CT3-12 p-value

[Howard O'Connor]

Hi all
Several questions on CT3-12:
1) In CT3-12 page 8, where does the second formula on the page come from (i.e. the formula starting P[Z < ...]) - how does it come from the formula of the previous line?
2) In Example 12.1 (page 10), how does one decide which hypothesis is H0 and which is H1?
3) Examples 12.2, 12.3, 12.5 and 12.6: what is meant by the italicised comment at the end of each of these examples, which states that one must double the probability found because the test is two-sided?
4) In Example 12.6 (page 22), where does the term "-0" in the numerator of the pivotal quantity come from?
5) In CT3-12 page 6, what is meant by 'Likelihood under H0' and similar for H1?
Many thanks
Howard

 

[John Lee]

1) Normal approx to binomial with continuity correction (from Chapter 8 but also covered again in Ch12 Section 3.3).
2) The null hypothesis must always be an equals (otherwise what would you substitute into the formula?)
3) For a two-sided test the p-value is double the one-sided probability
4) Yes - I can see the confusion - the CR already substitutes the zero into the formula whereas we use the formula given on the summary page (p40) and then substitute \(q_M = q_F\) into the formula, ie \(q_M - q_F = 0 \)
5. You calculate the likelihood substituting in the value assuming in \(H_0\).
I genuinely do recommend the CT3 online classroom on this topic as it goes through these points much more clearly than the Core Reading.