Question

A hotel wants to know if there's a relationship between gender and the way customers make room reservations. A manager takes a random sample of 160 reservations. She records whether they were made by a man or a woman, and also records how the reservation was made. She gets the following data: Phone 28 Men Women Fax 9 12 Email 37 29 45 Perform a chi-square significance test of association with a = .05. Be sure to include your null and alternative hypotheses, a justification for the use of this test, your test statistic calculations, your P-value, and your conclusion.

Answer 1

Explanation:

Here,

H_o: The way of reservation is independent of gender.

H_a: The way of reservation is not independent of gender.

We use a chi square test because we can calculate the expected frequencies for this chart.

Doing an Expected Value Chart,

33.7625 9.7125 30.525

39.2375 11.2875 35.475

Using chi^2 = Sum[(O - E)^2/E],

chi^2 = 4.482385929

With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,

a = 3

b = 2

df = 2

Thus, the critical value is

significance level = 0.05

chi^2(critical) = 5.991464547

Also, the p value is

P = 0.106331579

Thus, comparing chi^2 and chi^2(critical) [or, p and significance level], we FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, there is no significant evidence that the way of reservation is dependent of gender. [CONCLUSION]