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 44 week-days, daily fees collected averaged $1,264, with a sample standard deviation of $150.

1. What assumption must you make in order to use these statistics for inference (Hint: what assumptions are you used using sample data statistics to infer about the population)

2. Write a 90% confidence interval for the mean daily income this parking garage will generate, rounded appropriately.

3. 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 think the consultant was corrected? Why or why not?

Answer 1

1.

In order to use these statistics for inference, we make below assumptions:

• The sampling method is simple random sampling.
• The sampling distribution is approximately normally distributed. Generally, the sampling distribution will be approximately normally distributed when the sample size is greater than or equal to 30.

2.

Standard error of mean , SE = = 22.61335

Degree of freedom = n-1 = 44 - 1 = 43

Critical value of t at 90% confidence interval and df = 43 is 1.68

90% confidence interval for the mean daily income this parking garage is,

(1264 - 1.68 * 22.61335, 1264 + 1.68 * 22.61335)

(1226.01 , 1301.99)

3.

The predicted value of parking revenues ( $1,300 per day) lies inside the 90% confidence interval. On the basis of the computed confidence interval, we cannot reject the claim of the the consultant.