Question 1185303: Suppose we wish to design study to investigate the effect of load music on teenagers ability to concentrate we know from previous studies that the standard deviation of the time to complete this task is 3.4 minutes how many subjects would be required to ensure 90% confidence that the generated estimates is within 1 minute of the true mean time required
Answer by CPhill(2264)   (Show Source):
You can put this solution on YOUR website! Here's how to calculate the required sample size:
1. **Identify the key values:**
* Confidence level = 90% This means α = 1 - 0.90 = 0.10. Since we're dealing with a confidence interval, we need to split alpha into two tails to find the z-score. α/2 = 0.05
* Margin of error (E) = 1 minute
* Standard deviation (σ) = 3.4 minutes
2. **Find the z-score:**
For a 90% confidence level, the z-score corresponding to α/2 = 0.05 is 1.645. You can find this using a z-table or a calculator with statistical functions.
3. **Use the sample size formula:**
The formula for calculating the sample size (n) is:
n = (z * σ / E)²
4. **Plug in the values and calculate:**
n = (1.645 * 3.4 / 1)²
n = (5.593 / 1)²
n = 31.28
5. **Round up to the nearest whole number:**
Since you can't have a fraction of a subject, always round the sample size *up* to the next whole number. Therefore, you would need 32 subjects.
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