A farmer wants to test three brands of weight-gain diets for chickens to determine if the mean weight gain for each of these brands is the same. He selected 15 chickens and randomly put each of them on one of these three brands of diet. The following table lists the weights (in pounds) gained by these chickens after a period of 1 month. Brand A Brand B Brand C .8 .6 1.2 1.3 1.3 .8 1.7 .6 .7 .9 .4 1.5 .6 .7 .9 a. At a 1% significance level, can you reject the null hypothesis that the mean weight gain for all chickens is the same for each of these three diets? b. If you did not reject the null hypothesis in part a, explain the Type II error that you may have made in this case. Note that you cannot calculate the probability of committing a Type II error without additional information.