Parking Hoping to lure more shoppers downtown, a city builds a new public parkin
ID: 3175477 • Letter: P
Question
Parking Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. During a two-month period (44 weekdays), daily fees collected averaged $126, with a standard deviation of $15. What assumptions must you make in order to use these statistics for inference? Write a 90% confidence interval for the mean daily income this parking garage will generate. Interpret this confidence interval in context. Explain what "90% confidence" means in this context. The consultant who advised the city on this project predicted that parking revenues would average $130 per day. Based on your confidence interval, do you think the consultant was correct? Why?Explanation / Answer
a.
we assume that data is normally distributed
b.
Confidence Interval
CI = x ± t a/2 * (sd/ Sqrt(n))
Where,
x = Mean
sd = Standard Deviation
a = 1 - (Confidence Level/100)
ta/2 = t-table value
CI = Confidence Interval
Mean(x)=126
Standard deviation( sd )=15
Sample Size(n)=44
Confidence Interval = [ 126 ± t a/2 ( 15/ Sqrt ( 44) ) ]
= [ 126 - 1.681 * (2.261) , 126 + 1.681 * (2.261) ]
= [ 122.199,129.801 ]
c.
Interpretations:
1) We are 90% sure that the interval [122.199 , 129.801 ] contains the true population mean
2) If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population mean
d.
we are 90% confident that mean lies in the interval