Manufacturing organizations incur considerable cost in the training of new employees. Not only is there a direct cost involved in the training program, but there is also an indirect cost to the firm since employees in training do not contribute directly to the firm's manufacturing process. Hence, such organizations seek training programs that can bring new employees to maximum efficiency in the shortest possible time. An assembly operation in a manufacturing plant requires approximately a one month training period for new employees to reach maximum efficiency. A new method of training was suggested and a test conducted to compare the new method with the standard procedure. Two groups of nine new employees were trained for a period of three weeks, one group using the new method and the other following the standard procedure. The length of time (in minutes) required for each employee to assemble the device was recorded at the end of three-week period. These measurements appear as follows: Standard Procedure 32 37 35 28 41 44 35 31 34 New Procedure 35 31 49 25 34 40 27 32 21 a). At 5% level of significance, is there sufficient evidence to indicate that the new training method is more effective, on the average, than the standard training procedure? Your conclusion must be in terms of the P-Value. Show all necessary work. b). Explain the consequences of the Type I and Type II errors in terms of the problem. Which error could prove to be more devastating in terms of this problem? Explain c). Estimate the difference between the actual average length of time to assemble the device using the new and the standard procedure using a 95% confidence interval. Using this interval estimation, is there sufficient evidence to indicate that the new training method is more effective, on the average, than the standard training procedure? Explain d). Carefully interpret the confidence interval estimation
Manufacturing organizations incur considerable cost in the training of new employees. Not only is there a direct cost involved in the training program, but there is also an indirect cost to the firm since employees in training do not contribute directly to the firm's manufacturing process. Hence, such organizations seek training programs that can bring new employees to maximum efficiency in the shortest possible time. An assembly operation in a manufacturing plant requires approximately a one month training period for new employees to reach maximum efficiency. A new method of training was suggested and a test conducted to compare the new method with the standard procedure. Two groups of nine new employees were trained for a period of three weeks, one group using the new method and the other following the standard procedure. The length of time (in minutes) required for each employee to assemble the device was recorded at the end of three-week period. These measurements appear as follows:
| Standard Procedure | 32 | 37 | 35 | 28 | 41 | 44 | 35 | 31 | 34 |
| New Procedure | 35 | 31 | 49 | 25 | 34 | 40 | 27 | 32 | 21 |
a). At 5% level of significance, is there sufficient evidence to indicate that the new training method is more effective, on the average, than the standard training procedure? Your conclusion must be in terms of the P-Value. Show all necessary work.
b). Explain the consequences of the Type I and Type II errors in terms of the problem. Which error could prove to be more devastating in terms of this problem? Explain
c). Estimate the difference between the actual average length of time to assemble the device using the new and the standard procedure using a 95% confidence interval. Using this
d). Carefully interpret the confidence interval estimation
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