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

a=0.1 X^2(0.95)= 10.117 and X^2(0.05)= 30.144

7

X^2(0.975)= 10.982 and X^2(0.025)= 36.781

9

  1. Lower Bound= 7.94; Upper Bound= 23.66
  2. Lower Bound= 8.59; Upper Bound= 20.63; increasing the sample size decreases the width of the interval
  3. Lower Bound= 6.61; Upper Bound= 31.36; increasing the level of confidence increases the width of the interval

11

Lower Bound= 1.61; Upper Bound= 4.28; we are 95% confident that the population standard deviation of the price for a 4GB memory card is between 1.61 and 4.28 dollars

13

Lower Bound= 849.69; Upper Bound= 1655.34; we are 90% confident that the population standard deviation of the repair cost of a low impact bumper crach on a mini/micro car is between 849.69 and 1655.34 dollars

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? a type II 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? a type I error