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156 141 15? 124 142 137 157' 125 122 13? 141 151 122 133 161.6 158.8 142 0 {3) Compute the sum of squares between treatments. |:| {h} Compute the mean square between treatments. E {c} Compute the sum of squares due to error. E (d) Compute the mean square due to error. (Round your answer to two decimal places.) E (e) Set up the ANOVA table for this problem. (Round your values for MSE and Fto two decimal places, and your pvalue to four decimal places.) Treatments Error I I I I Tota | (f) At the a = 0.05 level of signicance, test whether the means for the three treatments are equal. State the null and alternative hypotheses. 0 Ho: Not all the population means are equal. Ha: \"A = \"B = \"c 0 Ho: l\Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Reject Ho. There is sufficient evidence to conclude that the means for the three treatments are not equal. O Reject Ho. There is not sufficient evidence to conclude that the means for the three treatments are not equal. O Do not reject Ho. There is not sufficient evidence to conclude that the means for the three treatments are not equal. O Do not reject H . There is sufficient evidence to conclude that the means for the three treatments are not equal.You may need to use the appropriate technology to answer this question. In a completely randomized design, seven experimental units were used for each of the five levels of the factor. Complete the following ANOVA table. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.) Source Sum Degrees Mean F of Variation of Squares of Freedom Square p-value Treatments 300 Error Total 46001 Variation {If Square; of Fred'm'n, Square 1 p \"In\": Treatments 380 4 95 55.42 0.0000 Error 50 35 1.? 1 Total 440 39 (a) what hypotheses are implied in this problem? OHo:\"1:02=1\"3=l\""4=l\""5 Ha: Not all the population means are equal. OHiplaEpzaEp3p4ap5 Ha: \"1:\"2 =\"3=-\"4=-\"5 O H\": Not all the population means are equal. Ha:#1=p2=-u'3=#4=#5 OHo:\"12%:l\"3=l\"'4=l\"'5 Ha:p1#p2#p3#p4#p5 0 HD: At least two of the population means are equal. Ha: At least two of the population means are different. {In} At the a = 0.05 level of signicance, can we reject the null hypothesis in part (a)? Explain. 0 Because the pvalue 1: a = 0.05, we can reject HO. 0 Because the pvalue 2- a = 0.05, we cannot reject HO. 0 Because the p-value g a = 0.05, we cannot reject HO. 0 Because the pvalue > a. = 0.05, we can reject H". A company manufactures printers and fax machines at plants located in Atlanta, Dallas, and Seattle. To measure how much employees at these plants know about quality management, a random sample of 6 employees was selected from each plant and the employees selected were given a quality awareness examination. The examination scores for these 18 employees are shown in the following table. The sample means, sample variances, and sample standard deviations for each group are also provided. Managers want to use these data to test the hypothesis that the mean examination score is the same for all three plants. Set up the ANDVA table for these data. (Round your values for MSE and Fto two decimal places, and your pvalue to four decimal places.) Treatments I I I I I I I I I Error | | | | | | Total l I Test for any signicant difference in the mean examination score for the three plants. Use a = [1.05. State the null and alternative hypotheses. 0 Ho: \"1 =\"22F'3 Ha: Not all the population means are equal. 0 Ho: At least two of the population means are equal. Ha: At least two of the population means are different. 0 H0: Not all the population means are equal. Ha: #1 = #2 = #3 O \"03-\"1 :\"22-"3 Ha: #1 i :12 i #3 O H0:p1#p2#ps Ha: \"1 Z \"2 Z \"3 Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. O Reject Ho. There is sufficient evidence to conclude that the means for the three plants are not equal. O Reject Ho. There is not sufficient evidence to conclude that the means for the three plants are not equal. O Do not reject H . There is sufficient evidence to conclude that the means for the three plants are not equal. O Do not reject Ho. There is not sufficient evidence to conclude that the means for the three plants are not equal.(a) At the a = 0.05 level of signicance, can we reject the null hypothesis that the means of the three treatments are equal? State the null and alternative hypotheses. 0 Ho: \"AZ-\"BZF'C Ha: Not all the population means are equal. 0 Ho: \"AZ-"th'c Ha: p A i #B # pic 0 HI}: At least two of the population means are equal. Ha: At least two of the population means are different. 0 HI}: Not all the population means are equal. Ha: \"A = \"E. = l"c OHD:pAaEpBaEpC Find the value of the test statistic. (Round your answer to two decimal places.) |:| Find the pvalue. (Round your answer to three decimal places.) State your conclusion. 0 Reject H0. There is not sufcient evidence to conclude that the means of the three treatments are not equal. 0 Reject H0. There is sufficient evidence to conclude that the means of the three treatments are not equal. 0 Do not reject H0. There is not sufcient evidence to conclude that the means of the three treatments are not equal. 0 Do not reject H0. There is sufcient evidence to conclude that the means of the three treatments are not equal. (b) Use Fisher's LSD procedure to test whether there is a signicant difference between the means for treatments A and B, treatments A and C, and treatments B and C. Use a = 0.05. Find the value of LSD. (Round your answer to two decimal places.) Find the pairwise absolute difference between sample means for each pair of treatments. IEA _;B' = \\:| FA T ;(3' = :| Fe _ Ec' = :l Which treatment means differ significantly? (Select all that apply.) There is a significant difference between the means for treatments A and B. There is a significant difference between the means for treatments A and C. There is a significant difference between the means for treatments B and C. There are no significant differences. (c) Use Fisher's LSD procedure to develop a 95% confidence interval estimate of the difference between the means of treatments A and B. (Use X - X. Round your answers to two decimal places.) to20 29 21 27 25 2D 23 31 22 26 31 25 (a) Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use a = 0.05. State the null and alternative hypotheses. O HO: Not all the population means are equal. Ha: \"1 = 1'2 = #3 O HO: At least two of the population means are equal. Ha: At least two of the population means are different. 0 HD:,u1#p.2#p.3 Ha: \"1 = \"2 = \"3 OHo:-\"1=-\"2=-\"3 Ha: Not all the population means are equal. OHo:-\"1:-\"2:\"3 Ha: p1 # p2 # #3 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 not sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. O Do not reject Ho. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. O Reject Ho. There is sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. O Do not reject Ho. There is not sufficient evidence to conclude that the mean time needed to mix a batch of material is not the same for each manufacturer. (b) At the a = 0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3. Find the value of LSD. (Round your answer to two decimal places. ) LSD = Find the pairwise absolute difference between sample means for manufacturers 1 and 3. * 1 - X 3 What conclusion can you draw after carrying out this test? O There is a significant difference between the means for manufacturer 1 and manufacturer 3. O There is not a significant difference between the means for manufacturer 1 and manufacturer 3.Machine Machine Machine Machine 1 2 3 5.5 9.1 10.7 10.0 7.9 7.6 10.1 12.8 5.3 9.8 9.4 12.2 7.4 10.4 9.9 10.8 8.4 9.6 8.9 11.2 7.1 9.9 8.6 11.4 (a) At the a = 0.05 level of significance, what is the difference, if any, in the population mean times among the four machines? State the null and alternative hypotheses. OH: H = H2 = M3 = H4 OH : H , # H z # Hg F H 4 H, : H 1 = Hz = H3 = H4 O Ho: My = Hz = M3 = H4 H: Not all the population means are equal. O Ho: At least two of the population means are equal. He: At least two of the population means are different. O H: Not all the population means are equal. Ha: Hj = H2 = M3 = H4Find 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 not sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines. O Do not reject Ho. There is sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines. O Reject Ho. There is sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines. O Reject Ho. There is not sufficient evidence to conclude that the mean time between breakdowns is not the same for the four machines. (b) Use Fisher's LSD procedure to test for the equality of the means for machines 2 and 4. Use a 0.05 level of significance. Find the value of LSD. (Round your answer to two decimal places.) LSD = Find the pairwise absolute difference between sample means for machines 2 and 4. X 2 - X 4 = What conclusion can you draw after carrying out this test? O There is a significant difference between the means for machines 2 and 4. O There is not a significant difference between the means for machines 2 and 4