A random sample of 10 miniature Tootsie Rolls was taken from a bag: Each piece w

Question

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 3.270 3.353 3.400 3.411 3.437 3.477
(a) Construct a 90 percent confidence interval for the true mean weight
(b) What sample size would be necessary to estimate the true weight with an error + 0.03 grams with 90 percent confidence?
(c) 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)

Explanation / Answer

(a) The standard error E = 1.96(s/sqrt(n)) = 1.96[0.131989/sqrt(10)] =1.96*0.41739 =0.081808 So, confidence interval is: (x-bar-E,x-bar+E) = (3.3048-0.0818, 3.3048+0.0818) =(3.223, 3.387) ------------------------------------------ (b) n=[z'*s/E]^2 n=[1.645*0.131989/0.03]^2 = 52.38; rounding up, n=53 (c) Precision of the amount of ingredients in the mix, humidity and temperature control, etc...

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