Question 1010549
you might be interest in this reference.


<a href = "http://blog.minitab.com/blog/adventures-in-statistics/understanding-hypothesis-tests%3A-significance-levels-alpha-and-p-values-in-statistics" target = "_blank">http://blog.minitab.com/blog/adventures-in-statistics/understanding-hypothesis-tests%3A-significance-levels-alpha-and-p-values-in-statistics</a>


your significant level is .01.


since your sample statistics can be more then or less than the desired level of 12, this would be a two tailed distribution.


therefore the alpha is equal to .01/2 = .005 on each end.


since you are using the sample standard deviation rather than the population standard deviation, then you will be using a t-test rather than a z-test.


the t-test uses the same size to calculate the t-score.


it uses what is called degrees of freedom.


with a sample size of 30, the degrees of freedom is equal to 30 - 1 = 29.


your critical t-score will be calculated using 29 degrees of freedom.


with an alpha of .005 on each end, your critical t-score will be plus or minus 2.756.


if the t-score of your sample is beyond these limits, you would need to re-calibrate your equipment.


if it is within these limits, there would be no need for re-calibration.


the mean of your sample is 11.92 with a standard deviation of .26


the standard error is equal to the standard deviation divided by the square root of the sample size.


this becomes .26 / sqrt(30) which is equal to .0475.


your t-score will be (x-m)/s.


x is the mean of your sample.
m is the mean of the population which is the desired measurement.
s is the standard error.


your t-score will be (12-11.92)/.0475 = 1.684.


this is well within the limits of t = plus or minus 2.756.


therefore, no calibration is required.


it makes no difference to this study if you had said x was the mean of the sample and m was the desired score.


your t-score would then have been (11.92-12)/.0475 = -1.684.


it will still have bee well within the limits of t = plus or minus 2.756.