An experiment has been conducted for four treatments with eight blocks. Complete the following analysis of variance table. (Round your values for mean squares and F to two decimal places, and your p-value to three decimal places.) Source Sum Degrees Mean F of Variation of Squares of Freedom Square p-value Treatments 2,700 Blocks 800 Error Total 5,000 Use a = 0.05 to test for any significant differences. State the null and alternative hypotheses. O Ho: At least two of the population means are equal. He: At least two of the population means are different. O Ho: My = H2 = H3 = H4 O H : Not all the population means are equal. Ha: H1 = H2 = M3 = H4 O Ho: M1 = H2 = H3 = H4 H: Not all the population means are equal. OHO: My # #2 * H3 # H4 Ha: H1 = M2 = M3 = H4 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. O Reject Ho. There is sufficient evidence to conclude that the means of the four treatments are not all equal. O Do not reject Ho. There is sufficient evidence to conclude that the means of the four treatments are not all equal. O Do not reject Ho. There is not sufficient evidence to conclude that the means of the four treatments are not all equal. O Reject Ho. There is not sufficient evidence to conclude that the means of the four treatments are not all equal.The price drivers pay for gasoline often varies a great deal across regions throughout the United States. The following data show the price per gallon for regular gasoline for a random sample of gasoline service stations for three major brands of gasoline (Shell, BP, and Marathon) located in 11 metropolitan areas across the upper Midwest region. Metropolitan Area Shell BP Marathon Akron, Ohio 3.77 3.83 3.78 Cincinnati, Ohio 3.72 3.83 3.87 Cleveland, Ohio 3.87 3.85 3.89 Columbus, Ohio 3.76 3.77 3.79 Ft. Wayne, Indiana 3.83 3.84 3.87 Indianapolis, Indiana 3.85 3.84 3.87 Lansing, Michigan 3.93 4.04 3.99 Lexington, Kentucky 3.79 3.78 3.79 Louisville, Kentucky 3.78 3.84 3.79 Muncie, Indiana 3.81 3.84 3.83 Toledo, Ohio 3.69 3.83 3.86 Use a = 0.05 to test for any significant difference in the mean price of gasoline for the three brands. State the null and alternative hypotheses. O Ho: HShell = HBP = /Marathon Ha: Not all the population means are equal. O Ho: Hshell * HBP * Marathon Ha: HShell = HBP = /Marathon O Ho: Not all the population means are equal. Ha: "Shell = HBP = /Marathon O Ho: At least two of the population means are equal. He: At least two of the population means are different. O Ho: Hshell = HBP = /Marathon Ha: "Shell * UBP * /Marathon Find the value of the test statistic. (Round your answer to two decimal places.)Find the p-value. (Round your answer to three decimal places.) p-value = State your conclusion. O Do not reject H . There is sufficient evidence to conclude that there is a significant difference in the mean price per gallon for regular gasoline among the three brands. O Reject Ho. There is not sufficient evidence to conclude that there is a significant difference in the mean price per gallon for regular gasoline among the three brands. O Do not reject H . There is not sufficient evidence to conclude that there is a significant difference in the mean price per gallon for regular gasoline among the three brands. O Reject Ho. There is sufficient evidence to conclude that there is a significant difference in the mean price per gallon for regular gasoline among the three brands.A factorial experiment involving two levels of factor A anc three leve s of factor B resulted in the following data. Factor B Level 1 Level 2 Level 3 135 8? ?8 Level 1 1.65 '53 95 Factor A 125 130 11? Level 2 95 13-8 133 Test for any significant main effects and any interaction. Use a = 0.05. Find the value of the test statistic for factor A. (Round your answer to two decimal places.) |:| Find the lbvalue for factor A. (Round your answer to three decimal places.) State your conclusion about factor A. '12:? Because the p-value S a = 0.05, factorA is not significant. '3 3' Because the p-value > a = 0.05, factorA is significant. Because the p-value > a = 0.05, factorA is not significant. '32:? Because the liJ-yalue E a = 0.05, factorA is signicant. Find the value of the test statistic for factor B. (Round your answer to two decimal places.) |:| Find the p-value for factor B. (Round your answer to three decimal places.) State your conclusion about factor B. Because the pvalue S a = 0.05, factor B is significant. Because the lbvalue g a = 0.05, factor B is not significant. Because the liJyalue > a = 0.05, factor B is significant. Because the p-value > a = 0.05, factor B is not significant. Find the value of the test statistic for the interaction between factors A and B. [Round your answer to two decimal places.)- |:| Find the pvalue for the interaction between factors A and B. (Round your answer to three decimal places.)- State your conclusion about the interaction between factors A and B. "' Because the pvalue > a = 0.05r the interaction between factors A and B is not significant. '1} Because the l.':I-\\.ra|LIe E a = 0.05r the interaction between factors A and B is not significant. " Because the p-Value S a = 0.05r the interaction between factors A and B is significant. Because the pvalue > a = 0.05r the interaction between factors A and B is significant. The calculations for a factorial experiment involving four levels of factor A, three levels of factor B, and three replications resulted in the following data: SST = 275, SSA = 29, SSB = 21, SSAB = 173. Set up the ANOVA table. (Round your values for mean squares and F to two decimal places, and your p-values to three decimal places.) Source Sum Degrees Mean of Variation of Squares p-value of Freedom Square Factor A Factor B Interaction Error Total Test for any significant main effects and any interaction effect. Use a = 0.05. Find the value of the test statistic for factor A. (Round your answer to two decimal places.) Find the p-value for factor A. (Round your answer to three decimal places.) P-value = State your conclusion about factor A. Because the p-value s a = 0.05, factor A is significant. Because the p-value > a = 0.05, factor A is significant. Because the p-value s a = 0.05, factor A is not significant. Because the p-value > a = 0.05, factor A is not significant. Find the value of the test statistic for factor B. (Round your answer to two decimal places.) Find the p-value for factor B. (Round your answer to three decimal places.) p-value = State your conclusion about factor B. O Because the p-value s a = 0.05, factor B is not significant. O Because the p-value > a = 0.05, factor B is not significant. O Because the p-value > a = 0.05, factor B is significant. Because the p-value s a = 0.05, factor B is significant.Find the value of the test statistic for the interaction between factors A and B. [Round your answer to two decimal places.)- :l Find the p-value for the interaction between factors A and B. (Round your answer to three decimal places.)- State your conclusion about the interaction between factors A and B. '32:? Because the p-value S a = 0.05r the interaction between factors A and B is not significant. Because the p-value E a 0.05r the interaction between factors A and B is significant. '3 13' Because the p-value } a ll 0.05r the interaction between factors A and B is significant. '32:? Because the p-value :> a 0.05r the interaction between factors A and B is not significant. An amusement park studied methods for decreasing the waiting time (minutes) for rides by loading and unloading riders more efficiently. Two alternative loading/unloading methods have been proposed. To account for potential differences due to the type of ride and the possible interaction between the method of loading and unloading and the type of ride, a factorial experiment was designed. Use the following data to test for any significant effect due to the loading and unloading method, the type of ride, and interaction. Use a = 0.05. Type of Ride Roller Coaster Screaming Demon Log Flume 41 52 50 Method 1 43 44 46 49 50 48 Method 2 51 46 44 Find the value of the test statistic for method of loading and unloading. Find the p-value for method of loading and unloading. (Round your answer to three decimal places.) p-value =Find the value of the test statistic for type of ride. :i Find the p-value for type of ride. (Round your answer to three decimal places.) Find the value of the test statistic for interaction between method of loading and unloading and type of ride. :l Find the p-value for interaction between method of loading and unloading and type of ride. (Round your answer to three decimal places.) Suppose the following data show the percentage of 17- to 24-year-olds who are attending college in several metropolitan statistical areas in four geographic regions of the United States. Northeast Midwest South West 29.4 37.2 59.4 16.3 40.3 34.1 37.3 32.8 32.2 23.6 27.4 22.4 47.1 43.6 40.3 12.3 32.4 32.1 33.4 43.9 14.2 58.8 18.8 26.5 36.0 30.4 29.8 56.9 35,9 63.5 66.8 14.3 37.0 28.0 32.1 37.0 58.4 55.0 30.1 28.4 60.4 79.4 39.4 17.7 41.5 29.8 33.1 75.2 29.2 51.7 37.1 23.6 52.1 27.9 34.8 25.6 60.5 23.9 29.5 58.8 54.3 27.5 20.5 30.4 31.5 28.3 42.4 23.5 25.6 70.0 35.1 74.6 23.2 32.5 36.5 30.4 36.928 3 31.3 34 5 27 T 21% 28 5 31 9 31.2 2]. ]. 57 3 37 3 27.5 43 7 32.6 35 4 39.4 22 4 39.9 35 2 25.3 32.9 Use or = 0.05 to test whet 1er the mean percentage of 17'- to 24-year-olds who are attending college is the same for the four geographic regions. State the null and alternative hypotheses. H0: INN = [NH = [as = #w Ha: Not all the population means are equal. H0: INN = [NH = [as = #w Ha: .uN :- '\"M .2' \"S .2' \"W H0: At least two of the population means are equal. Ha: At least two of the population means are different. H0: Not all the population means are equal. H : .u_ = lit = .\"5 = In\