Question

Find the 90% confidence interval for the variance and standard deviation for the price in dollars of an adult single-day ski lift ticket. Assume the data is normally distributed.

59        54        53        52        51

39        49        46        49        48

Answer 1

Here s = 5.3125 and n = 10
df = 10 - 1 = 9

α = 1 - 0.9 = 0.1
The critical values for α = 0.1 and df = 9 are Χ^2(1-α/2,n-1) = 3.325 and Χ^2(α/2,n-1) = 16.919

CI = (9*5.3125^2/16.919 , 9*5.3125^2/3.325)
CI = (15.01 , 76.39)

Here s = 5.3125 and n = 10
df = 10 - 1 = 9

α = 1 - 0.9 = 0.1
The critical values for α = 0.1 and df = 9 are Χ^2(1-α/2,n-1) = 3.325 and Χ^2(α/2,n-1) = 16.919

CI = (sqrt(9*5.3125^2/16.919) , sqrt(9*5.3125^2/3.325))
CI = (3.87 , 8.74)