Question

Question 5

Judging independence of two categorical datas.

Use the information below to perform a statistical test on whether a customer would recommend the bank is dependent on the gender of the customer. (Hint: use the chi square test for association)

1. There are 152 customers. Of which 77/152 are female and 75/152 are male

2. Of the female customers, 52/77 recommended the bank whilst 25/77 did not recommend the bank.

3. Of the male customers. 45/75 recommended the bank whilst 30/75 did not recommend the bank.

Is the result of the bank recommendation dependent on gender?

Answer 1

We will assume the level of significance be to 5%.

The following cross-tabulation has been provided. The row and column total have been calculated and they are shown below:

	Recommend Bank	Do not Recommend Bank	Total
Male	45	30	75
Female	52	25	77
Total	97	55	152

Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

H0​: The two variables are independent

Ha​: The two variables are dependent

This corresponds to a Chi-Square test of independence.

Rejection Region

Based on the information provided, the significance level is α=0.05 , the number of degrees of freedom is df=(2−1)×(2−1)=1, so then the rejection region for this test is R={χ2:χ2>3.841}.

Test Statistics

The Chi-Squared statistic is computed as follows:

The decision about the null hypothesis

Since it is observed that χ2=0.934≤χc2​=3.841, it is then concluded that the null hypothesis is not rejected.

Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is NOT enough evidence to claim that the two variables are dependent, at the 0.05 significance level. We even reject it at 1%, 10% level of significance. Hence bank recommendation is independent of gender.

The corresponding p-value for the test is

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