Question

The local city council wants to determine whether the pricing of their main car park is appropriate. Over a three months period, 20 days were randomly selected with the number of cars counted in the car park. The results of this sample are below:

Day 1	750	Day 11	462
Day 2	745	Day 12	710
Day 3	489	Day 13	732
Day 4	322	Day 14	714
Day 5	704	Day 15	769
Day 6	680	Day 16	798
Day 7	695	Day 17	576
Day 8	760	Day 18	499
Day 9	775	Day 19	702
Day 10	507	Day 20	698

(a)Summarise the sample data shown above by finding the mean, median and standard deviation.

Is the distribution of the sample data symmetrical or skewed? Explain your answer.

The general manager claims that the average occupancy rate of the car park for the ENTIRE YEAR is greater than 85%. The maximum occupancy of the car park is 800 cars. Test this claim, using a significance of = 5%. Be careful to state your conclusion.

(b)Determine the 95% confidence interval for the proportion of ALL days where the occupancy rate was greater than 85%.

(c)Further investigation of the sampling process revealed that the council worker sent to count cars was only walking up to the fourth floor of the car park on the weekend. Consequently, three levels were not counted. Identify the type(s) of bias that may have occurred and explain whether the validity of our conclusions in either (c) or (d) above have been impacted.