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 Ticket	Domestic Flight	International Flight
First class	29	22
Business class	95	121
Economy class	518	135

A) The study wants to test whether the type of ticket is independent of the type of flight. Clearly state the null and alternative hypotheses. (2 points)

B) Compute the expected frequencies by completing the table below. (3 points)

Type of Ticket	Domestic Flight	International Flight	Total
First Class
Business Class
Economy Class
Total

C) Compute the test statistic.

Please copy your R code and the result and paste them here.

D) At 5% significance level, compute the critical value for the test statistic and the p value for the test. Draw your conclusion. (5 points)

Please copy your R code and the result and paste them here.

E) Use the function chisq.test() in R to run the test directly to confirm your results above are correct. (4 points)

Please copy your R code and the result and paste them here.

Answer 1

A) The study wants to test whether the type of ticket is independent of the type of flight. Clearly state the null and alternative hypotheses. (2 points)

Ho: type of ticket is independent of the type of flight

H1: type of ticket is not independent of the type of flight

B) Compute the expected frequencies by completing the table below. (3 points)

Type of Ticket	Domestic Flight	International Flight	Total
First Class	35.5891	15.4109	51
Business Class	150.7304	65.2696	216
Economy Class	455.6804	197.3196	653
Total	642	278	920

C) Compute the test statistic.

Please copy your R code and the result and paste them here.

R code:

observed = c(29,22,95,121,518,135)    # observed frequencies

expected = c(35.5891, 15.4109, 150.7304, 65.2696, 455.6804, 197.3196)# expected frequencies

chi2 = sum((observed- expected)^2/ expected)

chi2

R output:

[1] 100.4334

D) At 5% significance level, compute the critical value for the test statistic and the p value for the test. Draw your conclusion. (5 points)

Please copy your R code and the result and paste them here.

R code:

qchisq(.95, df=2)        # 7 degrees of freedom

pchisq(chi2, df=2,lower.tail=FALSE)

R output:

> qchisq(.95, df=2)        # 7 degrees of freedom

[1] 5.991465

> pchisq(chi2, df=2,lower.tail=FALSE)

[1] 1.552954e-22

E) Use the function chisq.test() in R to run the test directly to confirm your results above are correct. (4 points)

Please copy your R code and the result and paste them here.

Rcode:

M <- as.table(rbind(c(29,22), c(95,121),c(518,135)))

chi2<- chisq.test(M)

chi2

R output:

        Pearson's Chi-squared test

data: M

X-squared = 100.43, df = 2, p-value < 2.2e-16

conclusion: calculated chi square 100.43 > 5.991, the critical value at 0.05 level of significance. Ho is rejected. we conclude that the type of ticket is not independent of the type of flight.