To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, a chemical company obtained the following data on the time (in minutes) needed to mix the material. Manufacturer 1 2 3 20 27 19 27 26 19 25 31 24 20 32 18 (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. OHo:/'1=\"z=\"3 Ha: Not all the population means are equal. .Ho:\"1=\"2=\"3 Ha: #1 * uz * \"3 O Ho: Not all the population means are equal. Ha: \"1 = \"2 = \"3 OHO=M1*#2*M3 Ha: \"1 = \"2 = \"3 O Ho: At least two of the population means are equal. Ha: At least two of the population means are different. Find the value of the test statistic. (Round your answer to two decimal places.) :J Find the p-value. (Round your answer to three decimal places.) State your conclusion. 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 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 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. X 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