Question

the number of hours of reserve capacity of 10 randomly selected automotive batteries is shown to the right. 1.78 1.85 1.53 1.67 1.77 1.91 1.38 1.53 1.49 2.08 assume the sample is taken from a normally distributed population. construct 98% confidence intervals for (a) the population variance σ² and (b) the population standard deviation σ. (a) the confidence interval for the population variance is (0.020, 0.205). (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 2% confidence, it can be said that the population variance is greater than. b. with 98% confidence, it can be said that the population variance is between and. c. with 2% confidence, it can be said that the population variance is between and. d. with 98% confidence, it can be said that the population variance is less than.

Explanation:

Step1: Understand confidence interval interpretation

A confidence interval for a parameter (here, population variance \(\sigma^{2}\)) gives a range of values. A \(98\%\) confidence interval means that if we were to take many samples and construct confidence intervals in the same way, about \(98\%\) of those intervals would contain the True population parameter.

Step2: Analyze each option

• Option A: A \(2\%\) confidence level is not relevant here. We constructed a \(98\%\) confidence interval. Also, a confidence interval for variance is a range, not a one - sided bound in this context (since we calculated a two - sided \(98\%\) interval).
• Option B: Since we constructed a \(98\%\) confidence interval for the population variance \(\sigma^{2}\) which is \((0.020,0.205)\), with \(98\%\) confidence, it can be said that the population variance is between the lower bound \(0.020\) and the upper bound \(0.205\) of the confidence interval.
• Option C: The confidence level mentioned (\(2\%\)) is incorrect. We are dealing with a \(98\%\) confidence interval.
• Option D: A confidence interval for variance is a range, not a one - sided upper bound in this case (since we calculated a two - sided \(98\%\) interval).

Answer:

B. With \(98\%\) confidence, it can be said that the population variance is between \(0.020\) and \(0.205\).