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Q. 21

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The Practice of Statistics for AP

Found in: Page 483

Book edition 4th

Author(s) David Moore,Daren Starnes,Dan Yates

Pages 809 pages

ISBN 9781319113339

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Short Answer

A researcher plans to use a random sample of $n = 500$ families to estimate the mean monthly family income for a large population. A $99 %$ confidence interval based on the sample would be ______ than a 90% confidence interval.
(a) narrower and would involve a larger risk of being incorrect
(b) wider and would involve a smaller risk of being incorrect
(c) narrower and would involve a smaller risk of being incorrect
(d) wider and would involve a larger risk of being incorrect
(e) wider, but it cannot be determined whether the risk of being incorrect would be larger or smaller

(b) wider and would involve a smaller risk of being incorrect

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given Information

(a) narrower and would involve a larger risk of being incorrect

(b) wider and would involve a smaller risk of being incorrect

(c) narrower and would involve a smaller risk of being incorrect

(d) wider and would involve a larger risk of being incorrect

(e) wider, but it cannot be determined whether the risk of being incorrect would be larger or smaller

Step 2: Explanation

A $99 %$ confidence interval will be wider than a $90 %$ confidence interval because a $99 %$ confidence interval will result in an interval that is more likely to contain the true population mean than the $90 %$ confidence interval.

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