Robots are being used with increasing frequency on production lines to perform manotonous task. To determine whether a robot welder should replace human welders in producing automobiles, an experiment was performed. The time for the robot to complete a series of welds was found to be 38 seconds.A random sample of 20 workers was taken, and the time for each worker to complete the welds was measured and the times are 35,25,30,36,37.42,34.44,39,44,40,46,38,42,33,33,39,39,43,41.The mean was calculated to be 38 seconds, the same as the robot's time. However, the robot's time did not vary, whreas there was variation among the workers times. An analysis of the production line revealed that if the variance exceeds 17 seconds^2, there will be problems. Perform an analysis of the data, and determine whether the problems using human welders are likely.

Question

Robots are being used with increasing frequency on production lines to perform manotonous task. To determine whether a robot welder should replace human welders in producing automobiles, an experiment was performed. The time for the robot to complete a series of welds was found to be 38 seconds.A random sample of 20 workers was taken, and the time for each worker to complete the welds was measured and the times are 35,25,30,36,37.42,34.44,39,44,40,46,38,42,33,33,39,39,43,41.The mean was calculated to be 38 seconds, the same as the robot's time. However, the robot's time did not vary, whreas there was variation among the workers times. An analysis of the production line revealed that if the variance exceeds 17 seconds^2, there will be problems. Perform an analysis of the data, and determine whether the problems using human welders are likely.

Answer 1

To analyze the data and determine whether the problems using human welders are likely, we need to calculate the variance of the workers' times and compare it to the given threshold of 17 seconds^2.

Here are the steps to perform the analysis:

1. Calculate the variance of the workers' times:
- Calculate the mean of the workers' times by summing up all the times and dividing by the number of workers (20 in this case).
Mean = (35 + 25 + 30 + 36 + 37 + 42 + 34 + 44 + 39 + 44 + 40 + 46 + 38 + 42 + 33 + 33 + 39 + 39 + 43 + 41) / 20 = 38 seconds
- For each worker's time, subtract the mean and square the difference.
- Sum up all the squared differences.
- Divide the sum by the number of workers minus 1 (N - 1) to calculate the variance.
Variance = Sum of squared differences / (number of workers - 1)

2. Compare the calculated variance to the threshold of 17 seconds^2:
- If the variance is greater than 17 seconds^2, then problems using human welders are likely.
- If the variance is less than or equal to 17 seconds^2, then problems using human welders are not likely.

Let's perform the calculations:

1. Calculate the variance of the workers' times:
- Subtract the mean from each worker's time, square the difference, and sum them up.
Sum of squared differences = (35 - 38)^2 + (25 - 38)^2 + (30 - 38)^2 + (36 - 38)^2 + (37 - 38)^2 + (42 - 38)^2 + (34 - 38)^2 + (44 - 38)^2 + (39 - 38)^2 + (44 - 38)^2 + (40 - 38)^2 + (46 - 38)^2 + (38 - 38)^2 + (42 - 38)^2 + (33 - 38)^2 + (33 - 38)^2 + (39 - 38)^2 + (39 - 38)^2 + (43 - 38)^2 + (41 - 38)^2
Sum of squared differences = 1259
- Divide the sum by the number of workers minus 1 to calculate the variance.
Variance = 1259 / 19 = 66.26 seconds^2 (rounded to two decimal places)

2. Compare the calculated variance to the threshold of 17 seconds^2:
- Since the calculated variance (66.26 seconds^2) is greater than the given threshold of 17 seconds^2, it indicates that problems using human welders are likely.

Therefore, based on the analysis of the data, it is likely that problems using human welders are anticipated due to the variance in their completion times exceeding the specified threshold.