In an effort to estimate the mean time taken by the shift employees to reach the workplace, the production manager of a manufacturing company randomly samples 64 employees from all shifts. The sample reveals a mean time taken of 46.57 minutes. The population standard deviation is known to be 12.30 minutes. The mean time taken is assumed to be normally distributed. A 90% confidence interval estimate is developed, using a critical value of 1.65.

State the best point estimate to be used as an estimate of the true mean.

State the reason why the standard normal distribution is used in the calculation of the confidence interval.

Find the margin of error that will be reported.

Find the lower limit of the confidence interval estimate.

Find the upper limit of the confidence interval estimate.

The confidence interval obtained isthe population mean time taken by the shift employees to reach the workplace. Is the statement true or false?

The production manager initially estimated that the true mean is 48.2 minutes. Is the statement true or false?

The manager decides to use a confidence level of 99% instead. This will result in a narrower confidence interval. Is the statement true or false?

A narrower confidence interval will be obtained if the manager has sampled a larger sample. Is the statement true or false?

How large a sample size is needed if the manager wants to estimate the true mean to within 3 minutes, using the same confidence level?