Question

A random sample of 43 chemistry students in a science program are selected for a study. Of those selected, only 27 passed the exam. At the 5% significance level, is there sufficient evidence that the majority of all chemistry students in this science program passed the exam? Show all steps for your hypothesis test. If you prefer, write your answers out and send in an email instead of using the essay box.
(Hint: a majority means more than 50%)

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.5
Alternative Hypothesis, Ha: p > 0.5

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.64.
Hence reject H0 if z > 1.64

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.6279 - 0.5)/sqrt(0.5*(1-0.5)/43)
z = 1.68

P-value Approach
P-value = 0.0465
As P-value < 0.05, reject the null hypothesis.

There is sufficient evidence to conclude that the majority of all chemistry students in this science program passed