Testing the null hypothesis that p = 0.50 for 10 up/down forecasts of the stock market provides insights into the nature of hypothesis testing.
Increasing the sample size to 10,000 improves our ability to distinguish between p = 0.50 and probabilities just a few percentage points higher.
The upper 5% tail of the standard normal distribution is above 1.645. The critical value for the sample proportion is 0.50 + 1.645 (0.005) = 0.5062.