In the article Sweetening StatisticsWhat M&Ms Can Teach Us (Minitab Inc., August 2008), M. Paret and E. Martz discussed several statistical analyses that they performed

In the article €œSweetening Statistics€”What M&M€™s Can Teach Us€ (Minitab Inc., August 2008), M. Paret and E. Martz discussed several statistical analyses that they performed on bags of M&Ms. The authors took a random sample of 30 small bags of peanut M&Ms and obtained the following weight, in grams (g).

a. Determine a 95% lower confidence bound for the mean weight of all small bags of peanut M&Ms. (Note: The sample mean and sample standard deviation of the data are 52.040 g and 2.807 g, respectively.)
b. Interpret your result in part (a).
c. According to the package, each small bag of peanut M&Ms should weigh 49.3 g. Comment on this specification in view of your answer to part (b).

55.02 50.76 52.08 57.03 52.13 53.51 51.31 5146 46.35 55.29 4552 54.10 55.29 50.34 47.18 53.79 50.68 51.52 50.45 51.75 53.61 5197 51.91 54.32 48.04 53.34 53.50 5598 49.06 53.92