Question 23

Question 8: The null and alternative hypothesis are: Ho : The selected field of study and state of residence are independent. Ha : The selected field of study and state of residence are dependent. Since both the variables are categorical, we will conduct a Chi-Square test of independence at a significance level of 0.05. Calculation of test statistic: Observed Frequencies (fo) Residence Field of Study Arizona Utah Total Law 60 20 80 Economics 80 40 120 Statistics 160 40 200 Total 300 100 400 Expected Frequencies (fe) Residence Field of Study Arizona Utah Total Law 60 20 80 Economics 90 30 120 Statistics 150 50 200 Total 300 100 400 (fo-fe) 2 /fe Residence Field of Study Arizona Utah Total Law 0.000 0.000 0.000 Economics 1.111 3.333 4.444 Statistics 0.667 2.000 2.667 Total 1.778 5.333 7.111 Chi-square statistic = 7.111 Degrees of freedom = (2 – 1) * (3 – 1) = 2 p-value = 0.0286 Since p-value is less than the significance value of 0.05, we reject the null hypothesis. Thus, there is sufficient evidence to conclude that the selected field of study and state of residence are related to each other.