Provide an appropriate response.
-Construct a $95 \%$ confidence interval for the population standard deviation $\sigma$ of a random sample of 15 crates which have a mean weight of $165.2$ pounds and a standard deviation of $12.7$ pounds. Assume the population is normally distributed.
A) $( 9.3,20.0 )$
B) $( 86.5,401.1 )$
C) $( 2.6,5.6 )$
D) $( 9.8,18.5 )$

Question

Quizplus · Accepted Answer

To construct a $95\%$ confidence interval for the population standard deviation $\sigma$, we use the chi-square distribution because the sample size is small and the population is assumed to be normally distributed. The formula involves the sample standard deviation $s = 12.7$, the sample size $n = 15$, and the chi-square values for the degrees of freedom $df = n - 1 = 14$ at the desired confidence level. The correct interval, given the provided options, is $(9.3, 20.0)$, which is calculated using the chi-square distribution values for $df = 14$ at the $95\%$ confidence level.

Provide an Appropriate Response 95%95 \%95% Confidence Interval for the Population Standard Deviation

Provide an Appropriate Response $95 \%$ Confidence Interval for the Population Standard Deviation