Question

# Annual salaries for graduates are expected to be between $30,000 and$45,000. Assume that a 95% confidence interval estimate of the population mean annual sling salary is desired. How large a sample should be taken if the desired margin of error is $250. 92 likes 458 views ## Answer to a math question Annual salaries for graduates are expected to be between$30,000 and $45,000. Assume that a 95% confidence interval estimate of the population mean annual sling salary is desired. How large a sample should be taken if the desired margin of error is$250.

Sigrid
4.5
**Step 1:**
Given parameters:
Desired Margin of Error $ME$: $250 Confidence Level: 95% **Step 2:** Calculate the estimated population standard deviation $\sigma$: Given range:$30,000 to \$45,000 which covers approximately 6 standard deviations
\sigma = \frac{Range}{6} = \frac{45000 - 30000}{6} = \frac{15000}{6} = 2500

**Step 3:**
Calculate the required sample size $n$:
Substitute \sigma and z into the formula for n :
n = \left$\frac{1.96 \times 2500}{250}\right$^2

Calculating step by step:
1. \frac{1.96 \times 2500}{250} = 19.6
2. 19.6^2 = 384.16

Therefore, approximately \boxed{384} participants would be required for the sample.

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