Question

A magazine subscriber study asked, "In the past 12 months, when traveling for business, what type of airline ticket did you purchase most often?" A second question asked if the type of airline ticket purchased most often was for domestic or international travel. Sample data obtained are shown in the following table.

Type of Ticket	Type of Flight
	Domestic	International
First class	29	22
Business class	96	122
Economy class	517	134

(a)

Using a 0.05 level of significance, is the type of ticket purchased independent of the type of flight?

State the null and alternative hypotheses.

H₀: The type of ticket purchased is independent of the type of flight.
H_a: The type of ticket purchased is not independent of the type of flight. H₀: The type of ticket purchased is mutually exclusive from the type of flight.
H_a: The type of ticket purchased is not mutually exclusive from the type of flight.     H₀: The type of ticket purchased is not mutually exclusive from the type of flight.
H_a: The type of ticket purchased is mutually exclusive from the type of flight. H₀: The type of ticket purchased is not independent of the type of flight.
H_a: The type of ticket purchased is independent of the type of flight.

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

State your conclusion.

Do not reject H₀. We cannot conclude that the type of ticket purchased and the type of flight are independent. Reject H₀. We conclude that the the type of ticket purchased is not independent of the type of flight.     Do not reject H₀. We cannot conclude that the type of ticket purchased and the type of flight are not independent. Reject H₀. We conclude that the type of ticket purchased is independent of the type of flight.

(b)

Discuss any dependence that exists between the type of ticket and type of flight.

The type of ticket purchased is independent of the type of flight. A higher percentage of first class and business class tickets are purchased for international flights compared to domestic flights. Economy class tickets are purchased more for domestic flights.     A lower percentage of economy class tickets are purchased for domestic flights compared to international flights. First class and business class tickets are purchased more for domestic flights. A higher percentage of first class and business class tickets are purchased for domestic flights compared to international flights. Economy class tickets are purchased more for international flights.

Answer 1

The statistical software output for this problem is:

Contingency table results: Rows: vari Columns: None Domestic International Total First class 22 51 Business class 122 218 Economy class 134 651 Total 642 278 920 29 96 Chi-Square test: Statistic DF Value P-value Chi-square 2 101.21772 <0.0001

Hence,

a) Hypotheses: Option A is correct.

Test statistic = 101.218

p - Value = 0.0000

Conclusion: Option B is correct.

b) A higher percentage of first class and business class tickets are purchased for international flights compared to domestic flights.