Two semiconductor factories are being compared to see if the

Two semiconductor factories are being compared to see if there is a difference in the average defect rates of the chips they produce. In the first factory, 100 chips are sampled. In the second factory, 300 chips are sampled. The proportions of defective chips are 5% and 10%, respectively. Using a confidence level of 90%, which of the following statements is supported by the data?

Answer: Reject the null of no difference in the defect rate. The 90% CI for the rate in the 1st factory minus that in the 2nd factory = [-9.58%, -0.42%] indicate that the 1st factory has a lower defect rates (i.e., better) than the 2nd factory.

Solution

From the given data the 90% confidence interval for the difference between two population proportions is between -0.0958 and -0.0042.

Here, the confidence interval does not includes 0. So, reject the null hypothesis and conclude that there is no difference in the defect rates.

So, the first statement is exactly true.

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Megastat output shows the calculations below: