A distributor of soft drink vending machines knows from experience that the mean number of drinks a machine will sell per day varies according to the location of the machine. At a local mall, two machines are placed in what the distributor believes to be two optimal locations (Location A and B). The number of drinks sold per day for each machine is recorded for a random sample of 20 days. For each day, the number of drinks purchased at Location A is compared to the number of drinks purchased at Location B (D = Number of Location A drinks - Number of Location B drinks).

1. Explain WHY the samples of the drinks for Locations A and B for the 20 days are dependent.
2. Using the summary statistics on page 2, test (BY HAND) the hypothesis that the mean number of drinks sold at Location A is greater than the mean number of drinks sold at Location B on all possible days. Use = 0.05 and remember to list all parts of the hypothesis test.
3. Using the summary statistics on page 2, construct and interpret (BY HAND) a 95% confidence interval for the mean of the differences in the number of drinks sold at locations A and B (D = Location A - Location B) on all possible days.
4. Using the information in the problem and information on page 2 (if needed) to determine whether the test and confidence interval in parts B and C are valid. Remember to discuss validity in the context of the problem.

Drink location summary statistics

D=Location A - Location B

n=20

mean=2.25

variance= 17.144737

std. dev=4.1406203

std.err=0.92587086