This activity is a practice in preliminary understanding of confidence interval estimation. Please read the following scenario and respond to the questions related to the scenario:
You want to estimate the production days that would be lost during the next three months by sampling the vacation intentions of a sample of employees. You randomly select 36 employees in the organization and find that the average number of days they intend taking off is 16 days during the coming three Summer months, with a standard deviation of seven (7) days. Based on these sample statistics, you want to estimate at a 99% confidence level, the days that will be lost because of the entire population of workers taking vacation time during the next three months, so that the plant manager knows how much temporary help he should plan on hiring during the summer months in order for work to proceed smoothly. Assume that days of intending to take vacation by an employee is independent of all other employees’ vacation intentions.
1. Construct the confidence interval for the mean vacation time of an employee based on the above sample results.
2. If there are 100 employees in the organization expected to take vacation during Summer, what is the maximum (most pessimistic) and minimum (most optimistic) number of days of labor that temporary help would be needed for production to proceed smoothly?
3. Based on the same sample results how can you reduce the interval estimated in Number 2 above? Please, provide an example and calculate the new confidence interval. What would be a trade-off for reducing the confidence interval length?