Question: An airline wishes to assess the amount of money spent on duty free purchases on an international flight by different types of passengers. The airline hires a consultant to conduct an analysis, and the consultant decides to categorize the passengers according to the fare type paid. 6 passengers in each fare category who made duty free purchases were selected at random. The total amounts of their purchases were as follows:

T1 = 457.61 T2 = 363.03 T3 = 357.16

\(\sum{x_{1}^{2}}=35464\) \(\sum{x_{2}^{2}}=22328\) \(\sum{x_{3}^{2}}=21581\)

a) Construct the analysis of variance table for this data.

b) Is there enough evidence to suggest a difference in the mean expenditures on duty-free purchases based on the fare category of the passengers? Test your hypotheses with α = 0.05.

c) Use Tukey’s method of paired comparisons (α = 0.05) to identify the significant pairwise differences between categories.