Rohitha Goonatilake February 26, 2010 1
One of the most difficult topics for those learning how to use statistics is hypothesis testing. Solving a number of examples will help convince potential and new Six Sigma practitioners of the importance of the concepts behind this tool. However, the necessary steps and their formulation take some additional effort. An appropriately designed solution template for this purpose can ease the difficulties of the learning process.
Suppose that we want to decide whether the mean (m) of the population under consideration exceeds, does not exceed or differs from a given value (m_{0}). To make that decision, we take a random sample, compute the mean (), and then apply a statistical inference technique called hypothesis testing. First, we describe the hypothesis tests for onepopulation mean. The results from this exercise will translate to other hypothesistest analogies of the onesample zinterval and onesample tinterval confidenceinterval procedures, respectively. The third is a nonparametric method called Wilcoxon signedrank test, which applies when the variable under consideration has a symmetric distribution. For other hypothesis tests beyond the tests for onepopulation mean, the formulas for test statistics (Z) will be used in Step 3 instead of test statistics:
We will solve the following hypothesis tests for a onepopulation problem using the template to be designed. The solution text will appear as underlined or as a choice to be selected or deleted, appropriately.
Example: The Food and Nutrition Board of the National Academy of Sciences states that the recommended daily allowance (RDA) of iron for adult females under the age of 51 is 18 milligrams (mg). A sample of iron intake in was obtained during a 24hour period from 45 randomly selected adult females under the age of 51. It revealed that the sample mean () was 14.68 mg. At the 1 percent significance level, does the data suggest that adult females under the age of 51 are, on average, getting less than the RDA of 18 mg of iron? Assume that the population standard deviation is 4.2 mg.
This can also be modified to examine a second approach to hypothesis testing, the pvalue approach with a minor modification. The pvalue (alsoknown as the observed significance level or the probability value) indicates how likely or unlikely observation of the valueobtained for the test statistics wouldbe if the null hypothesis (H_{0}) is true. In particular, a small pvalue (close to 0) indicates that observation of the value obtained for the test statistics would be unlikely if the null hypothesis (H_{0}) is true. Accordingly, Steps 4 and 5 will be modified as follows for the pvalue approach. For a twotailed test, as required, the amount a of will be halved in the alterative Steps 4 and 5.
The solving of a problem using these steps will draw the attention of new Black Belts to the important aspects of the concepts. Following this solution template, they will find it easier to solve difficult hypothesis testing questions.
Note: The author acknowledges the work of Neil A. Weiss in his book Introductory Statistics (Pearson Education Inc., 2005).


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Comments
This helped me understand the concept much better. Thank you very much. Now I do not feel as though I will completely fail my statistics final tomorrow morning. Thank you! :)