have an effect on sales the analyst decided to control for store differences by blocking on stores (the analyst believes the stores could be a nuisance in the analysis). Three blocks were used in the analysis. The results of the hypothesis tests for whether blocking is effective or not resulted in an F calculated of 1.76 which had a p-value of 0.206. If the analyst wants to control for the probability of a Type 1 Error to be no more than 0.025 (a=0.025), then the analyst would a. Reject the null hypothesis and conclude that there is a store effect (blocking was effective) b. Not reject the null hypothesis and conclude that there is no store effect (blocking was not effective) C. Reject the null hypothesis and conclude that there is no effect due to stores (blocking was not necessary) d. Not reject the null hypothesis and conclude that there is a store effect (blocking was necessary) 7. A machine is set to produce a product whose diameter is 35 cm. The company is concerned about the variation in the diameter of the product because if there is significant variation in the standard deviation of the diameter then the product must be thrown away. A random sample of 19 items is selected and sample standard deviation of the diameter is computed. The sample results are shown below: Sample Size = 19 Sample Standard Deviation = S = 0.004 Using the sample data provided, you want to construct a 95% confidence interval estimate for the true population variance, 02, for the product's diameter. In order to do so you must first determine the appropriate values from the x distribution for computing the confidence interval. The upper and lower tail critical values of the xdistribution that are used to construct the 95% confidence interval for this problem would be: a. x = 8.9065 b. x2 = 8.2307 c. x = 10.1170 d. XZ = 10.8649 xi = 32.8523 xi = 31.5264 x = 30.1435 x = 28.8693 8. A quick service restaurant wants drive through service times to have a variance that does not exceed 2 minutes. A random sample of 200 customers was taken and a formal hypothesis test conducted to determine if the restaurant was within its service time variance target. The correct specification of the hypotheses of interest would be a. Ho: 02= 2 vs. Ha: 02 2 b. Ho: 0= 2 vs. Ha: 0 # 2 C. Ho: 02= 22 vs. Ha: 02 22 d. Ho: 0252 vs. Ha: 02 > 2 e. Ho: 02 > 2 vs. Ha: 02 4 9. To estimate the standard deviation in the diameter of parts produced by a machine a random sample of 15 parts was selected and the sample standard deviation of the sample was computed to be 0.02 inches. Using the sampled data, the 90 percent confidence interval estimate for the true standard deviation in the diameter of parts produced by this machine would be a. 0.0154 0.052 vs. Ha : 02 0.0522 C. Ho: o 20.052 vs. Ha : 0 F critical = 2.901, reject the null hypothesis and conclude that there is a difference in video stores. b. Because F calculated = 26.7 > F critical = 3.287, reject the null hypothesis and conclude that there is a difference in video stores. C Because F calculated = 26.7 is > Fcritical = 3.287, do not reject the null hypothesis and conclude that there is not a difference in video stores. d. No decision can be made as to whether there is a difference in video stores without conducting a post-test comparison of all possible contrasts. 13. Suppose in the video store ANOVA problem above, a post-test comparison is conducted to determine where differences exist between all possible contrasts (all pairs) of video stores. For this question focus only on the contrast between Video Store A and Video Store D. If Fisher's Least Significant Difference is computed to be 293 then what conclusion would you make concerning whether there is a significant difference between Video Store A and Video Store D? a. No conclusion can be reached unless a pooled t-test is conducted. b. Because the absolute difference in sample means between Video Store A and Video Store Dis greater than Fisher's Least Significant Difference, we conclude the cash sales for the two video stores is equal. c Because the absolute difference in sample means between Video Store A and Video Store Dis greater than Fisher's Least Significant Difference, we conclude the average cash sales for the two video stores is different. The confidence interval for the difference between the two video stores would need to include the value of 0 (zero) for us to conclude that the average cash sales for the two video stores is different