Consider the trash bag problem. Suppose that an independent laboratory has tested trash bags and has found that no 30-gallon bags that are currently on the market have 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. The mean and the standard deviation of the sample of 40 trash bag breaking strengths in Table 1.10 are and s 1.6438. If we let m denote the mean of the breaking strengths of all possible trash bags of the new type:

a. Calculate 95 percent and 99 percent confidence intervals for m.

b. Using the 95 percent confidence interval, can we be 95 percent confident that m is at least 50 pounds? Explain.

c. Using the 99 percent confidence interval, can we be 99 percent confident that m is at least 50 pounds? Explain.

d. Based on your answers to parts b and c, how convinced are you that the new 30-gallon trash bag is the strongest such bag on the market?

The mean and the standard deviation of the sample of 40 trash bag breaking strengths are and x
50.575 s
1.6438.