 Solution

The normal distribution standardized statistic for the binomial distribution count isBecause the alternative is two-sided, the approximate p-value is $2\{1-\Phi (3)\}\approx 0.0027$. A continuity correction replaces $3$ by $(149.5)/50=2.99$ and gives approximately $0.0028$, with the same conclusion. Thus the result is statistically significant at both the 5% and 1% levels. The p-value is a null tail probability, not a posterior probability that the null hypothesis is true.