In the article Sweetening StatisticsWhat M&Ms Can Teach Us (Minitab Inc., August 2008), M. Paret and E.

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).

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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