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.
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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
4.5120 Answers
**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 z 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}
Given parameters:
Desired Margin of Error (ME): $250
Confidence Level: 95%
**Step 2:**
Calculate the estimated population standard deviation (
Given range: $30,000 to $45,000 which covers approximately 6 standard deviations
**Step 3:**
Calculate the required sample size (
Substitute
Calculating step by step:
1.
2.
Therefore, approximately
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