Question

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 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 calculated value for the test statistic equals

Answer 1

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, $\hat p$ = 90/300 × 100 = 30%

The test statistic for the difference in two proportions is given as follows;

$z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p \cdot q}{n}}}$

Where;

$\hat p$ = The sample proportion

p = The population proportion

q = 1 - p

n = The sample size

The test statistic for Business College is;

$z=\dfrac{0.3-0.35}{\sqrt{\dfrac{0.35 \times 0.65}{90}}} \approx -0.9944$

The test statistic for Liberal Arts College is;

$z=\dfrac{0.4-0.35}{\sqrt{\dfrac{0.35 \times 0.65}{120}}} \approx 1.1483$

The test statistic for Education College is;

$z=\dfrac{0.3-0.3}{\sqrt{\dfrac{0.3 \times 0.70}{120}}} \approx 0$