# Managerial Statistics

**Topics:**Normal distribution, Sample size, Confidence interval

**Pages:**2 (641 words)

**Published:**July 30, 2011

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 = 40x-bar = 50.575s = 1.65% = 95Standard Error, SE = σ/Ön = 0.2609z- score = 1.9600Width of the confidence interval = z * SE = 0.5113Lower 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 = 40x-bar = 50.575s = 1.65% = 99Standard Error, SE = σ/Ön = 0.2609z- score = 2.5758Width of the confidence interval = z * SE = 0.6720Lower 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 50...

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