Q. 21 - The Practice of Statistics for AP

Question

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 

Step-by-Step Solution

Answer

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

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.