Smoke detectors are highly recommended safety devices for early fire detection in homes. It is very important that they emit a loud warning signal when needed; if they don't, they are considered faulty. Officials at the companies that make Brand A and Brand B smoke detectors tested random samples of 200 Brand A detectors and 180 Brand B detectors. They found that 20 Brand A detectors were faulty, while only 12 of the Brand B detectors were faulty.

NOTE: You can use pa-hat to indicate the sample proportion of Brand A detectors that are faulty and pb-hat to indicate the sample proportion of Brand B detectors that are faulty.

Question 18 (3 points)

Are the normality criteria met? Show work to explain how you know.

Calculate the sample proportion,, of Brand A smoke detectors that were faulty.

Calculate the sample proportion,, of Brand B smoke detectors that were faulty

Calculate the standard error for the difference in proportions,. You can type sqt to indicate taking the square root.

Calculate a 95% confidence interval for the difference in the population proportions,. Be sure to show your calculation of the margin of error.