Question

Suppose a coin toss turns up 12 heads out of 20 trials. At .05 significance level, can one reject the null hypothesis that the coin toss is fair?

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 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 = (0.6 - 0.5)/sqrt(0.5*(1-0.5)/20)
z = 0.89

P-value Approach
P-value = 0.3735
As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the coin toss is not fair.