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

10.117, 30.144

7

9.542, 40.289

9

  1. 7.94, 23.66
  2. 8.59, 20.63 Interval width decreases.
  3. 6.61, 31.36 Interval width increases.

11

1.612, 4.278 We can be 95% confident that the population standard deviation of the prices of 4gig memory cards is between 1.612 and 4.278 13

849.7, 1655.3 We can be 90% confident that the population standard deviation of repair costs of bumper crashes in mini/micro cars is between 849.7 and 1655.3 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? Type II

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? Type I