Hi there, Can I know the continuity correction's "rules" in Chapter 8 are the same as in Chapter 12? In Example 12.3, why is it 45.5? thanks Ps: Let me know if the image URL isnt working BR Z
In Chapter 12 we use a shortcut rule of adjust it towards the mean to save you having the consider the p-value. So if we were calculating the p-value with our value of 45 we go towards the nearest critical region (which is the -1.96 one as our value is smaller than the mean) and so the p-value will be \(P(X \leq 45)\) using your chapter 8 knowledge this is equivalent to \(P(X \leq 45.5)\). Similarly if we have a value of, say 55, the p-value will go towards the nearest critical region (which is 1.96 as our value is bigger than the mean) and so the p-value will be \(P(X \geq 45)\) using your chapter 8 knowledge this is equivalent to \(P(X \geq 44.5)\). So you see - the towards the mean is a handy shortcut when calculating continuity corrections for hypothesis tests.
Nope, because it can take the values ...44, 45, 46, .... so we use either 44.5 or 45.5. If it could only take the values ....40, 50, 60, ... then we would use 45 and 55.
