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 15 customers and find that the average dollar amount spent per transaction per customer is $119.375 with a standard deviation of $12.1991. Create a 95% confidence interval for the true average spent for all customers per transaction.

Question 1 options:

1)	( 116.225 , 122.525 )

2)	( 112.663 , 126.087 )

3)	( 112.619 , 126.131 )

4)	( -112.619 , 126.131 )

5)	( 117.23 , 121.52 )

Question 2 (1 point)

Suppose you want to determine the average height of basketball players in the NCAA Division I. In a random sample of 26 players, the sample average is 70.71 inches with a standard deviation of 6.669 inches. A 99% confidence interval for the average height is (67.06, 74.36). Which of the following is an appropriate interpretation of this interval?

Question 2 options:

1)	We are certain that 99% of the average heights of all basketball players will be between 67.06 and 74.36 inches.

2)	We are 99% confident that the average height of all NCAA D-I basketball players is between 67.06 and 74.36 inches.

3)	We are 99% confident that the proportion of all NCAA D-I basketball players heights is between 67.06 and 74.36 inches.

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

5)	We are 99% confident that the average height of all NCAA D-I basketball players surveyed is between 67.06 and 74.36 inches.

Question 3 (1 point)

Independent random samples are taken at a university to compare the average GPA of seniors to the average GPA of sophomores. Given a 99% confidence interval for the difference between the true average GPAs (seniors - sophomores) of (-0.58, 0.6), what can you conclude?

Question 3 options:

1)	We do not have enough information to make a conclusion.

2)	We are 99% confident that the average GPA of seniors is less than the average GPA of sophomores.

3)	We are 99% confident that the average GPA of seniors is greater than the average GPA of sophomores.

4)	We are 99% confident that the difference between the two sample GPAs falls within the interval.

5)	There is no significant difference between the true average GPA for seniors and sophomores.

Answer 1

1)

sample mean 'x̄=	119.375
sample size   n=	15.00
sample std deviation s=	12.20
std error 'sx=s/√n=	3.1498

for 95% CI; and 14 df, value of t=		2.145
margin of error E=t*std error    =		6.756
lower bound=sample mean-E =		112.619
Upper bound=sample mean+E =		126.131
from above 95% confidence interval for population mean =(112.62,126.13)

correct option is": ( 112.619 , 126.131 )

2)

We are 99% confident that the average height of all NCAA D-I basketball players is between 67.06 and 74.36 inches.

3)since 0 is in the interval:

There is no significant difference between the true average GPA for seniors and sophomores