Suppose that for budget planning purposes the city in Exercise 39 needs a better estimate of the mean daily income from parking fees.
(a) Someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first created. Would this interval be better for the city planners? (You need not actually create the new interval.)
(b) How would the 95% interval be worse for the city planners?
(c) How could city planners achieve an interval estimate that would better serve their planning needs?
(d) How many days’ worth of data must planners collect to have 95% confidence of estimating the true mean to within $10? Does this seem like a reasonable objective? (Use a
-interval to simplify the calculations.)
Exercise 39
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 $1,264 with a standard deviation of $150.
(a) What assumptions must you make in order to use these statistics for inference?
(b) Write a 90% confidence interval for the mean daily income this parking garage will generate, rounded appropriately.
(c) The consultant who advised the city on this project predicted that parking revenues would average $1,300 per day. On the basis of your confidence interval, do you think the consultant was correct? Why or why not?
(d) Give a 90% confidence interval for the total revenue earned during five weekdays.