An engineer worker of a coal production plant A would like to estimate the mean amount of time an employee takes to assemble a new maintenance component . The standard deviation of this assembly is 3.6 hours.

(1) After observing 20 employees assembling similar devices, the manager noticed that their average time was 16.2 hours.

Construct a 95% confidence interval for the mean assembly time. And estimate the mean amount of time an employees takes to assemble the same maintenance component of production plant B.

(2) Construct a 95% confidence interval for the mean assembly time of production plant B if the data he collected are as follows in hours per worker: 20.0 17.5 16.016.3 17.2 16.7 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 minutes with 95% 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.