Question

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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. basis of these results, the producer of the new, improved trash bag feels sure that i pounds. The mean of the sample of 42 trash bag breaking strengths in Table 1.9 is 50.579. If we let denote the mean of the breaking strengths of all possible trash bags of the new type and assume that o equals 1.60: On the 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 percent and 99 percent confidence intervals for . (Round your answers to 3 decimal places.) (a) Calculate 95 percent confidence intervals for u is 99 percent confidence intervals for uis t least 50 pounds? Explain. (b) Using the 5 percent confidence interval, can 95 percent oonfident that u is 95 percent Interval is 50. Nu below (c) Using the 9 percent confidence interval, can we be 99 percent confident that u is at least 50 pounds? Explain. 99 percent interval extends below 50 No (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? confident, since the 95 percent Cl while the 99 percent CI contains 50. Not above

Answer 1

X= 50.519, b0 ,Y42 (a) 95 C99 1-o.9 O.01 1-o.95 O.05 2 0.025 Lusing tble] ta 0.095 - t 1960 95 Con dee intral or he ue mean 250.519 tj.960x l'66 J42 50.57 O.4839 -50.05 51.062C) LoweY limit 50 .095 C upper imit 5 063 inderval the ur. meah A. 99Cnidence 1.66 50 579a576 % S42 -50.579 O13598 49.9430, 51-21498 lboerlinit 9.943 utper limit 51.215

lie bJuw (b) Condidenee that we are 5/. 50 kound to5 peund 95. Condence thJ u lieblw5ndk to 51 Pound ialea5ounl 99Canfidence tht (d) yes, hepducer o he heu Sheyat Sre thet 30-ll bay oill bt the mtan benkiSgh Can be shoon to b atleat 50 found the roducen of the he Sur hat 30-Jallon oill b the Shoget such mean Jhemarket ig he ne takin ShimhCan be Shooh be ad leaxt