Question

20. In a survey of 735 students at Broward College, North Campus, results revealed that 283 students were foreign-born and 452 were native-born. Using these results, conduct a hypothesis test to test the claim, at the .03 significance level, that the proportion of students who are born outside of the USA is greater than 35 percent. Be sure to show all the steps in the hypothesis testing procedure including the null and alternative hypotheses, the calculation of the test statistic, and correct wording of the final conclusion.

21. In a survey of 735 students at Broward College, North Campus, the mean GPA was found to be 3.02 with a standard deviation of .42. Using these results, test the claim at the .05 significance level that the mean GPA of students at North Campus is equal to 3.00. Be sure to show all the steps in the hypothesis testing procedure including the null and alternative hypotheses, the calculation of the test statistic, and correct wording of the final conclusion.

Answer 1

Solution:

Question 20

Here, we have to use z test for population proportion.

H₀: p = 0.35 versus H_a: p > 0.35

This is an upper tailed or right tailed test.

We are given level of significance = α = 0.03

x = 283, n = 735

Sample proportion = P = x/n = 283/735 = 0.385034014

Test statistic = Z = (P – p)/sqrt(pq/n)

Where, P is sample proportion, p is population proportion, q = 1 – p, n is sample size.

q = 1 – 0.35 = 0.65

Z = (0.385034014 – 0.35) / sqrt(0.35*0.65/735)

Z = 1.9913

P-value = 0.0232

(by using z-table)

P-value < α = 0.03

So, we reject the null hypothesis

There is sufficient evidence to conclude that the proportion of students who are born outside of the USA is greater than 35 percent.

Question 21

One sample t test

H₀: µ = 3.00 versus H_a: µ ≠ 3.00

Two tailed test

Given: Xbar = 3.02,

S = .42,

n = 735,

df = n – 1 = 734,

α = 0.05

Test statistic = t = (Xbar - µ)/[S/sqrt(n)]

t = (3.02 – 3.00)/[0.42/sqrt(735)]

t = 0.02/ 0.0155

t = 1.2910

P-value = 0.1971

(by using t-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that the mean GPA of students at North Campus is equal to 3.00.