Question

Following a wave of politics, a poll of 191 individuals found that 115 would vote for a certain nominee during the town council election. The nominee is believed to have a center support of 52%, and his movement would like to know if this support has increased. α = 0.05.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.52
Alternative Hypothesis, Ha: p > 0.52

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 = (0.6021 - 0.52)/sqrt(0.52*(1-0.52)/191)
z = 2.27

P-value Approach
P-value = 0.0116
As P-value < 0.05, reject the null hypothesis.

Yes the support has increased.