Question

The quality control people at your company have tested a sample of 1024 widgets and found that 140 were defective. Suppose that the warranty cost of defective widgets is such that their proportion should not exceed 5% for the production to be protable. Being very cautious, you set a goal of having 0.05 as the upper limit of a 90% condence interval, when repeating the previous experiment.
What should the maximum number of defective widgets be, out of 1024, for this goal to be reached. The direction is to use the worst case estimate for the variance of our sample, that is 1/4 (for a standard deviation of 1/2), not the common choice of p, b especially since you don't have the sample yet!

Answer 1

The following information has been provided:

Since no estimate of the population proportion p is provided, we use the estimate p = 0.5 (which corresponds to the worst-case scenario).

The critical value for the significance level is . The following formula is used to compute the minimum sample size required to estimate the population proportion p within the required margin of error:

Therefore, the sample size needed to satisfy the condition , and it must be an integer number, we conclude that the minimum required sample size is

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