Question

Test at α =.05 the hypothesis that a majority (more than 50%) of students favor the plus/minus grading system at a university if in a random sample of 400 students, 216 favor the system?

Answer 1

Solution:
We need to test the hypothesis that a majority of students favor the plus/minus grading at a university
So Null hypothesis and alternate hypothesis can be written as
Null hypothesis H0: p = 0.5
Alternate hypothesis Ha: p>0.5
No. of random sample(n) = 400
No. of students favor the plus/minus grading = 216

So sample proportion Pcap = 216/400 = 0.54
Here we will use one proportion Z test to solve this hypothesis test,
First, we will calculate Z-score which can be calculated as
Z-score = (Pcap - p)/sqrt(p*(1-p)/n)
Z-score = (0.54-0.50)/sqrt(0.50*(1-0.50)/400) = 0.04/0.025 = 1.6
This is a right-tailed test and one-tailed test so P-value from Z-table is
P-value = 0.0578
At alpha = 0.05, we are failed to reject the null hypothesis as P-value is greater than the alpha value (0.0578>0.05). So we don't have significant evidence to support the claim that a majority of students favor the plus/minus grading system at a university.