A manufacturing company’s quality control personnel have recorded the proportion of defective items for each of 500 monthly shipments of one of the computer components that the company produces. The data are in the file P07_07.xlsx. The quality control department manager does not have sufficient time to review all of these data. Rather, she would like to examine the proportions of defective items for a sample of these shipments.
a. Use StatTools to generate a simple random sample of size 25.
b. Using the sample generated in part a, construct a 95% confidence interval for the mean proportion of defective items over all monthly shipments. Assume that the population consists of the proportion of defective items for each of the given 500 monthly shipments.
c. Interpret the 95% confidence interval constructed in part b.
d. Does the 95% confidence interval contain the actual population mean in this case? If not, explain why not. What proportion of many similarly constructed confidence intervals should include the true population mean?