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 3

Click here to see ALL problems on Probability-and-statistics

Question 136270: 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
construct a 90 percent confidence interval for the true mean weight.
what sample size would be necessary to estimate the true weight with an error of + 0.03 grams with 90 percent confidence?
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 3.3.241 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) Discuss the factors which might cause variation in the weight of Tootsie Rolls during manufacture.
Temperature; consistency of batches; machine tolerances
=========================
cheers,
Stan H.