Question 1193583: You want to obtain a sample to estimate the average number of hours per week community college students in the United States work at their job while being a full-time student. Based on previous evidence, you believe the population standard deviation is 10. You would like to be 99% confident that your estimate is within 1.5 hours of the true population mean.
Assume that the number of statistics students is unknown, but very large. How large of a sample size is required?
Answer by yurtman(42)   (Show Source):
You can put this solution on YOUR website! **1. Define the parameters:**
* **Confidence level:** 99%
* **Margin of error (E):** 1.5 hours
* **Population standard deviation (σ):** 10 hours
**2. Find the Z-score:**
* For a 99% confidence level, the Z-score is 2.576 (found using a standard normal distribution table or calculator).
**3. Calculate the required sample size (n):**
* Use the formula:
n = (Z-score * σ / E)²
* Substitute the values:
n = (2.576 * 10 / 1.5)²
* Calculate:
n ≈ 294.81
**4. Round up:**
* Since we can't have a fraction of a student, round up the sample size to the nearest whole number.
**Therefore, a sample size of 295 community college students is required to be 99% confident that the estimate of the average number of hours worked per week is within 1.5 hours of the true population mean.**
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