申論題

Please provide your solutions in detail. 

1. A large candy manufacturer produces packs of candy targeted to weigh 52 grams. A quality control manager was concerned that the variation in the actual weights was larger than acceptable. hhat is, he was concerned that some packs weighed significantly less than 52 grams and some weighed significantly more than 52 grams. In order to estimate σ, the standard deviation of the weights of the nominal 52-gram packs, he took a random sample of n = 10 packs off of the factory line. hhe random sample yielded a sample variance of 4.2 grams.