Week 5 Essay

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E-Text Christopher Shaw RES341 1. A random sample of 10 miniature Tootsie Rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were 3.087 3.131 3.241 3.241 3.270 3.353 3.400 3.411 3.437 3.477 (a) Construct a 90 percent confidence interval for the true mean weight. E = z*sigma/sqrt(n) E = 1.645*0.13199/sqrt(10) E = 0.06866 -------------- x-bar = 3.3048 ----------------- 90% CI = (3.3048-0.06866 , 3.3048+0.06866) --------------------------------------… (b) What sample size would be necessary to estimate the true weight with an error of } 0.03 grams with 90 percent confidence? E = z*sigma/sqrt(n) n = [z*sigma/E]^2 z* for 90% confidence = 1.645 sigma = 0.13199 E = 0.03 ------------ n = [1.645*0.13199/0.03]^2 = 52.38 rounded up: n = 53 (c) Q: Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture. (Data are from a project by MBA student Henry Scussel.) Tootsie (c) A: Precision of the amount of ingredients in the mix, humidity and temperature control, etc. consistency of batches; machine tolerances utilized during candy manufacture, sharpness of cutting tools utilized to form pieces. Precision of the amount of ingredients in the mix, humidity and temperature control, etc. consistency of batches; machine tolerances utilized during candy manufacture, sharpness of cutting tools utilized to form pieces. 2. 8.63 The State of Michigan tested 766 water samples from private wells in Lapeer County, Michigan, and found that 112 exceeded the EPA guidelines of 50 ppb. (a) Find the standard error of the estimated proportion. (b) Find the 95 percent confidence interval width for the true proportion. (c) Is normality an issue here? Explain. (d) Try the Very Quick Rule. Does it work well here? Explain. (Data are from Detroit Free Press, November 27, 1997,

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