Exercise 7.11.4

Model Answers to 07 Hypothesis Testing in Six Sigma Statistics using Minitab 17, Green Belt Edition.

Example 7.11.4

Conduct a 1 sample StDev Test


Analyse the data in File 07Hypothesis Testing.xlsx worksheet Ex 7.11.3 and answer the questions shown below. The data was collected randomly and is recorded in time order.

  1. Is the sample data within Column Pressure likely to have come from a population where the StDev was different to 5?
  2. What is the confidence interval for the StDev of the population?
  3. Have the requirements of the test that you have used been met?
  4. What was the Power of the test when you want to detect a difference of 1?
  5. Are there any issues associated with this level of  Power ?
  6. Does the Report Card generate any warnings?





Set-Up

Analysis

1.  Click Stat<<Assistant<< Hypothesis Test

2. Click on 1 Sample StDev




2.  Complete the menu as shown and click OK to execute the procedure.


Starting at the top left of the Summary Report we cannot say if the sample data within Column Pressure is likely to have come from a population where the StDev was different to 5. This is because the P-value is within the marginal range.




The confidence interval for the StDev of the population was 4.89 to 6.70. Interestingly, the target value of 5 is within the confidence interval.

Also, note that the sample size was 75. It had to be above 40 for Minitab to be able to check if the sample data had come from a population with heavy tails.



On the Diagnostic Report we see that the control chart shows that there were no usual data points that could affect the validity of the test.

It also shows the distribution was not bi-modal.




 We have two different Power values. If we had been checking for a difference of +1 the Power would be 64.5% and if we were checking against -1 it would be 81.4%.




The Report Card shows a warning for sample size. Our sample size was insufficient to generate an adequate Power for the test conditions. We should obtain more samples in order to improve the Power. The additional data might change the P-value so we do not deem it to be marginal. If it does not we might be willing to accept a different risk level.