Question

5. 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 weekdays, daily fees collected averaged $126, with a standard deviation of $15.

   1. What assumptions must you make in order to use these statistics for inference?

   2. Find a 90% confidence interval for the mean daily income this parking garage will generate.

   3. Explain in context what this confidence interval means.

   4. Explain what 90% confidence means in this context.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 126

Population standard deviation =    = 15
Sample size = n =44

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2    * ( /n)

= 1.645 * ( 15 /  44 )

= 3.7199
At 90% confidence interval estimate of the population mean
is,

- E < < + E

126 - 3.7199 <   < 126 + 3.7199

122.2801 <   < 129.7199

( 122.2801 ,129.7199 )

At 90% confidence interval estimate of the population mean
is,( 122.2801 ,129.7199 )