Two teachers enter their students for a national examination which has a pass rate of 80% nationwide. Teacher A enters 100 students and 75 of them pass. Teacher B enters 1000 students and 750 of them pass. Both teachers do a hypothesis test against H0 : p = 0.8. Teacher A gets a P-value of 0.26, and Teacher B gets a P-value of 0.0001.

Say whether each of the following statements is true or false.

a. If the sample size is large (e.g. 1000), a small P-value is almost inevitable so it doesn’t mean strong evidence against H0.

b. The large class of 1000 students gives enough evidence to detect that p , 0.8, but the small class of 100 students does not contain evidence to detect p , 0.8.

c. The correct conclusion from the test is that the teachers should change their teaching style in the future if they are teaching a large class, but there’s no need if they are teaching a small class.

d. If p = 0.8 we would expect close to 80 students to pass in Teacher A’s class, and close to 800 students to pass in Teacher B’s class. The P-values show that the deficit of 5 passes could have happened by chance in Teacher A’s class, but it’s barely believable that the deficit of 50 passes in Teacher B’s class could have happened by chance, if p really was 0.8.