# 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

Algebra ->  Algebra  -> Probability-and-statistics -> 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      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Probability and statistics Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Probability-and-statistics Question 293565: 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. (Data are from a project by MBA student Henry Scussel.)Answer by stanbon(57940)   (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.