Questions: - The owner of a large equipment rental company wants to make a rather quick estimate of the average number days a piece of ditch digging equipment is rented out per person per time. The company has records of all rentals, but the amount of time required to conduct an audit of all accounts would be prohibitive. The owner decides to take a random sample of rental invoices. Fourteen different rentals of ditch diggers are selected randomly from the flies, yielding the following data, She uses these data to construct a 99% confidence interval to estimate the average number of days that a ditch digger is rented and assumes that number of days per rental is normally distributed in the population.

3    1    3    2    5    1    2    1    4    2    1    3     1    1

Solution: -
As n = 14, the df = 13. The 99% level of confidence results in α/2 = .005 area in each tail of the distribution. The table t value is
                t._005.13 = 3.012
The sample mean is 2.14 and the sample standard deviation is 1.29. The confidence interval is

                x + t s/√n


1.10 < μ < 3.18

The point estimate of the average length of timer per rental is 2.14 days, with an error of + 1.04. With a 99 % level of confidence, the company’s owner can estimate that the average length of time per rental is between 1.10 and 3.18 days. Combining this figure with variables such as frequency of rentals per year can help the owner estimate potential profit or loss per year for such a piece of equipment.