Question

Suppose that the training director of a manufacturing company wanted to compare three different team-based approaches (A, B, C). Each member of a group of 26 new employees was randomly assigned to one of three team-based methods. After completing training, the employees in the study were evaluated on the time it took (in minutes) to assemble the product. The results are summarized as follows Time To Assemble Product Methods B A C 8.82 8.21 8.57 9.26 6.65 8.50 8.70 7.44 9.11 8.97 7.95 8.20 8.20 8.64 8.32 8.29 7.88 7.75 9.45 8.84 9.90 9.42 8.40 9.43 9.25 7.98 9 9 8 Sample Size: n Sample means: X; 8.9778 7.9356 8.7387 Sample standard deviation: S 0.3971 0.6239 0.6817 The grand mean: 3 n nTn22nz3. _ i=1 j=1 8.543 nT where n n1+ 2+ 13 Assume that the underlying populations are normally distributed with unknown but equal variances. a. At the 0.05 level of significance, analyze the data to determine whether there is evidence of a difference in the average assembly time among the team- based methods. b. If the results you obtained in (a) indicate it is appropriate, determine which groups differ in average assembly time

Answer 1

assembly time due to method B assembly time due to method C a. Let uA HB true mean true mean Null hypothesis, Ho A HB C Alter native hypothesis, H At least one H's is different from others. S 3 Σ(Ε of square due to between group SSB sum 2-1 - 9* (8.9778- 8.543)29* (7.9356 8.543)2 8*(8.7387 8.543)2 5.3283 with df 3- 1 2 Σ SSE of square due to error sum S -1 0.39712 0.62392 0.68172 =1.0117 with df 26 3 23 SSB 2 (5.3283/2)/(1.0117/23) F - ratio 60.5668 _ SSE/23 P(F 60.5668|F p- value Hence we reject Ho at 5% level of significance and conclude that there is evidence of a difference in the average assembly time among the team based methods. F2,23) 0.0000< 0.05

b. Null hypothesis, Hoi HA HB US. Alter native hypothesis, H HAHB .2 Test statistic 10.5400 ( 7.9356 - SSE / 23 = 1.0117/23 0.0440 1 MSE where, 8.9778, T n2 9, MSE _ p - value 2P(t> 10.5400t. t3)0.0000 < 0.05 assembly times of Method A and Method E reject Ho1 and hence mean Hence we dif fer significantly Null hypothesis, Ho2 HA HC vs Alternative hypothesis, H12 HA Hc 3. Test statistic 2.3458 _ 1 MSE 1 n3 where, 3. 8.7387, n3 p - value 8 2P(t> 2.3458t~t3) reject Ho2 and hence mean 0.0280 0.05 assembly times of Method A and Method C Hence We dif fer significantly

Null hypothesis, Ho3 HB c Us. Alter native hy pothesis, H3 HB HC 2.T3 Test statistic -7.8793 1 1 MSE ( n3 p value 2P(t > 7.8793 t Hence we 0.0000 0.05 t23) reject Ho3 and hence mean assembly times of Method B and Method C dif fer significantly