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. X20.95=10.117, X20.05=30.144

7. X20.99=9.542, X20.01=40.289

9.

  1. X20.95=10.117, X20.05=30.144 Lower Bound: (20-1)(12.6)/30.144=7.94 Upper Bound: (20-1)(12.6)/10.117=23.66
  2. X20.95=17.708, X20.05=42.557 Lower Bound: (30-1)(12.6)/42.557=8.59 Upper Bound: (30-1)(12.6)/17.708=20.63 The qidth of the interval dereases as the sample size increases.
  3. X20.99=7.633, X20.01=36.191 Lower Bound: (20-1)(12.6)/36.191=6.61 Upper Bound: (20-1)(12.6)/7.633=31.36 The width of the interval increases as the confidence level increases.

11. s2=0.102 X20.975=3.816, X20.025=21.92 Lower Bound: Square root: (12-1)(0.102)/21.92=0.226 Upper bound: Square root: (12-1)(0.102)/3.816=0.542 We can be 95% confident that the poopulation standard deiviation of the pH of rainwater in Tucker County, West Virginia is between 0.226 and 0.542.

13. S2=1,014,963.9651 X20.95=3.325, X20.05=16.919 Lower Bound: Square root:(10-1)(1,014,963.9651)/16.919=734.8 Upper Bound: Square root: (10-1)(1,014,963.9651)/3.325=1657.5 We are 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