The number of hours of reserve capacity of 10 randomly selected automotive batteries is shown to the right.
$\begin{array}{lllll}1.79 & 1.85 & 1.54 & 1.68 & 1.71 \\ 1.98 & 1.31 & 1.53 & 1.44 & 2.06\end{array}$
Assume the sample is taken from a normally distributed population. Construct $90 \%$ confidence intervals for (a) the population variance $\sigma^{2}$ and (b) the population standard deviation $\sigma$.
(a) The confidence interval for the population variance is $(0.030,0.154)$ (Round to three decimal places as needed.)
Interpret the results. Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to three decimal places as needed.)
A. With $10 \%$ confidence, it can be said that the population variance is greater than
C. With $10 \%$ confidence, it can be said that the population variance is between $\square$ and
B. With $90 \%$ confidence, it can be said that the population variance is less than
D. With $90 \%$ confidence, it can be said that the population variance is between $\square$ and
Answer
Final Answer: \(\boxed{\text{With } 90 \% \text{ confidence, it can be said that the population variance is between } 0.030 \text{ and } 0.154}\)
Step 1 ：The number of hours of reserve capacity of 10 randomly selected automotive batteries is shown to the right. The numbers are: 1.79, 1.85, 1.54, 1.68, 1.71, 1.98, 1.31, 1.53, 1.44, 2.06. Assume the sample is taken from a normally distributed population. Construct $90 \%$ confidence intervals for (a) the population variance $\sigma^{2}$ and (b) the population standard deviation $\sigma$.
Step 2 ：The confidence interval for the population variance is $(0.030,0.154)$ (Round to three decimal places as needed.)
Step 3 ：The question is asking for the interpretation of the confidence interval for the population variance. The confidence interval is given as (0.030, 0.154). This means that we are 90% confident that the true population variance lies within this interval.
Step 4 ：Final Answer: \(\boxed{\text{With } 90 \% \text{ confidence, it can be said that the population variance is between } 0.030 \text{ and } 0.154}\)
