Use the given confidence level and sample data to find a confidence interval for the population standard deviation

Question

Use the given confidence level and sample data to find a confidence interval for the population standard deviation α. Assume that a simple random sample has been selected from a population that has a normal distribution. Salaries of college graduates who took a geology course in college. 

80% confidence; n=81, x¯= $56,500, s= $18,782

Answer 1

The formula for confidence interval of a standard deviation is:

√[(n-1)s² / χ_R²] < σ < √[(n-1)s² / χ_L²]

 

n is the sample size of the data

s is the standard deviation of the data

χ_R² and χ_L² are the critical values from a chi-square chart

 

In your problem,

n = 81

s = 18,782

 

To find the critical values,

df = n-1 = 80

CL = 80% = 0.80

α = 1 - CL = 0.20

α/2 = 0.10

You want the critical values that correspond to 0.10 area to the right, and 0.10 area to the left (=0.90 area to the right)

The chart I have gives:

χ_L² = 64.278

χ_R² = 96.578

 

Now you can plug the values in and solve. If you still have questions, please comment and ask!