Question

Construct the confidence interval specified to estimate \(\mu\). Arrange the intervals from lowest to highest based on length of the interval:
A. \(95\%\) confidence for \(\bar{x}=20,\ \sigma=3,\ n=49\);
B. \(95\%\) confidence for \(\bar{x}=20,\ \sigma=3,\ n=81\);
C. \(95\%\) confidence for \(\bar{x}=115,\ \sigma=25,\ n=49\);
D. \(95\%\) confidence for \(\bar{x}=115,\ \sigma=25,\ n=81\).

• A. \(A,C,B,D\)
• B. \(D,B,C,A\)
• C. \(B,A,D,C\)
• D. \(A,B,C,D\)

Hint:

For same confidence level, interval length increases with \(\sigma\) and decreases with \(\sqrt{n}\).

Answer 1

The Correct Option is C