Consider a data sample consisting of 12 values with a mean of 22 and variance of 1.5. What is the approximate 95% confidence interval for the standard deviation?

Question

Quizplus · Accepted Answer

The 95% confidence interval for the standard deviation can be calculated using the Chi-Square distribution and the formula for the confidence interval of the variance. Given the variance (s^2) is 1.5 and the sample size (n) is 12, we first find the degrees of freedom (df = n - 1 = 11). Using the Chi-Square distribution table for df = 11 and a 95% confidence level, we find the critical values (let's denote them as χ²(lower) and χ²(upper)). The confidence interval for the variance is given by [(n-1)s²/χ²(upper), (n-1)s²/χ²(lower)]. After calculating the interval for the variance, we take the square root of those bounds to find the confidence interval for the standard deviation. The correct calculation leads to the interval 0.87 < σ < 2.08, which corresponds to choice B.

Consider a Data Sample Consisting of 12 Values with a Mean