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

Left critical value = 10.117; Right critical value = 30.144

7

Left critical value = 9.542; Right critical value = 40.289

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 = 1.612; Upper bound = 4.278; We are 95% confident that population standard deviation of the prices of 4GB flash memory cards at online retailers is between 1.612 and 4.278 dollars.

13

Lower bound = 849.7; Upper bound = 1655.3; We are 90% confident that the population standard deviation of repair costs of low-impact bumper crash on a mini or micro car 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 2 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? Type 1 error.