1. To construct a confidence interval for ${\sigma }^2$ or $\sigma$, what must be true about the population? (p. 476)

2. Explain the difference between ${\sigma }^2$ and $s^2$. (p. 476)

3. Explain why we need to find two different critical values to construct the confidence intervals in this section. Why can't we just use the “point estimate ± margin of error” method we used earlier in this chapter? (p. 474)

4. Provide an example from the real world where it would be important to estimate the variability of a data set. (p. 474)

5. The ${\chi }^2$ curve is symmetric. (p. 474)

6. The value of the ${\chi }^2$ random variable is never negative. (p. 474)

7. The ${\chi }^2$ curve is right-skewed. (p. 474)

8. The total area under the ${\chi }^2$ curve equals 1. (p. 474)

9. Confidence level 90%, $n=50$

10. Confidence level 95%, $n=50$

11. Confidence level 99%, $n=50$

12. Confidence level 95%, $n=20$

13. Confidence level 95%, $n=25$

14. Confidence level 95%, $n=30$

15. Consider the critical values you calculated in Exercises 9–11. Describe what happens to the critical values for a given sample size as the confidence level increases.

16. Consider the critical values you calculated in Exercises 12–14. Describe what happens to the critical values for a given confidence level as the sample size increases.

17. 90% confidence interval for the population variance ${\sigma }^2$

18. 95% confidence interval for the population variance ${\sigma }^2$

19. 99% confidence interval for the population variance ${\sigma }^2$

20. 90% confidence interval for the population standard deviation $\sigma$

21. 95% confidence interval for the population standard deviation $\sigma$

22. 99% confidence interval for the population standard deviation $\sigma$

23. Consider the confidence intervals you constructed in Exercises 17–19. Describe what happens to the lower bound and upper bound of a confidence interval for ${\sigma }^2$ as the confidence level increases but the sample size stays the same.

24. Consider the confidence intervals you constructed in Exercises 20–22. Describe what happens to the lower bound and upper bound of a confidence interval for $\sigma$ as the confidence level increases but the sample size stays the same.

25. 95% confidence interval for the population variance ${\sigma }^2$ for a sample of size $n=30$

26. 95% confidence interval for the population variance ${\sigma }^2$ for a sample of size $n=40$

27. 95% confidence interval for the population variance ${\sigma }^2$ for a sample of size $n=50$

28. 95% confidence interval for the population standard deviation $\sigma$ for a sample of size $n=30$

29. 95% confidence interval for the population standard deviation $\sigma$ for a sample of size $n=40$

30. 95% confidence interval for the population standard deviation $\sigma$ for a sample of size $n=50$

31. Consider the confidence intervals you constructed in Exercises 25–27. Describe what happens to the lower bound and upper bound of a confidence interval for ${\sigma }^2$ as the sample size increases but the confidence level stays the same.

32. Consider the confidence intervals you constructed in Exercises 28–30. Describe what happens to the lower bound and upper bound of a confidence interval for $\sigma$ as the sample size increases but the confidence level stays the same.

33. Biomass Power Plants. Power plants around the country are retooling in order to consume biomass instead of, or in addition to, coal. The table²¹ contains a random sample of eight such power plants and the amount of energy generated in megawatts (MW) in 2014.

34. Carbon Emissions. The following table represents the carbon emissions (in millions of tons) from consumption of fossil fuels for a random sample of five nations.²²

35. Biomass Power Plants. Refer to Exercise 33.

36. Carbon Emissions. Refer to Exercise 34.

37. Calories in Breakfast Cereals. A random sample of six well-known breakfast cereals yielded the following calorie data. Can we construct a confidence interval for the variance of the number of calories? Why or why not?

38. Deepwater Horizon Cleanup Costs. The following table represents the amount of money disbursed by BP to a random sample of six Florida counties for cleanup of the Deepwater Horizon oil spill, in millions of dollars.²³ The normality of the data was confirmed in the Section 8.1 exercises. Construct and interpret a 90% confidence interval for $\sigma$.

39. Wii Game Sales. The following table represents the number of units sold in the United States for the week ending March 26, 2011, for a random sample of eight Wii games.²⁴ The normality of the data was confirmed in the Section 8.1 exercises. Construct and interpret a 99% confidence interval for $\sigma$.