Question

To test for any significant difference in the mean number of hours between breakdowns for four machines, the following data were obtained: Machine 1: 6.4 Machine 2: 8.7 Machine 3: 11.1 Machine 4: 9.9 Machine 1: 7.8 Machine 2: 7.4 Machine 3: 10.3 Machine 4: 12.8 Machine 1: 5.3 Machine 2: 9.4 Machine 3: 9.7 Machine 4: 12.1 Machine 1: 7.4 Machine 2: 10.1 Machine 3: 10.3 Machine 4: 10.8 Machine 1: 8.4 Machine 2: 9.2 Machine 3: 9.2 Machine 4: 11.3 Machine 1: 7.3 Machine 2: 9.8 Machine 3: 8.8 Machine 4: 11.5 The mean times between breakdowns are 7.1, 9.1, 9.9, and 11.4 hours respectively. In the analysis of variance, MSTR = 19.26 and MSE = 0.97. Use the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experiment error rate of 0.05 is desired. There are six pairwise comparisons among the 4 machines. What error rate should be used for each pairwise comparison (to 4 decimals)? Using t = 2.845 for the above error rate, calculate the Bonferroni LSD value (to 2 decimals).

          To test for any significant difference in the mean number of hours between breakdowns for four machines, the following data were obtained:

Machine 1: 6.4
Machine 2: 8.7
Machine 3: 11.1
Machine 4: 9.9
Machine 1: 7.8
Machine 2: 7.4
Machine 3: 10.3
Machine 4: 12.8
Machine 1: 5.3
Machine 2: 9.4
Machine 3: 9.7
Machine 4: 12.1
Machine 1: 7.4
Machine 2: 10.1
Machine 3: 10.3
Machine 4: 10.8
Machine 1: 8.4
Machine 2: 9.2
Machine 3: 9.2
Machine 4: 11.3
Machine 1: 7.3
Machine 2: 9.8
Machine 3: 8.8
Machine 4: 11.5

The mean times between breakdowns are 7.1, 9.1, 9.9, and 11.4 hours respectively. In the analysis of variance, MSTR = 19.26 and MSE = 0.97. Use the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experiment error rate of 0.05 is desired.

There are six pairwise comparisons among the 4 machines. What error rate should be used for each pairwise comparison (to 4 decimals)?

Using t = 2.845 for the above error rate, calculate the Bonferroni LSD value (to 2 decimals).

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Added by Mitchell M.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Madhur L

08/24/2023

Step 1

Since there are 6 pairwise comparisons and we want a maximum overall experiment error rate of 0.05, we can divide the overall error rate by the number of comparisons to find the error rate for each pairwise comparison. Error rate for each pairwise comparison = Show more…

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To test for any significant difference in the mean number of hours between breakdowns for four machines, the following data were obtained: Machine 1: 6.4 Machine 2: 8.7 Machine 3: 11.1 Machine 4: 9.9 Machine 1: 7.8 Machine 2: 7.4 Machine 3: 10.3 Machine 4: 12.8 Machine 1: 5.3 Machine 2: 9.4 Machine 3: 9.7 Machine 4: 12.1 Machine 1: 7.4 Machine 2: 10.1 Machine 3: 10.3 Machine 4: 10.8 Machine 1: 8.4 Machine 2: 9.2 Machine 3: 9.2 Machine 4: 11.3 Machine 1: 7.3 Machine 2: 9.8 Machine 3: 8.8 Machine 4: 11.5 The mean times between breakdowns are 7.1, 9.1, 9.9, and 11.4 hours respectively. In the analysis of variance, MSTR = 19.26 and MSE = 0.97. Use the Bonferroni adjustment to test for a significant difference between all pairs of means. Assume that a maximum overall experiment error rate of 0.05 is desired. There are six pairwise comparisons among the 4 machines. What error rate should be used for each pairwise comparison (to 4 decimals)? Using t = 2.845 for the above error rate, calculate the Bonferroni LSD value (to 2 decimals).

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Transcript

00:01 Hello students in this question, the bonferroni test is a test for multiple comparisons.

00:15 It allows us to compare the mean of the levels of the factor after rejecting the null hypothesis of equal means with an anova test.

00:24 So here the bonferroni significant difference is calculated as bst is equal to t n minus t into alpha divided by 2 m into square root of se square, se cap square into 1 divided by n i plus 1 divided by n j.

00:50 So here n is the total number of observations.

00:54 So here we have n is equal to 24 and t is the levels of the factor.

01:00 So here t is equal to 4 and n i and n j are the sample size.

01:06 So here we have n i equal to n j is equal to 6 and se cap square is the estimation of the variance of the error.

01:16 So here mse estimates this value.

01:21 So here we have se cap square is equal to 0 .97 and t n minus t into alpha divided by 2 m, t student value with n minus t degrees of freedom.

01:38 So here and the significance level of alpha divided by 2 m.

01:43 In our problem this value is given as 2 .845 for alpha is equal to 0 .5 and here m, m is the number of combinations of levels taken at taken two at a time.

02:05 So here m is equal to 6 and the corrected alpha value from bonferroi test that is alpha corrected.

02:20 So that is is equal to alpha divided by m.

02:25 So that is equal to 0 .05 divided by 6.

02:32 So that is equal to 0 .0083.

02:38 Sorry here we have alpha 0 .05 and next the critical significance value that is alpha critical that is 1 minus 1 minus alpha divided by m power m...

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