Final answer:
To construct a 99% confidence interval for the population standard deviation from a sample size of 11 and sample standard deviation of 15, use the Chi-square distribution with 10 degrees of freedom to find upper and lower chi-square values and apply them in the confidence interval formula.
Step-by-step explanation:
To construct a 99% confidence interval for the population standard deviation σ when a sample of size 11 has a standard deviation s = 15, we use the Chi-square distribution because we do not know the true population standard deviation.
The degrees of freedom (df) for this calculation would be n - 1, where n is the sample size. In this case, df = 11 - 1 = 10.
The formula to calculate the confidence interval for the standard deviation is:
σ = s * sqrt(n-1 / Χ2))
where:
s is the sample standard deviation
n is the sample size
Χ2 is the chi-square value corresponding to the desired confidence level and degrees of freedom
To find the 99% confidence interval, we need to look up the chi-square values for the 0.5% and 99.5% percentiles (since it's two-tailed) in a chi-square distribution table with 10 degrees of freedom.
Using these chi-square values, we can calculate the upper and lower limits of the confidence interval for the population standard deviation.