Assume the sample is taken from a normally distributed population and construct the indicated confidence interval.
-Construct a 95% confidence interval for the population standard deviation σof a random sample of 15 men who have a mean weight of 165.2 pounds with a standard deviation of 10.5 pounds. Assume the population is
Normally distributed.
A)(7.7, 16.6)
B)(59.1, 274.2)
C)(2.4, 5.1)
D)(8.1, 15.3)

Question

Quizplus · Accepted Answer

To construct a 95% confidence interval for the population standard deviation when the population is normally distributed, we use the chi-square distribution. The formula involves the sample standard deviation (s), the sample size (n), and the chi-square values for the desired level of confidence. The confidence interval is given by $\sqrt{\frac{(n-1)s^2}{\chi^2_{\alpha/2}}}$ to $\sqrt{\frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}}$, where $n=15$, $s=10.5$, and the chi-square values depend on the degrees of freedom ($n-1$) and the confidence level (95%). Calculating with these values leads to the interval (7.7, 16.6).

Assume the Sample Is Taken from a Normally Distributed Population