Katrina wants to estimate the proportion of adults who read at least 10 books last year. to do so, she obtains a simple random sample of 100 adults and constructs a 95% confidence interval. matthew also wants to estimate the proportion of adults who read at least 10 books last year. he obtains a simple random sample of 400 adults and constructs a 99% confidence interval. assuming both katrina and matthew obtained the same point estimate, whose estimate will have the smaller margin of error? justify your answer.