Question

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 α = 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.deviation=4.1406203

std.error=0.92587086

Answer 1

1.

Because the observations are paired as per the optimal location of the two machines and day too.

2.

df = n-1

= 19

p-value = 0.0126 < 0.05 i.e. we can reject the null hypothesis and hence we can conclude that mean number of drinks sold at Location A is greater than the mean number of drinks sold at Location B on all possible days

3.

4.

We need to assume that the populations of the two samples are normally distributed for part 2 and 3 to be valid.