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 43 weekdays, daily fees collected averaged $128, with standard deviation of $12. Complete parts a through e below. b) Find a 99% confidence interval for the meandaly Income this parking garage will generate The 99% confidence interval for the mean daily income is ($ ). (Round to two decimal places as needed.) c) Explain in context what this confidence interval means. Choose the correct answer below. O A. There is 99% confidence that the daily income for a weekday falls in the interval O B. There is 99% confidence that the mean daily income will always fall in the interval OC. There is 99% confidence that the interval contains the mean daily income O D. There is 99% confidence that the daily income for all weekdays falls in the interval d) Explain what 99% confidence means in this context Choose the correct answer below. O A 90% of all samples of size 43 produce intervals that contain the mean daily income R90% of all w a s samnind have all incomes that fall in the interval Click to select your answer(s).

Answer 1

Here, we have given that,

X: daily income of parking garage

n= Number of weekdays=43

$1585950166930_blob.png$ = sample mean =$ 128

S= sample standard deviation= $ 12

Now, we want to find the 99% confidence interval for population mean (mean daily income this parking garage $1585950166952_blob.png$

The formula is as follows,

Τ – Ε <μ<1+E

Where

E=Margin of error =

S t(critical) * - in)

Now,

Degrees of freedom = n-1 = 43-1=42

c=confidence level =0.99

$1585950166957_blob.png$ =level of significance=1-c=1-0.99=0.01

and we know that confidence interval is always two-tailed

t-critical = 2.698 ( using EXCEL =TINV(probability =0.01, D.F=42)

Now,

E = t(critical) * Vin)

=$2.698 * \frac{12}{\sqrt 43}$

=4.937

We get the 99% confidence interval for the population mean $1585950167393_blob.png$

Τ – Ε <μ<1+E

$128 - 4.937< \mu < 128 + 4.937$

$123.06 < \mu < 132.94$

The 99% confidence interval for the mean daily income is ($ 123.06, $ 132.94)

Interpretation:

There are 99% confidence that the mean daily income will always fall in the interval

i.e. here option B is correct.