Using Minitab to compute an upper confidence bound for std deviation.

Question

I've got a set of data and I want to answer the following:

Calculate an upper confidence bound with confidence level 95% for the population standard deviation of maximum pressure.

The set of data is

33.2, 41.8, 37.3, 40.2, 36.7, 39.1, 36.2, 41.8

36.0, 35.2, 36.7, 38.9, 35.8, 35.2, 40.1

We are learning how to use Minitab and we've been asked to solve this using Minitab. I only see an option to compute the one-sample t for the mean, and I'm unsure how to compute the one-sample t for standard deviation.

Edit: I just found the 1 variance computation and got this as the result:

95% Confidence Intervals

                         CI for         CI for
Variable  Method          StDev        Variance
C1        Chi-Square  (1.88, 4.06)  (3.54, 16.45)
          Bonett      (1.95, 3.91)  (3.79, 15.28)

Which of these is the answer I'm looking for? I'm not sure what Chi-square and Bonnett are?

Answer 1

I believe you need to do a one-sided confidence interval. (Your question is somewhat ambiguous. If you want the upper-end of a two-sided CI, then your procedure gives 16.45 for the variance.)

The code generated by what I suppose to be the appropriate menu choices (STAT > Basic > One variance > data in C1, Omit test, Option > Less than) is as follows:

 MTB > set c1
 DATA> 33.2, 41.8, 37.3, 40.2, 36.7, 39.1, 36.2, 41.8 
 DATA> 36.0, 35.2, 36.7, 38.9, 35.8, 35.2, 40.1
 DATA> end
 MTB > OneVariance C1;
 SUBC>   Confidence 95.0;
 SUBC>   Alternative -1.

 Test and CI for One Variance: C1 

 Method

 The chi-square method is only for the normal distribution.
 The Bonett method is for any continuous distribution.


 Statistics

 Variable   N  StDev  Variance
 C1        15   2.57      6.61


 95% One-Sided Confidence Intervals

                       Upper
                       Bound
                         for   Upper Bound
 Variable  Method      StDev  for Variance
 C1        Chi-Square   3.75         14.09
           Bonett       3.63         13.15

The above is from Minitab 16. (Bonnett's procedure does not assume the data are normal.) I will leave it to you to figure out exactly what distribution theory Minitab is using to get the one-sided chi-squared upper confidence bound.

In R, the computation for the upper-bound on the variance is:

 (14)*2.572^2/qchisq(.05, 14)
 ## 14.09493

Take the square root to get a bound for the SD.