In Chapter 10, signs test, how do we know when to accept or reject the null hypothesis? In the question on page 31-32, it is mentioned that since the p value is greater than 5% there is sufficient evidence to reject the null hypothesis at 5% significance level. Can anyone please tell me the logic behind it? Thanks, in advance.
This goes back to the CT3 (and CS1) principles. If there is no bias in the signs then you expect 50% of them to be positive. What the p-value tells you in this instance is how likely the number (or proportion) of positive observations that was observed would happen. So the larger the p-value, the more likely such an observation would happen given the null hypothesis of no biased signs. If p-value is 0.02, then there's only a 2% chance that said observation would happen if the signs were truly not biased, and hence you would reject at the 5% level (but not at the 1% level).
