Parking II Suppose that, for budget planning purposes, the city in Exercise 24 n
ID: 3244118 • Letter: P
Question
Parking II Suppose that, for budget planning purposes, the city in Exercise 24 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. How would this interval be better for the city? (You need not actually create the new interval.) b) How would the 95% interval be worse for the planners? c) How could they achieve an interval estimate that would better serve their planning needs? d) How many days' worth of data should they collect to have 95% confidence of estimating the true mean to within exist3?Explanation / Answer
a)An interval I(x), which is a subset of , said to be a confidence interval of with confidence coefficient (1-) if P[ I(x)] = (1-), for all .
The length of a 95% confidence interval will be more than that of a 90% C.I, since for the population mean C.I = (Xbar – Z/2*/n, Xbar + Z/2*/n), when standard deviation () of the population is known and Z/2 decreases as increases. Since the length will be more, we will have wider range of values which is better for the city.
b) The length of a 95% confidence interval will be more than that of a 90% C.I, so we will have wider range of values with the value of the parameter actually falling in this range defined with some probability. Thus, planners will have problem since lesser the range, easier is to get the estimate.
c) By decreasing the level of significance or by decreasing the standard deviation in the population or by increasing the sample size.
d)Margin of error = 3
or, Z/2*/n = 3 [ = 0.05]
or, 1.96* /n = 3
or, n = 0.4268*, where is population s.d.