Question 1208176: What is the relationship between level of confidence and sample needed, given other parameters are constant?
Answer by PPCHLOE(2)   (Show Source):
You can put this solution on YOUR website! Here is the solution to your statistics problem.Hope you find this helpful.
Let's break it down step by step:
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*Given parameters:*
- Constant population size (N)
- Constant margin of error (E)
- Constant desired confidence level (Z-score)
*Question:* How does the level of confidence affect the sample size needed?
*Step 1: Understand the formula*
The sample size (n) formula is:
n = (Z^2 * σ^2) / E^2
where:
- n = sample size
- Z = Z-score (related to confidence level)
- σ = population standard deviation
- E = margin of error
*Step 2: Analyze the Z-score*
The Z-score increases as the confidence level increases. For example:
- 80% confidence: Z ≈ 1.28
- 90% confidence: Z ≈ 1.645
- 95% confidence: Z ≈ 1.96
- 99% confidence: Z ≈ 2.576
*Step 3: Observe the relationship*
As the confidence level increases (Z-score increases), the sample size (n) also increases.
*Step 4: Explain the relationship*
A higher confidence level requires a larger sample size to achieve the same margin of error. This is because a higher confidence level means we want to be more certain about our results, which requires more data.
*In summary:*
- As the level of confidence increases, the sample size needed also increases.
- This is because a higher confidence level requires more data to achieve the same margin of error.
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