Suppose in Example 3.2 we were to reject H0 if all the jelly beans in a sample of size four were red. (a) What is α? (b) What is β? Example 3.2 There are two identically appearing bowls of jelly...

Suppose in Example 3.2 we were to reject H0 if all the jelly beans in a sample of size four were red.

(a) What is α?

(b) What is β?

Example 3.2

There are two identically appearing bowls of jelly beans. Bowl 1 contains 60 red and 40 black jelly beans, and bowl 2 contains 40 red and 60 black jelly beans. Therefore the proportion of red jelly beans, p, for the two bowls are

Bowl 1: p = 0:6;

Bowl 2: p = 0:4:

One of the bowls is sitting on the table, but you do not know which one it is (you cannot see inside it). You suspect that it is bowl 2, but you are not sure. To test your hypothesis that bowl 2 is on the table you sample five jelly beans.¹
The data from this sample, specifically the number of red jelly beans, is the sample statistic that will be used to test the hypothesis that bowl 2 is on the table. That is, based on this sample, you will decide whether bowl 2 is the one on the table.