Respuesta :
Answer:
The test statistic for Business College is -0.9944
The test statistic for Liberal Arts College is 1.1483
The test statistic for Education College is 0
Step-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 students
In the sample, the number of students in;
Business College = 90
Liberal Arts College = 120
Education College = 90
Therefore;
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 proportion
p = The population proportion
q = 1 - p
n = 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]
