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Q. 21

Expert-verified
Found in: Page 483

### The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339

# 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

See the step by step solution

## 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.