Question

An urn contains 10 marbles, of which M are white and 10 −M are black. To test that
M = 5 against the alternative hypothesis that M = 6, one draws 3 marbles from the
urn without replacement. The null hypothesis is rejected if the sample contains 2 or
3 white marbles; otherwise it is accepted. Find the size of the test and its power.

Answer 1

Size of the test = = P(2 or 3 white marbles | M = 5)

= P(2 white marbles | M = 5) + P(3 white marbles | M = 5)

{In the first case, 2 white marbles are to be selected out of 5 and in the second case, 3 white marbles are to be selected out of 5}

Now,

Power of the test = = P(2 or 3 white marbles | M = 6)

= P(2 white marbles | M = 6) + P(3 white marbles | M = 6)