(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? There is a significant difference between the means for machines 2 and 4. There is not a significant difference between the means for machines 2 and 4.
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H0: μ2 = μ4 (no difference) Ha: μ2 ≠ μ4 (two-sided) Show more…
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Adi S.
To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained. Machine 1 Machine 2 Machine 3 Machine 4 6.8 9.0 10.9 9.8 8.2 7.6 10.1 12.5 5.7 9.7 9.5 11.8 7.6 10.5 9.9 10.5 8.6 9.4 8.8 11.1 7.5 10.2 8.4 11.5 Use the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experiment-wise error rate of 0.05 is desired. Find the value of LSD. (Round your comparison wise error rate to three decimal places. Round your answer to two decimal places.) LSD = ___ Find the pairwise absolute difference between sample means for each pair of machines. x1 − x2 = x1 − x3 = x1 − x4 = x2 − x3 = x2 − x4 = x3 − x4 = Which treatment means differ significantly?
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Two machines are used to fill plastic bottles with dishwashing detergent. The standard deviations of fill volume are known to be $\sigma_{1}=0.10$ fluid ounces and $\sigma_{2}=0.15$ fluid ounces for the two machines, respectively. Two random samples of $n_{1}=12$ bottles from machine 1 and $n_{2}=10$ bottles from machine 2 are selected, and the sample mean fill volumes are $\bar{x}_{1}=30.87$ fluid ounces and $\bar{x}_{2}=30.68$ fluid ounces. Assume normality. (a) Construct a $90 \%$ two-sided confidence interval on the mean difference in fill volume. Interpret this interval. (b) Construct a $95 \%$ two-sided confidence interval on the mean difference in fill volume. Compare and comment on the width of this interval to the width of the interval in part (a). (c) Construct a $95 \%$ upper-confidence interval on the mean difference in fill volume. Interpret this interval. (d) Test the hypothesis that both machines fill to the same mean volume. Use $\alpha=0.05 .$ What is the $P$ -value? (e) If the $\beta$ -error of the test when the true difference in fill volume is 0.2 fluid ounces should not exceed $0.1,$ what sample sizes must be used? Use $\alpha=0.05 .$
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