Question

Write a one to two (1–2) page short paper in which you perform a Chi-square test on data, present your findings and conclusion. Upload the paper in the coursework area. Hot Dogs Hamburgers Men 207 282 Women 231 38.

Answer 1

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

	Hot Dogs	Hamburgers	Total
Men	207	282	489
Women	231	38	269
Total	438	320	758

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.

At 5% level of significance

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}.

Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the two variables are dependent, at the 0.05 significance level.

The corresponding p-value for the test is p=Pr(χ12​>134.874)=0

We reject H0 at every level of significance. Hence we can conclude that the variables (gender and type of food preference) are dependent.

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