Question

A Bloomberg BusinessWeek 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 Flight
Type of Ticket	Domestic	International
First Class	26	23
Business Class	99	123
Economy Class	518	132

a. Using a .05 level of significance, is the type of ticket purchased independent of the type of flight? Use Table 12.4.

Compute the value of the  2 test statistic (to 2 decimals). ????

Answer 1

Solution:

   We are given that: A Bloomberg BusinessWeek 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.

   We have to test if the type of ticket purchased independent of the type of flight or not.

Level of significance = 0.05

We use the following steps:

Step 1) State H0 and H1:

H0: the type of ticket purchased is independent of the type of flight

Vs

H1: the type of ticket purchased does not independent of the type of flight.

Step 2) Find test statistic:

where O_ij = Observed frequency for i^th row and j^th column.

E_ij = Expected frequency for i^th row and j^th column.

	Type of Flight
Type of Ticket	Domestic	International	Row Totals
First Class	26	23	R1=49
Business Class	99	123	R2=222
Economy Class	518	132	R3=650
Column totals	C1=643	C2=278	N=921

Thus

we get:

Oij	Eij	Oij^2 / Eij
26	34.2096	19.76
23	14.7904	35.77
99	154.9902	63.24
123	67.0098	225.77
518	453.8002	591.28
132	196.1998	88.81
N=921

Thus Chi square test statistic is:

Step 3) Find Chi-square critical value:

df = (R-1) x ( C- 1)

df = ( 3-1) x ( 2-1)

df = 2 x 1

df = 2

Look in Chi-square critical value table for df = 2 and level of significance = 0.05

Chi-square critical value = 5.991

Step 4) Decision rule:

Reject H0, if Chi-square test statistic value > Chi-square critical value, otherwise we fail to reject H0.

Since Chi-square test statistic value = > Chi-square critical value =5.991,

we reject H0.

Step 5) conclusion: the type of ticket purchased does not independent of the type of flight.

that is: the type of ticket purchased is dependent on the type of flight.