Answer to Question #38779 in Statistics and Probability for yancey

Question

The weight of a carton of a dozen eggs produced by a certain breed of hens is supposed to be 780 grams. A quality manager randomly checks five cartons of eggs (n = 5) to see whether the mean weight differs from 780 grams. She finds \bar{x} = 797 grams and computes a 95% confidence interval estimate for the mean weight of all cartons to be (781.82 grams, 812.18 grams). On the basis of this interval, at \alpha = 0.05, what can she conclude about H_0: \mu = 780 versus H_a: \mu \neq 780?