The marketing consultant for a travel agency wants to determine whether travel concerns are related to travel purpose. The contingency table shows the results of a random sample of 300 travelers classified by their primary travel concern and travel purpose. At a = 0.01, can the consultant conclude that the variables travel concern and travel purpose are related? (The expected frequencies are displayed in parentheses.
Travel
Hotel
Leg room
Rental
purpose
room
on plane
car size
Other
Total
Business
36 (44.4)
108 (97.2)
14 (16.8)
22 (21.6)
180
Leisure
38 (29.6)
54 (64.8)
14 (11.2)
14 (14.4)
120
74
162
28
36
300
a. Identify the claim and state H0 and Ha.
b. Identify the level of significance a.
c. Determine the degrees of freedom.
d. Find the critical value x2
0 and identify the rejection region.
e. Use the observed and expected frequencies to find the chi-square test
statistic. Sketch a graph.
f. Decide whether to reject the null hypothesis.
g. Interpret the decision in the context of the original claim.
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