Question

A popular blog reports that 42% of college students use Twitter. The director of media relations at a large university thinks that the proportion may be different at her university. She polls a simple random sample of 200 students, and 101 of them report that they use Twitter. Can she conclude that the proportion of students at her university who use Twitter differs from 0.42? Answer by showing the five steps of signigicance test, allowing a Type I error rate of 0.05.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.42
Alternative Hypothesis, Ha: p ≠ 0.42

Rejection Region
This is two tailed test, for α = 0.05
Critical value of z are -1.96 and 1.96.
Hence reject H0 if z < -1.96 or z > 1.96

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.505 - 0.42)/sqrt(0.42*(1-0.42)/200)
z = 2.44

P-value Approach
P-value = 0.0147
As P-value < 0.05, reject the null hypothesis.

Yes, the proportion has is different