Statistics Question

Question

If a specimen is weighed 8 times on a scale.  σ = 0.001.  The average weight is 4.1602 grams.  A 99% confidence interval for the true weight of this specimen would be?

Answer 1

Vivian, the Standard error of the mean (SEM) is the standard deviation (s or σ) divided by the square root of the sample size or in this case σ/√n = 0.001/√8

 

Since we are given the population standard deviation (σ, rather than s), you can use a z-table value for the 99% confidence interval or 2.576

Lower limit = M - z SEM = 4.1602 - (2.576)(0.001)/√8)

Upper limit = M + z SEM = 4.1602 + (2.576)(0.001)/√8)

Lower limit ≤ μ ≤ Upper limit