Consider the trash bag problem. Suppose that an independentlaboratory has tested trash bags and has found that no 30-gallonbags that are currently on the market have a mean breaking strengthof 50 pounds or more. On the basis of these results, the producerof the new, improved trash bag feels sure that its 30-gallon bagwill be the strongest such bag on the market if the new trash bag’smean breaking strength can be shown to be at least 50 pounds. Themean of the sample of 39 trash bag breaking strengths in Table 1.9is x⎯⎯x¯ = 50.573. If we let µ denote the mean of thebreaking strengths of all possible trash bags of the new type andassume that σ equals 1.61:

  

(a) Calculate 95 percent and 99 percentconfidence intervals for µ. (Round your answers to3 decimal places.)

95 percent confidence intervals for µ is	[, ].
99 percent confidence intervals for µ is	[, ].

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

(Click to select)NoYes , 95 percent interval is (Click toselect)belowabove 50.

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

(Click to select)NoYes , 99 percent interval extends (Click toselect)abovebelow 50.

(d) Based on your answers to parts band c, how convinced are you that the new 30-gallon trashbag is the strongest such bag on the market?

(Click to select)FairlyNot confident, since the 95 percent CI is(Click to select)belowabove 50 while the 99 percent CI contains50.

rev : 08_22_2016_QC_CS-57697