Question

You may need to use the appropriate technology to answer this 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	93	119
Economy class	520	137

(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.)

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

p-value =

Answer 1

The null and alternative hypothesis is

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.

Level of significance = 0.05

Test statistic is

O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total

Type of Ticket	Type of Flight
	Domestic	International	Total
First class	29	22	51
Business class	93	119	212
Economy class	520	137	657
Total	642	278	920

O	E	(O-E)	(O-E)^2	(O-E)^2/E
29	35.58913	-6.58913	43.41664	1.219941
22	15.41087	6.58913	43.41664	2.817274
93	147.9391	-54.9391	3018.308	20.40236
119	64.06087	54.93913	3018.308	47.11625
520	458.4717	61.52826	3785.727	8.257274
137	198.5283	-61.5283	3785.727	19.06896
			Total	98.882

Degrees of freedom = ( Number of rows - 1 ) * ( Number of column - 1) = ( 3 - 1) * (2 - 1) = 2 * 1 = 2

P-value = P( ) = 0.0000

P-value < 0.05 we reject null hypothesis.

Conclusion:

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