A recent increase in sales of microchips has forced a computer company to buy a new processing machine to help keep up with demand. The builders of the new machine claim that it produces fewer defective microchips than the older machine. From a random sample of 90 microchips produced on the old machine, 5 were found to be defective. From a random sample of 83 microchips produced on the new machine, 3 were found to be defective. The quality control manager wants to construct a confidence interval to estimate the difference between the proportion of defective microchips from the older machine and the proportion of defective microchips from the new machine.
Why is it not appropriate to calculate a two-sample z-interval for a difference in proportions?
The microchips were not randomly assigned to a machine.
There is no guarantee that microchips are approximately normally distributed.
The normality of the sampling distribution of the difference in sample proportions cannot be established.
Both sample proportions are less than 0.10.
The sample sizes are not the same.
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