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. x^2(0.95)=10.117, x^2(0.05)=30.144

7. x^2(0.99)=9.542, x^2(0.01)=40.289

9.

  1. x^2(0.95) = 10.117 , x^2(.05) = 30.144 Lower bound = 7.94 Upper bound = 23.66
  2. x^2(0.95)=17.708, x^2(0.05)=42.557 Lower bound = 8.59 Upper bound = 20.63 -The width of the interval increases as the confidence level increases
  3. x^2(0.095)=2.700, x^2(0.025)=19.023 Lower bound = 12.07 Upper bound = 38.32 -The width of the interval decreases as the sample size increases

11. s^2=(0.319)=0.102 x=0.226 x=21.920 Lower bound = 0.226 Upper bound = 0.542 We are 95% confident that the population standard devation is between 0.226 and 0.542

13. s2=(1007.4542)2=1,014,963.9651 x=3.325 x=16.919

  Lower bound = 734.8 
  Uper bound = 1657.5
  
  We are 90% confident that the population standard deviation is between $734.8 and $1657.5