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Part 1
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.
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Part 1
Whose estimate will have the smaller margin of error and​ why?
A.
​Katrina's estimate will have the smaller margin of error because the lower level of confidence more than compensates for the smaller sample size.
B.
​Matthew's estimate will have the smaller margin of error because the sample size is larger and the level of confidence is higher.
C.
​Katrina's estimate will have the smaller margin of error because the sample size is smaller and the level of confidence is lower.
D.
​Matthew's estimate will have the smaller margin of error because the larger sample size more than compensates for the higher level of confidence.