A hotel wants to know if theres an relationship between gend

A hotel wants to know if theres an relationship between gender and the way customers make room reservations. A manager takes a random sample of 160 reservation. 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:

Perform a chi square significance test of association with a = 0.05. be sure to include your null and alternative hypotheses, justification for the use of this test, your test statistic calculations, your p-value , and your conclusion.

Solution

Here,

Ho: The way of reservation is independent of gender.
Ha: 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(crit) [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]