Question

You own a small storefront retail business and are interested in determining the average amount of money a typical customer spends per visit to your store. You take a random sample over the course of a month for 45 customers and find that the average dollar amount spent per transaction per customer is $90.422 with a standard deviation of $13.895. When creating a 90% confidence interval for the true average dollar amount spend per customer, what is the margin of error?

1)

2.695

2)

3.4787

3)

3.4803

4)

2.0713

5)

0.7203

Suppose you are a civil engineer, specializing in traffic volume control for the City of Grand Rapids. Your department has been receiving a multitude of complaints about traffic wait times for a certain intersection in the heart of downtown. To see if these claims are valid, you want to monitor the true average wait time at that intersection. Over the course of a few months, you record the average number of minutes a car waits at the intersection between 4:00 PM and 5:00 PM. With a sample size of 10 cars, the average wait time is 6.163 minutes with a standard deviation of 1.4246 minutes. Construct a 99% confidence interval for the true average wait time for a car at the intersection between 4:00 PM and 5:00 PM.

1)	( 4.699 , 7.627 )

2)	( 2.913 , 9.413 )

3)	( 4.735 , 7.591 )

4)	( 5.713 , 6.613 )

5)	( -4.699 , 7.627 )

Suppose you want to determine the average height of college basketball players in NCAA Division I. In a random sample of 8 players, the sample average is 74.188 inches with a standard deviation of 3.6499 inches. What is the 99% confidence interval for the average height of all NCAA D-I players?

1)	( 69.859 , 78.517 )

2)	( -69.672 , 78.704 )

3)	( 70.689 , 77.687 )

4)	( 72.898 , 75.478 )

5)	( 69.672 , 78.704 )

In a climate survey, it was determined that in a random sample of 16 days, the average temperature in Kalamazoo at 2:00 PM in the months of July and August is 79.66 degrees with a standard deviation of 3.068 degrees. Using this information, a 90% confidence interval for the average is (78.32, 81). Which of the following is the appropriate interpretation of this interval?

1)	We are 90% confident that the average daily temperature for the months of July and August at 2:00 PM for the days recorded is between 78.32 and 81.

2)	We cannot determine the proper interpretation of this interval.

3)	We are 90% confident that the proportion of all days' temperatures will fall between 78.32 and 81.

4)	We are 90% confident that the average daily temperature for the months of July and August at 2:00 PM is between 78.32 and 81.

5)	We are certain that 90% of the days in the months of August and July will have a temperature at 2:00 PM between 78.32 and 81.

Answer 1

1) Given data Descriptive Statistics

N	Mean	StDev
45	90.42	13.895

confidence level = 90%

critical value for 90% CI with 44 degrees of freedom = t_0.05,44 = 1.68023

Margin of error E = = 1.68023*13.895/sqrt(45) = 3.4803

2) Descriptive Statistics

N	Mean	StDev
10	6.163	1.4246

99% CI =

t_0.005,9 = 3.249823

99% CI = (6.163 - 3.4298*1.4246/sqrt(10) , 6.163 + 3.4298*1.4246/sqrt(10)) = (4.699 , 7.627)

3)

Descriptive Statistics

N	Mean	StDev	SE Mean	99% CI for μ
8	74.188	3.6499	1.29	(69.67, 78.70)

μ: mean of Sample

t_0.005,7 = 3.499425

99% CI = (74.188 - 3.4994*3.6499/sqrt(8) , 74.188 + 3.4994*3.6499/sqrt(8) ) = ( 69.672 , 78.704 )

4) We are 90% confident that the average daily temperature for the months of July and August at 2:00 PM is between 78.32 and 81.