Question

Problem: In a recent poll, the CW estimated that about 25% of viewers watch Legends of Tomorrow weekly. February 25, 2016 is the crossover with the 2046 version of Arrow. The CW conducts a new random survey of 350 viewers and finds that 102 now plan to watch that episode. Does this provide strong evidence that having Arrow on Legends of Tomorrow increased viewership?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis: p = 0.25
Alternative Hypothesis: p > 0.25

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 = (0.2914 - 0.25)/sqrt(0.25*(1-0.25)/350)
z = 1.79

P-value Approach
P-value = 0.0367
As P-value < 0.05, reject the null hypothesis.