Question

a magazine includes a report on the energy costs per year for 32 - inch liquid crystal display (lcd) televisions. the article states that 14 randomly selected 32 - inch lcd televisions have a sample standard deviation of $3.54. assume the sample is taken from a normally distributed population. construct 99% confidence intervals for (a) the population variance $\sigma^{2}$ and (b) the population standard deviation $\sigma$. interpret the results.
(a) the confidence interval for the population variance is (5.46, 45.70).
(round to two 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 two decimal places as needed.)
○ a. with 99% confidence, you can say that the population variance is between and.
○ b. with 1% confidence, you can say that the population variance is less than.
○ c. with 99% confidence, you can say that the population variance is greater than.
○ d. with 1% confidence, you can say that the population variance is between and.

Explanation:

Step1: Understand confidence interval interpretation

A 99% confidence interval for the population variance means that if we were to take many samples and construct confidence intervals in the same way, about 99% of those intervals would contain the true population variance.

Step2: Analyze each option

• Option A: A 99% confidence interval for variance is constructed to estimate where the population variance lies. With 99% confidence, we can say the population variance is within the calculated interval (5.46, 45.70).
• Option B: 1% confidence is not relevant here as we constructed a 99% confidence interval.
• Option C: A confidence interval gives a range, not just a lower bound.
• Option D: Again, 1% confidence is not what we constructed.

Answer:

A. With 99% confidence, you can say that the population variance is between 5.46 and 45.70.