The operations manager of a production plant A would like to estimate the mean amount of timea worker takes to assemble a new electronic component. Assume that the standard deviation of this assembly time is 3.6 minutes.

(1) After observing 20 workers assembling similar devices, the manager noticed that their average time was 16.2 minutes. Construct a 92% confidence interval for the mean assembly time. Also, he would like to estimate the mean amount of time a worker takes to assemble the same electronic component of production plant B.

(2) Construct a 92% confidence interval for the mean assembly time of production plant B if the data he collected are as follows:

20.0 17.5 16.016.3 17.216.7 15.3 15.9 16.0 18.0 18.3 17.0 19.0 19.1 15.6

(3) How many workers should be involved in this study in order to have the mean assembly time estimated up to + or - 15 seconds with 92% confidence?

(4) Discuss the effect of the change in sample size to the margin of error and the confidence interval based on the context of the problem.