A Parking Enforcement Officer in Wollongong is conducting an analysis on the amount of time left on parking meters in the CBD. A quick survey of 15 metered parking spaces where cars had just left provided the following times (in minutes).

20

15

1

14

4

13

21

29

18

27

18

31

14

21

3

(a) What assumptions must you make to obtain a confidence interval for the mean amount of time left for all vacant meters?

(b) Construct a 95% confidence interval estimate for the mean amount of time left for all vacant meters.

(c) Interpret the confidence interval obtained in (b).

(d) The Policy Manager is not totally convinced with the confidence interval estimated in (b), because it is too wide. They would like to be 99% sure that the sample mean is within 4 minutes of the true mean. What sample size is required to meet this requirement? Assume the population standard deviation is equal to the one identified for the sample of the 15 parking spaces.