Consider the trash bag problem. Suppose that an independent laboratory has tested 30- gallon trash bags and has found that none of the 30- gallon bags currently on the market has a mean breaking strength of 50 pounds or more. On the basis of these results, the producer of the new, improved trash bag feels sure that its 30- gallon bag will be the strongest such bag on the market if the new trash bag’s mean breaking strength can be shown to be at least 50 pounds. Recall that Table 1.9 presents the breaking strengths of 40 trash bags of the new type that were selected during a 40- hour pilot production run. Figures 3.10 and 3.12 give the MINITAB and Excel outputs of statistics describing the 40 breaking strengths.
a. Find the sample mean on the outputs. Does the sample mean provide some evidence that the mean of the population of all possible trash bag breaking strengths is at least 50 pounds? Explain your answer.
b. Find the sample median on the outputs. How do the mean and median compare? What does the histogram in Figure 2.17 tell you about why they compare this way?