The six graphs are for two different sample sizes: one small
(25) and one large (225). Your challenge in this exercise is to figure out how
to tell the difference between a small-sample curve and a large-sample curve.
ExerciseÂ 1.4.33 illustrates that the form of the alternative hypothesis
determines the shape of the curve.
Â a. Consider two sample sizes with the same distance: If
Buzz is right 30 times out of 32, the p-value will be _________ than if Buzz is
right 15 times out of 16. (Choose from: higher, lower, canâ€™t tellâ€”it depends on
Â b. More generally, for any given value of the distance pË†
âˆ’ Ï€ (x-axis), the p-value is smaller when the sample size n is
_______ (larger, smaller, canâ€™t tellâ€”it depends on the alternative).
Â c. This means that compared to the graph for n = 225, the
graph for n = 25 ____________ (always lies above, always lies below, neither:
it depends on the alternative hypothesis.).
Â d. â€œAbove/belowâ€ is not a useful comparison. Instead, use
the steepness of the curve. Compared to the graph for n = 225, the graph for n
= 25 is ________ (steeper, less steep).