Question

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 of the sample of 45 trash bag breaking strengths in Table 1.9 is ¯ x¯ = 50.566. If we let µ denote the mean of the breaking strengths of all possible trash bags of the new type and assume that σ equals 1.63:

(a) Calculate 95 percent and 99 percent confidence intervals for µ. (Round your answers to 3 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 50 pounds? Explain. (Click to select)Yes or No , 95 percent interval is (Click to select)above or below 50.

(c) Using the 99 percent confidence interval, can we be 99 percent confident that µ is at least 50 pounds? Explain. (Click to select)Yes or No , 99 percent interval extends (Click to select)above or below 50.

(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? (Click to select)Fairly or Not confident, since the 95 percent CI is (Click to select)above or below 50 while the 99 percent CI contains 50.

Answer 1

(a)

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The 99% confidence interval is

(b)

Since 95% confidence interval does not contain 50 so we cannot conclude that µ is at least 50 pounds.

Conclusion: No , 95 percent interval is above 50.

(c)

Since 99% confidence interval contains 50 so we can conclude that µ is at least 50 pounds.

Conclusion: Yes

(d)

Fairly, since the 95 percent CI is above 50 while the 99 percent CI contains 50.