Measurements were made of the milk fat content (in percent) in six brands of feta cheese variety of goat cheese), with the following results. Assume that the population is normally distributed.
$\begin{array}{llllll}
\hline 27.5 & 19.3 & 32.0 & 23.5 & 24.6 & 16.9 \
\hline
\end{array}$

Construct a $90 \%$ confidence interval for the population standard deviation $\sigma$.
A) $3.44

Question

Measurements were made of the milk fat content (in percent) in six brands of feta cheese variety of goat cheese), with the following results. Assume that the population is normally distributed.
$\begin{array}{llllll}
\hline 27.5 & 19.3 & 32.0 & 23.5 & 24.6 & 16.9 \
\hline
\end{array}$

Construct a $90 \%$ confidence interval for the population standard deviation $\sigma$.
A) $3.44 < \sigma < 9.56$
B) $3.77 < \sigma < 10.47$
C) $3.67 < \sigma < 11.42$
D) $4.02 < \sigma < 9.63$

Quizplus · Accepted Answer

The correct answer is C) $3.67 < \sigma < 11.42$.The sample standard deviation is:$$s = \sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i - \bar{x})^2} = 6.55$$The degrees of freedom is:$$df = n-1 = 5$$The critical value for a 90% confidence interval with 5 degrees of freedom is:$$t_{0.05,5} = 2.571$$The confidence interval for the population standard deviation is:$$\left(\frac{s}{\sqrt{\chi^2_{\alpha/2,df}}}, \frac{s}{\sqrt{\chi^2_{1-\alpha/2,df}}}\right) = (3.67, 11.42)$$

Measurements Were Made of the Milk Fat Content (In Percent) 27.519.332.023.524.616.9\begin{array}{llllll}\hline 27.5 & 19.3 & 32.0 & 23.5 & 24.6 & 16.9 \\\hline\end{array}27.5​19.3​32.0​23.5​24.6​16.9​​

Measurements Were Made of the Milk Fat Content (In Percent) $\begin{array}{llllll}\hline 27.5 & 19.3 & 32.0 & 23.5 & 24.6 & 16.9 \\\hline\end{array}$