In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students from the university was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College. The expected frequency for the Business College is

Answer:The test statistic for Business College is -0.9944The test statistic for Liberal Arts College is 1.1483The test statistic for Education College is 0Step-by-step explanation:The percentage of ABC University college students in Business College = 35%Liberal Arts College = 35%Education College = 30%The number of students in the sample = 300 studentsIn the sample, the number of students in;Business College = 90Liberal Arts College = 120Education College = 90Therefore;The percentage of Business College students = 90/300 × 100 = 30% The percentage of Liberal Arts College,  = 120/300 × 100 = 40%The percentage of Education College, [tex]\hat p[/tex] = 90/300 × 100 = 30%The test statistic for the difference in two proportions is given as follows;[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p \cdot q}{n}}}[/tex]Where;[tex]\hat p[/tex] = The sample proportionp = The population proportionq = 1 - pn = The sample size The test statistic for Business College is;[tex]z=\dfrac{0.3-0.35}{\sqrt{\dfrac{0.35 \times 0.65}{90}}} \approx -0.9944[/tex]The test statistic for Liberal Arts College is;[tex]z=\dfrac{0.4-0.35}{\sqrt{\dfrac{0.35 \times 0.65}{120}}} \approx 1.1483[/tex]The test statistic for Education College is; [tex]z=\dfrac{0.3-0.3}{\sqrt{\dfrac{0.3 \times 0.70}{120}}} \approx 0[/tex]