```Question 338671
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 3.3.241 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
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x-bar = 3.3048
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90% CI = (3.3048-0.06866 , 3.3048+0.06866)
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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?
E = z*sigma/sqrt(n)
n = [z*sigma/E]^2
z* for 90% confidence = 1.645
sigma = 0.13199
E = 0.03
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n = [1.645*0.13199/0.03]^2 = 52.38
rounded up: n = 53
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(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture.
Temperature; consistency of batches; machine tolerances
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cheers,
Stan H.

```