Examine the data set about labeling discrepancies. The data sets can be found in the appendix of this workbook, and perhaps also in a spreadsheet that your instructor may have made available to you. Suppose the 32 food items listed form a simple random sample of all of the "low calorie" items in a particular grocery store on a particular day. To simplify the problem for teaching purposes, suppose somehow we know the population standard deviation of the labeling discrepancy on all "low calorie" food items in the store is known to be 14.7 cal/g. For the more "theoretical" questions, see the heading "Validity Condi- tions for Confidence Interval Estimates " 1. Find the margin of error for estimating the true population mean labeling discrepancy at the 95 percent confidence level with the given data. Your answers should always include the units of measure- ment along with the number. 2. Find the sample mean labeling discrepancy for the given data. Your answers should always include the units of measurement along with the member. 3. Estimate the true population mean labeling discrepancy us- ing a 95 percent confiderico interval. There is a probability that the population mean labeling discrepancy is between and calories per gram. 4. How large would a sample need to be to obtain the true population labeling discrepancy to within plus or mims 2 calories per gram at the 95 percent confidence level?