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	24	29
Business Class	121	98
Economy Class	131	517

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

H ₀: - Select your answer -Type of ticket purchased is independent of the type of flightType of ticket purchased is not independent of the type of flightItem 1

H _a: - Select your answer -Type of ticket purchased is independent of the type of flightType of ticket purchased is not independent of the type of flightItem 2

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


The p-value is Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 4 .

What is your conclusion?

Answer 1

Chi-squared test

	Type of Flight
Type of Ticket	Domestic	International	Total
First Class	24	29	53
Business Class	121	98	219
Economy Class	131	517	648
Total	276	644	920

H0: Type of ticket and type of flight are independent

H1: Type of ticket and type of flight are associated

	Expected Number (E) (assuming that H0 is true)	Observed Number (O)	(O-E)2/E
First Class & Domestic	(53×276)/920 = 15.9	24	4.13
Business Class & Domestic	(219×276)/920 = 65.7	121	46.55
Economy Class & Domestic	(648×276)/920 = 194	131	20.68
First Class & International	(53×644)/920 = 37.1	29	1.77
Business Class & International	(219×644)/920 = 153.3	98	19.95
Economy Class & International	(648×644)/920 = 453.6	517	8.86
Total	920	920	101.93

Chi-square statistics (calculated) = 101.93

Degree of freedom (df)= (number of rows-1) (number of columns-1) = (3-1) (2-1) = 2

We shall accept the H0 if Chi-square (calculated) is smaller than Chi-square table value at given significance level and df=2 and reject H0 (or accept H1) if Chi-square (calculated) is greater than Chi-square table value at given significance level and df=2.

Chi-squared table value at df=2 and .05 significance level= 7.38

Thus, we shall reject H0 (i.e. accept H1) and conclude that the type of ticket and type of flight are associated.

Since the Chi-square statistics (calculated) is greater than 10.597, the results are significant at .005 level of significance.