As standard deviation increases, samples size _____________ to achieve a specified level of confidence.
A. Increases
B. Decreases
C. Remains the same
increas
B. Decreases
To determine how the sample size changes as the standard deviation increases, we need to consider the relationship between these two variables.
The formula for the sample size needed to achieve a specified level of confidence is given by:
n = (Z * σ / E)²
Where:
- n represents the sample size
- Z is the critical value corresponding to the desired level of confidence
- σ is the standard deviation of the population
- E is the desired margin of error
Now, let's analyze the formula for sample size. As the standard deviation (σ) increases, the numerator of the formula also increases. This implies that to maintain the same level of confidence (Z) and margin of error (E), the sample size (n) needs to increase as well.
Therefore, the correct answer is:
A. Increases