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 19 29 21 25 26 18 25 30 22 19 31 23 (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 OH: 4 # H 2 # My Hai My = H2 = Ng O Ho: Not all the population means are equal. He: u, = M2 = H3 OH: H1 = 42 = My He: Not all the population means are equal. O H : At least two of the population means are equal. H : At least two of the population means are different. OH: H1 = H2 = My 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 the mean time needed to mix a batch of material is not the same for each manufacturer. Do not reject H . 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 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. (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 =