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	97	123
Economy class	516	133

(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 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 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 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 =

State your conclusion.

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.    

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.

(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 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.     

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.

Answer 1

Given table data is as below

MATRIX	col1	col2	TOTALS
row 1	29	22	51
row 2	97	123	220
row 3	516	133	649
TOTALS	642	278	N = 920

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calculation formula for E table matrix

E-TABLE	col1	col2
row 1	row1*col1/N	row1*col2/N
row 2	row2*col1/N	row2*col2/N
row 3	row3*col1/N	row3*col2/N

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expected frequecies calculated by applying E - table matrix formulae

E-TABLE	col1	col2
row 1	35.589	15.411
row 2	153.522	66.478
row 3	452.889	196.111

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calculate chisquare test statistic using given observed frequencies, calculated expected frequencies from above\

Oi	Ei	Oi-Ei	(Oi-Ei)^2	(Oi-Ei)^2/Ei
29	35.589	-6.589	43.415	1.22
22	15.411	6.589	43.415	2.817
97	153.522	-56.522	3194.736	20.81
123	66.478	56.522	3194.736	48.057
516	452.889	63.111	3982.998	8.795
133	196.111	-63.111	3982.998	20.31
				chisqr^2 o = 102.009

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set up null vs alternative as
null, ho: the type of ticket purchased is independent of the type of flight.
alternative, h1: the type of ticket purchased is not independent of the type of flight.
level of significance, alpha = 0.05
from standard normal table, chi square value at right tailed, chisqr^2 alpha/2 =5.991
since our test is right tailed,reject Ho when chisqr^2 o > 5.991
we use test statistic chisqr^2 o = Σ(Oi-Ei)^2/Ei
from the table , chisqr^2 o = 102.009
critical value
the value of |chisqr^2 alpha| at los 0.05 with d.f (r-1)(c-1)= ( 3 -1 ) * ( 2 - 1 ) = 2 * 1 = 2 is 5.991
we got | chisqr^2| =102.009 & | chisqr^2 alpha | =5.991
make decision
hence value of | chisqr^2 o | > | chisqr^2 alpha| and here we reject Ho
chisqr^2 p_value =0
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a.
H0: The type of ticket purchased is independent of the type of flight.
Ha: The type of ticket purchased is not independent of the type of flight.   
b.
test statistic: 102.009
c.
p-value:0
d.
decision: Reject H0. We conclude that the the type of ticket purchased
is not independent of the type of flight.                                  
e. a higher percentage of first class and business class tickets are purchased for international flights compared to domestic flights