Problem 1: The defect rate of a disk drive manufacturing process is within 0.9% - 1.7%, with 98% confidence. We inspect a sample of 1000 drives from one of our plants. Consider the following scenarios (i) We observe 12 defects in our sample and (ii) there are 27 defects in the sample.

(a) What should we do in each case and why? Your explanation should mention confidence intervals, differences of means, normal data', $\mu$, $\sigma$, p-value, null hypothesis, alternative hypothesis, significance testing, 'type 1 and type 2 errors'

(b) How would you go about choosing the appropriate test for this situation to test for significance ?

(c) What should you do to deal with the case of different sample sizes? Your answer should mention power, effect size, and significance ?

Problem 2: Explain why you would want to use cross validation. If you had 200 data points, how would you do 10-fold cross validation and how many experiments would you have to do?