The Department of Consumer Affairs is interested in difference, D, between the price that people are quoted online for a taxi trip, and the price that they are actually charged. They seek online quotes for cost of a taxi trip between twelve pairs of random locations, and then take these taxi rides and record the actual price changed. They subtract the quoted price from the charged price. The results (in $), and their accumulations appear below.

25.10

12.45

-2.60

5.60

13.80

-1.20

7.30

0.10

15.10

3.15

9.95

17.35

a) Determine the mean and standard deviation of price differences for this sample.

b) The Taxi Owners Association claims that the average difference between charged and quoted prices is no more than $5.00. Using = 5% and stating any assumptions required, test the Associations claim.

c) Explain the difference between statistical significance and practical significance, and state whether your mean difference between quoted and actual price is statistically significant. How would you interpret an outcome that was statistically significant but not practically significant?

d) Using the sample standard deviation from part (a) as an estimate for population standard deviation, determine the sample size required in order to be 90% confident of estimating mean price difference within $1.00 of its true value.