You can use the following syntax to check your answers. Note the answers you get in R will not be EXACTLY the same you get by hand but they should be pretty close.

If you sample standard deviation s = 2 and the sample size = 35, and your confidence level is 95% this is how you can have R calculate a Confidence Interval for \(\sigma\).

conf_sig(s = 2, size = 35, conf = .95)
## [1] 1.617744 2.620404

9.3

5. Area to the right of right critical value (0.05) = 30.144 Area to the right of left critical value (0.95) = 10.117

7. Area to the right of right critical value (0.01) = 40.289 Area to the right of left critical value (0.99) = 9.542

9.

  1. Lower bound = 7.94 Upper bound = 23.66
  2. Lower bound = 8.59 Upper bound = 20.63. Width of interval decreases
  3. Lower bound = 6.61 Upper bound = 31.36. Width of interval increases

11. Lower bound = 0.226 Upper bound = 0.542. We can be 95% confident that the population standard deviation of pH of rainwater in Tucker Country, WV is between 0.226 and 0.542

13. Lower bound = 734.8 Upper bound = 1657.5. We can be 90% confident that the population standard deviation of repair costs of a low impact bumper crash on a mini or micro car is between 734.8 and 1657.5