Final answer:
To construct a 90% two-sided confidence interval for the standard deviation σ, we can use the chi-square distribution. The formula for the confidence interval is given and can be used to calculate the lower and upper bounds. Plugging in the values, we can calculate the confidence interval for σ.
Step-by-step explanation:
To construct a confidence interval for the standard deviation σ, we can use the chi-square distribution. The formula for the confidence interval is:
σ ≥ σL = sqrt((n-1)s2 / χ1-α/2,n-1)
σ ≤ σU = sqrt((n-1)s2 / χα/2,n-1)
Where n is the sample size, s is the sample standard deviation, σL is the lower bound of the confidence interval, and σU is the upper bound of the confidence interval. For a 90% two-sided confidence interval, χ1-α/2,n-1 is the value from the chi-square distribution that leaves 5% in each tail, so we have χ1-0.05/2,101-1 = χ0.975,100.
Plugging in the values, we have:
σ ≥ σL = sqrt((101-1)(0.152) / χ0.975,100)
σ ≤ σU = sqrt((101-1)(0.152) / χ0.025,100)
Calculate the values for σL and σU to get the confidence interval for σ.