9.3

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, 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

5

chi1 = 10.117 chi2= 30.144

7

chi1 = 9.542 chi2= 40.289

9

  1. LB = 7.94 UB = 23.66
  2. LB = 8.59 UB = 20.63. Width would decrease
  3. LB = 6.61 UB = 31.36. Width would increase

11

LB = 1.612 UB = 4.278. There is a 95% confidence that the SD will be between these bounds.

13

LB = 849.7 UB = 1655.3. There is a 90% confidence that the SD wll be between these bounds

Questions

A)

If your Confidence Interval contains the “status quo” value the data does not indicate your new process is different from the “status quo”.

In truth it is possible your new process is different from the “status quo” thus in this scenario you potentially made what type of error? This is a type one error.

B)

If your Confidence Interval does not contain the “status quo” value the data does indicate your new process is different then the “status quo”.

In truth it is possible your new process is not different then the “status quo” thus in this scenario you potentially made what type of error? This is a type two error.