Question

A random sample of 250 smartphone users is selected. They are asked to state their gender as well as the operating system of the smartphone they possessed at the moment. The resulting frequencies are shown below

	iOS	Android	Total
Male	74	44	118
Female	89	43	132
Total	163	87	250

At 1% level of significance, use a Chi-square test to determine whether there is any evidence to reveal that gender and the choice of the smartphone’s operating system are independent.

Answer 1

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=0.01 , 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>6.635}.

Test Statistics

The Chi-Squared statistic is computed as follows:

The decision about the null hypothesis

Since it is observed that χ2=0.61≤χc2​=6.635, 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 0.01 significance level.

The corresponding p-value for the test is

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