Final answer:
To construct a 95% confidence interval for the population standard deviation σ, use the chi-square distribution and the sample standard deviation.
Step-by-step explanation:
To construct a 95% confidence interval for the population standard deviation σ, we can use the chi-square distribution. The formula for the confidence interval is:
(n-1)s^2 / χ^2(α/2,n-1), (n-1)s^2 / χ^2(1-α/2,n-1)
where n is the sample size, α is the level of significance (1 - confidence level), s is the sample standard deviation, and χ^2 is the chi-square value corresponding to the desired confidence level and degrees of freedom.
In this case, the sample size is 18, the sample standard deviation is 20, and the confidence level is 95%. Using a chi-square calculator or a chi-square table, we can find the chi-square values corresponding to α/2 and 1- α/2 with 17 degrees of freedom. Substituting the values into the formula, we can calculate the confidence interval for the population standard deviation σ.