For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when σ is known?
A) If the sample standard deviation is smaller, the interval is wider.
B) If the population standard deviation is greater, the interval is wider.
C) If the population standard deviation is smaller, the interval is wider.
D) If the population standard deviation is greater, the interval is narrower.

Question

Quizplus · Accepted Answer

The formula used for interval estimation of the population mean when σ is known is:
interval = Zcrit*σ / sqrt(n)
where Zcrit is the critical value from the standard normal distribution for the desired confidence level, σ is the population standard deviation, and n is the sample size.
From the above formula, we can infer that if the population standard deviation is greater, the entire interval will be wider, thus giving us more room for error in our estimation. On the other hand, if the population standard deviation is smaller, the interval shrinks to a smaller range, requiring a more accurate estimate. Hence, option B is correct.

For a Given Confidence Level and Sample Size, Which of the Following