Quality Associates, Inc.

Case Study

Case Synopsis

In this case, we have Quality Associates, Inc. a consulting firm advising its client about sampling and statistical procedures that can be used to control their manufacturing process. Their client has offered samples to be analyzed, so they can quickly learn whether the process is operating satisfactorily or corrective actions needs to be taken.

The numbers given in the case were as follows: assumed population standard deviation is equal to .21, sample size is equal to 30 and the test value of the mean was 12. They also stated the two hypotheses to be tested: the null hypothesis that the population is equal to 12 and the alternative hypothesis that the mean is not equal to 12.
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At .0038, the p-value for sample 3 was less than the significance level set by the client. Sample 3 provides evidence to reject Ho and accept Ha. However, samples 1, 2 and 4 all have p-values larger than alpha, indicating that the process is working satisfactorily with a mean equal to 12. According to samples 1,2 and 4, corrective measures do not need to be taken.

A second approach to hypothesis testing is the critical value approach, which states to reject Ho if the z value is larger than z alpha/2 or smaller than –z alpha/2. Alpha was given at .01, alpha/2 is equal .005. Table 8.1, Values of Z alpha/2 for the most commonly used Z values, in the book states that for alpha/2 equal to .005, the z value is equal to 2.576. This is the z critical value for a two tailed test, outside of which lies the rejection area. Again, out of the 4 samples, only one had a critical value in the rejection area. The z value of sample 3, -2.8982, was smaller than the z critical value of -2.576. This leads to a rejection of Ho. Samples 1,2, and 4 all fall between the 2 critical values and provide evidence to not reject Ho.

Assumption

Based on the results of the hypothesis tests, both p-value approach and critical value approach, corrective action should be taken for sample 3. Samples 1,2 and 4 provide evidence that we cannot reject Ho, and therefore the

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