Math Problem Statement
Solution
To solve this problem, we need to compute the margin of error (M.E.) using the given formula for estimating a population proportion:
Where:
- is the critical value for a given confidence level.
- is the sample proportion (success rate).
- is the sample size.
Given Data:
- Sample size
- Success rate
- Confidence level = 99% (corresponding value = 2.576)
Step 1: Compute
Step 2: Plug into the formula
Step 3: Simplify
Step 4: Convert to percentage
Step 5: Round to one decimal place
Thus, the margin of error is 6.4%.
Would you like further details on any part of the calculation?
Here are five related questions:
- How do we find the critical value for different confidence levels?
- How does increasing the sample size affect the margin of error?
- What is the relationship between confidence level and margin of error?
- Can this method be applied to other types of population parameters?
- How is the formula different when we don't know the population proportion?
Tip: As the confidence level increases, the critical value increases, which also increases the margin of error.
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Math Problem Analysis
Mathematical Concepts
Statistics
Population Proportion
Margin of Error
Confidence Interval
Formulas
Margin of Error (M.E.) = z* * sqrt(p̂(1 - p̂) / n)
p̂ = sample proportion
n = sample size
z* = critical value based on confidence level
Theorems
Central Limit Theorem
Normal Distribution
Suitable Grade Level
Grades 11-12, College
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