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

30.144 10.117

7

40.289 9.542

9

  1. (7.94,23.66)
  2. (8.59,20.63) Increasing the sample size decreases the width of the CI
  3. (6.61,31.36) Increasing the level of confidence increases the width of the CI.

11

(1.612,4.278) We are 95% confident that the population standard deviation of the price of a 4GB flash memory card at online retailers is between $1.612 and $4.277.

13

(849.7,1655.3) We are 90% confident that the population standard deviation of the repair costs of a low- impact bumper crash on a mini- or micro-car is between $849.7 and $1655.3.

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 2

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 1