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 45 ​weekdays, daily fees collected averaged ​$128​, with standard deviation of ​$12. Complete parts a through e below. ​a) What assumptions must you make in order to use these statistics for​ inference? Select all that apply. A. The data values should be dependent. B. The data are a random sample of all days. C. The sample size is at least​ 10% of the population. D. The distribution is unimodal and symmetric with no outliers. ​b) Find a 90​% confidence interval for the mean daily income this parking garage will generate. The 90​% confidence interval for the mean daily income is ​($ nothing​,$ nothing​). ​(Round to two decimal places as​ needed.) ​c) Explain in context what this confidence interval means. Choose the correct answer below. A. There is 90​% confidence that the interval contains the mean daily income. B. There is 90​% confidence that the mean daily income will always fall in the interval. C. There is 90​% confidence that the daily income for all weekdays falls in the interval. D. There is 90​% confidence that the daily income for a weekday falls in the interval. ​d) Explain what 90​% confidence means in this context. Choose the correct answer below. A. 90​% of all samples of size 45 have a mean daily income that is in the interval. B. 90​% of all weekdays sampled have daily incomes that fall in the interval. C. 90​% of all weekdays have daily incomes that fall in the interval. D. 90​% of all samples of size 45 produce intervals that contain the mean daily income. ​e) The consultant who advised the city on this project predicted that parking revenues would average ​$129 per day. Based on your confidence​ interval, what do you think of the​ consultant's prediction?​ Why? Since the 90​% confidence interval ▼ does not contain contains the predicted​ average, the​ consultant's prediction is ▼ plausible. not plausible.

Answer 1

In order to use these statistics for inference,

B) The data are a random sample of all days

C.) The sample size is at least 10% of the population

b) 90% confidence interval for the mean is: (since population s.d is unknown we will use t score)

128 +- t0.05,44*12/√45

= 128 +-1.6805*12/√45

= (124.994, 131.006)

c)Interpretation: There is a 90% confidence that the mean daily income will always fall in the interval.

d) 90% of all samples of size 45 have a mean daily income that is in the interval.

Since the c.i contains the predicted value, the consultants prediction is plausible.