SOLUTION: 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

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Question 172151: 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
(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 of � 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.) Tootsie

Answer by stanbon(75887) (Show Source):
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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
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x-bar = sample mean = 3.28567 ; s = 0.12442
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(a) Construct a 90 percent confidence interval for the true mean weight.
E = 1.645(0.12442/sqrt(9) = 0.06822
90% CI: x-bar-E < mu < x-bar+E
3.28567,0.12442 < my < 3.28567 + 0.1244
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(b) What sample size would be necessary to estimate the true weight with an error of � 0.03 grams with 90 percent confidence?
Since E = z*(s/(sqrt(n))
sqrt(n) = z(s/E)
n = [z(s/E)]^2
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n = [1.645(0.12442/0.03)^2
n = [6.82236]^2 = 46.55
Rounding up n = 47
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Cheers,
Stan H.

(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture.