Another type of confidence interval is called a one-sided confidence interval. A one-sided confidence interval provides either a lower confidence bound or an upper confidence bound for the parameter in question. You are asked to examine one-sided confidence intervals in Exercises M&Ms. In the article “Sweetening 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 weights, in grams (g). 55.02 50.76 52.08 57.03 52.13 53.51 51.31 51.46 46.35 55.29 45.52 54.10 55.29 50.34 47.18 53.79 50.68 51.52 50.45 51.75 53.61 51.97 51.91 54.32 48.04 53.34 53.50 55.98 49.06 53.92 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 peanutM&Msshould weigh 49.3 g. Comment on this specication in view of your answer to part (b).

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.