Question

Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation​ σ. Assume that the population has a normal distribution. List the critical​ value(s) for full credit. Number of ounces of coffee in a 13.7oz bottle of Starbucks Frappuccino Mocha drink​ (measured cold at 40 degrees ​F)​: ​95% confidence; n​ = 18, oz​, s​ = 0.03oz.

Answer 1

Here s = 0.03 and n = 18
df = 18 - 1 = 17

α = 1 - 0.95 = 0.05
The critical values for α = 0.05 and df = 17 are Χ^2(1-α/2,n-1) = 7.564 and Χ^2(α/2,n-1) = 30.191

CI = (sqrt(17*0.03^2/30.191) , sqrt(17*0.03^2/7.564))
CI = (0.0225 , 0.0450)