Question

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. For a random sample of 38 weekdays, daily fees collected averaged $134,
with a standard deviation of $10.
Construct a 90% confidence interval estimate for the mean daily income this parking
garage will generate. Round your final answers to whole numbers. Show your work!
Formula(s), substitutions, answer! Round your z or t value to 3 decimal places.
The consultant who advised the city on this project predicted that parking revenues
would average at least $135 per day. Based on your confidence interval, revenues
(could / could not) average at least $135 per day. Briefly defend your answer.

Answer 1

a)

sample mean, xbar = 134
sample standard deviation, s = 10
sample size, n = 38
degrees of freedom, df = n - 1 = 37

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 1.687

ME = tc * s/sqrt(n)
ME = 1.687 * 10/sqrt(38)
ME = 2.7

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (134 - 1.687 * 10/sqrt(38) , 134 + 1.687 * 10/sqrt(38))
CI = (131 , 137)

Based on your confidence interval, revenues  
( could not) average at least $135 per day.

Because confidence interval contains 135