Cooling pipes at three nuclear power plants are investigated for deposits that would inhibit the flow of water. From 30 randomly selected spots at each plant, 13 from the first plant, 8 from the second plant, and 19 from the third were clogged.

(a) Use the 0.05 level to test the null hypothesis of equality.

(b) Plot the confidence intervals for the three probabilities of being clogged.