(c) Using the 99 percent confidence interval, can we be 99 percent confident that u is at least 50 pounds?99 percent interval extends50.(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 themarket?confident, since the 95 percent Cl is50 while the 99 percent Cl contains 50. Consider the trash bag problem. Suppose that an independent laboratory has tested trash bags and has found that no 30-gallon bagsthat are currently on the market havemean breaking strength of 50 pounds or more. On the basis of these results, the producer ofthe 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 meanbreaking strength can be shown to be at least 50 pounds. The mean of the sample of 40 trash bag breaking strengths in Table 1.10 isx = 50.560. If we let u denote the mean of the breaking strengths of all possible trash bags of the new type and assume that o equals1.68:(a) Calculate 95 percent and 99 percent confidence intervals for u. (Round your answers to 3 decimal places.)95 percent confidence intervals for u is99 percent confidence intervals for u is(b) Using the 95 percent confidence interval, can we be 95 percent confident that u is at least 50 pounds?95 percent interval is50.

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Description: (c) Using the 99 percent confidence interval, can we be 99 percent confident that u is at least 50 pounds?99 percent interval extends50.(d) Based on your answers to parts b and c, how convinced are you that the new 30-gallon trash bag is the stronge

Given, x=50.560σ=1.68n=40 a).Here, α=1-0.95=0.05 As per z-distribution table, critical value of z at 0.05 level of significance is obtained as 1.96. The required 95% confidence interval for the true mean μ is obtained as- CI=x±zcrit×σn=50.560±1.96×1.6840=50.560±0.520637=50.039,51.081 Here, α=1-0.99=0.01 As per z-distribution table, critical value of z at 0.01 level of significance is obtained as 2.326. The required 99% confidence interval for the true mean μ is obtained as- CI=x±zcrit×σn=50.560±2.326×1.6840=50.560±0.617858=49.9421,51.1779b). From part (a), we are 95 % confidence that μ lies between 50.039~50 pounds to 51.081~51 pounds. Therefore, we are 95% confidence that μ is at least 50. Thus, 95% interval is at least 50. c). From part (a), we are 99% confidence that μ lies between 49.9421~50 pounds to 51.1779~51 pounds. Therefore, we are 99% confidence that μ is at least 50. Therefore, 99% interval is at least 50. d). Yes, the producer of the new improved trash bag feels sure that its 30-gallon bag will be the strongest such bag on the market since the new trash bags' mean breaking strength can be shown to be at least 50 pounds.

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

MATLAB: An Introduction with Applications

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(c) Using the 99 percent confidence interval, can we be 99 percent confident that u is at least 50 pounds?
99 percent interval extends
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?
confident, since the 95 percent Cl is
50 while the 99 percent Cl contains 50.

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
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 40 trash bag breaking strengths in Table 1.10 is
x = 50.560. If we let u denote the mean of the breaking strengths of all possible trash bags of the new type and assume that o equals
1.68:
(a) Calculate 95 percent and 99 percent confidence intervals for u. (Round your answers to 3 decimal places.)
95 percent confidence intervals for u is
99 percent confidence intervals for u is
(b) Using the 95 percent confidence interval, can we be 95 percent confident that u is at least 50 pounds?
95 percent interval is
50.

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