Suppose that a box contains a large number of chips of three different colors, red, brown, and blue, and it is desired to test the null hypothesis H0 that chips of the three colors are present in equal proportions against the alternative hypothesis H1 that they are not present in equal proportions. Suppose that three chips are to be drawn at random from the box, and H0 is to be rejected if and only if at least two of the chips have the same color.
a. Determine the size of the test.
b. Determine the power of the test if 1/7 of the chips are red, 2/7 are brown, and 4/7 are blue.