Managerial Statistics
1) 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 40 trash bag breaking strengths in Table 1.9 is x=50.575. If we let u denote the mean of the breaking strengths of all trash bags of the new type and assume that o equals 1.65: a. Calculate 95 percent and 99 percent confidence intervals for u.
b. Using the 95 percent confidence interval, can we be 95 percent confident that u is at least 50 pounds? Explain
c. Using the 99% confidence interval, can we be 99% confident that u 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?
(a) (i) 95% confidence interval for μ:n = 40 x-bar = 50.575 s = 1.65 % = 95 Standard Error, SE = σ/Ön = 0.2609 z- score = 1.9600 Width of the confidence interval = z * SE = 0.5113 Lower Limit of the confidence interval = x-bar - width = 50.0637Upper Limit of the confidence interval = x-bar + width = 51.0863The confidence interval is [50.0637 pounds, 51.0863 pounds](ii) 99% confidence interval for μ:n = 40 x-bar = 50.575 s = 1.65 % = 99 Standard Error, SE = σ/Ön = 0.2609 z- score = 2.5758 Width of the confidence interval = z * SE = 0.6720 Lower Limit of the confidence interval = x-bar - width = 49.9030Upper Limit of the confidence interval = x-bar + width = 51.2470The confidence interval is [49.9030 pounds, 51.2470 pounds](b) Yes, we can be 95% confident that μ is at least 50 pounds, since the entire 95% confidence interval lies above 50 pounds (c) No, we can’t be 99% confident that μ is at least
b. Using the 95 percent confidence interval, can we be 95 percent confident that u is at least 50 pounds? Explain
c. Using the 99% confidence interval, can we be 99% confident that u 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?
(a) (i) 95% confidence interval for μ:n = 40 x-bar = 50.575 s = 1.65 % = 95 Standard Error, SE = σ/Ön = 0.2609 z- score = 1.9600 Width of the confidence interval = z * SE = 0.5113 Lower Limit of the confidence interval = x-bar - width = 50.0637Upper Limit of the confidence interval = x-bar + width = 51.0863The confidence interval is [50.0637 pounds, 51.0863 pounds](ii) 99% confidence interval for μ:n = 40 x-bar = 50.575 s = 1.65 % = 99 Standard Error, SE = σ/Ön = 0.2609 z- score = 2.5758 Width of the confidence interval = z * SE = 0.6720 Lower Limit of the confidence interval = x-bar - width = 49.9030Upper Limit of the confidence interval = x-bar + width = 51.2470The confidence interval is [49.9030 pounds, 51.2470 pounds](b) Yes, we can be 95% confident that μ is at least 50 pounds, since the entire 95% confidence interval lies above 50 pounds (c) No, we can’t be 99% confident that μ is at least