FRM Part I · FRM Exam Part I · Hypothesis Testing
Holding the sample standard deviation constant, which change would produce a narrower confidence interval for a population mean?
Quadrupling the sample size narrows the interval, because the standard error falls with the square root of n and is halved. Higher confidence levels widen the interval, and doubling the sample reduces width only by about 29%, not half.
- ARaising the confidence level from 95% to 99%
- BQuadrupling the sample sizeCorrect
- CDoubling the sample size, which halves the width
- DLowering the sample size while raising the confidence level
Explanation
Width is proportional to z x s/sqrt(n). Quadrupling n halves the standard error, narrowing the interval. Raising the confidence level increases z and widens it. Doubling n reduces the width only by a factor of 1/sqrt(2), not half. Lowering n widens it.
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