H2

Statistics

You may need to use the appropriate technology to answer this question. 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 21 27 20 26 25 19 25 32 22 20 28 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. O Ho: At least two of the population means are equal. Ha: At least two of the population means are different. O Ho: H 1 * H2* H3 Hai H1 = H2 = H3 O Ho: M1 = H2 = H3 Hai H1 * H2 * M3 O Ho: H 1 = H2 = M3 H: Not all the population means are equal. O H: Not all the population means are equal. Ha: M1 = M2 = M3 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 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 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. 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 o = 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 absclute difference between sample means for manufacturers 1 and 3. What conclusion can you draw after carrying out this test? ) There is a significant difference between the means for manufacturer 1 and manufacturer 3. () There is not a significant difference between the means for manufacturer 1 and manufacturer 3