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	26	19
Business class	98	124
Economy class	518	135

(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 not independent of the type of flight.
H_a: The type of ticket purchased is independent of 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 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.

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

I came up with 100.484 but this is incorrect

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 type of ticket purchased is 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 the type of ticket purchased is not independent of the type of flight.

(b)

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

The type of ticket purchased is independent of the type of flight.

Answer 1

a)

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.

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Domestic	International	Total
	first class	31.40	13.60	45
	Business	154.92	67.08	222
	Economy	455.68	197.32	653
	total	642	278	920
chi square    χ2	=(Oi-Ei)2/Ei	Domestic	International	Total
	first class	0.929	2.146	3.0755
	Business	20.912	48.293	69.2043
	Economy	8.523	19.682	28.2053
	total	30.3640	70.1212	100.4851
test statistic X2 =		100.485

p value =0.0000

Reject H₀. We conclude that 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.