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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
a1 Summarise the sample data shown above by finding the mean, median and standard deviation.
a2 Is the distribution of the sample data symmetrical or skewed? Explain your answer.
= 5%. Be careful to state your conclusion.aa3 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
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.
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