11.
Suppose we are estimating m. What happens to the required sample size as the population standard deviation increases while the confidence level and desired margin of error remain constant?
A)
It increases.
B)
It decreases.
C)
It does not change.
A) It increases.
To determine what happens to the required sample size as the population standard deviation increases while the confidence level and desired margin of error remain constant, we need to understand the relationship between these variables.
The relationship can be explained by the formula for calculating the sample size for estimating a population mean:
n = (Z * σ / E)^2
Where:
n = sample size
Z = Z-score corresponding to the desired confidence level
σ = population standard deviation
E = desired margin of error
From this formula, we can see that the sample size is directly proportional to both the population standard deviation (σ) and the desired margin of error (E). This means that as either the population standard deviation or the desired margin of error increases, the required sample size also increases.
So, in the scenario described, if the population standard deviation increases while the confidence level and desired margin of error remain constant, the required sample size will also increase. Therefore, the correct answer is A) It increases.