An editorial house does error checks on its publications by proofreading a sample of 50 pages from each book it publishes. If the rate of mistakes is estimated to be at most 10% per page (i.e. the probability that there is a mistake in a given page is 10%) the book is sent to print. If it is greater than that, it needs to be fully proof-read again, which is a costly process. A book is being checked for errors and mistakes are found on 7 out of 50 pages sampled. As an editor you now face a decision of whether to send this book to print or not.

a) Define your null and the alternative hypotheses. 

b) Is it a one- or two-sided test? Justify. 

c) Calculate the test statistic and the p-value.

d) Calculate the p-value for this test and interpret. 

e) Can you reject the null hypothesis at 5% significance level? Justify 

f) Find a threshold rate of errors above which the book needs to be fully proof-read, assuming the probability of type I error of 5%. (10 points)

g) What is the probability of detecting the actual rate of about 14%? Calculate the probability of type II error and the power of the test assuming the significance level of 5%. (10 points)

h) What would happen to the power if the significance threshold was increased to 1%? (10 points)

i) The power of this test against a rate of 14% is very low (assume 22% if you were unable to solve the previous question). How can you improve the power of this test? (10 points)

j) You realize that by sampling 50 pages only, the margin of error is too high. You want to reduce your margin of error to about 3 percentage points at 95% confidence. What should your sample size be in this case. (10 points)

Answer rating: 100% (QA)

Quiz a The null hypothesis is that the book has less than 10 errors on each page while the alternative hypothesis is that the book has more than 10 errors on each page What are your reasons for believ... View the full answer