STAT QUA2220-The mean and the standard deviation of the sample
THE TRASH BAG EXAMPLE The mean and the standard deviation of the sample of 40 trash bag breaking strengths are x 5 22.990 and s 5 0.7428, respectively.a. What do the stem-and-leaf display and histogram in Figures 2.14 and 2.15 say about whether the empirical rule should be used to describe the trash bag breaking strengths? b. Use the empirical rule to calculate estimates of tolerance intervals containing 68.26 percent, 95.44 percent, and 99.73 percent of all possible trash bag breaking strengths. c. Does the estimate of a tolerance interval containing 99.73 percent of all breaking strengths provide evidence that almost any bag a customer might purchase will have a breaking strength that exceeds 20 kg? Explain your answer. d. How do the percentages of the 40 breaking strengths in Table 2.9 that actually fall into the intervals 3x 6 s4 , 3x 6 2s4, and 3x 6 3s4 compare to those given by the empirical rule? Do these comparisons indicate that the statistical inferences you made in parts (b) and (c) are reasonably valid?
