Question 124239: Please help me. I am new to statistics. I have tried this problem many times and having problem solving.
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.
(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.
Thank you kindly.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
The standard error is E = 1.96(s/sqrt(n)) = 1.96[0.131989/sqrt(10)]=1.96*0.41739
=0.081808
C.I. = (x-bar-E,x-bar+E) = (3.3048-0.0818,3.3048+0.0818)
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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?
n=[z'*s/E]^2
n=[1.645*0.131989/0.03]^2 = 52.38; rounding up, n=53
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(c) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture.
I'll leave that to your imagination.
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Cheers,
Stan H.
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