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. 30.144; 10.117

7. 40.289; 9.542.

9. Type answer here.

  1. Lower bound= 7.942 Upper bound= 23.633.
  2. Lower bound= 8.6 Upper bound= 20.6. If the sample size increases, width of the interval decreases.
  3. Lower bound= 6.6 Upper bound= 31.3. If the level of confidence increases, the width of the confidence interval increases too.

11. Lower bound= 0.226 Upper bound=0.542. We are 95% confident that the population standard of deviation of the pH of rainwater in Tucker County is between 0.226 and 0.542.

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