A production manager is interested in the difference in the proportion defective being produced on two machines that are making the same product. To assess this difference he takes a random sample of 100 items from machine 1 and has them inspected to determine the number of defects: 15 defects were found. A random sample of 100 items from machine 2 revealed 25 defects. Based upon this information, find a 95% confidence interval for the difference in the proportion of defects between these two machines that will be produced if the operating conditions remain the same.
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