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.

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

H0: >= 135

HA: < 135

95% Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 38- 1 ) = 2.026
134 ± t(0.05/2, 38 -1) * 10/√(38)
Lower Limit = 134 - t(0.05/2, 38 -1) 10/√(38)
Lower Limit = 130.7134
Upper Limit = 134 + t(0.05/2, 38 -1) 10/√(38)
Upper Limit = 137.2866
95% Confidence interval is ( 130.7134 , 137.2866 )

Since 135 contained in confidence interval ,

we conclude that revenues could not average at least $135 per day