Margin Mastery Worksheet
Margin Mastery
Name:
Date:
Statistical Analyst Lab Sheet: Confidence Interval Components
Reference Guide
Margin of Error (E)
\[ E = z^* \cdot \frac{\sigma}{\sqrt{n}} \]
Critical Values (\(z^*\))
- 95% Confidence Level: 1.96
- 99% Confidence Level: 2.576
PROBLEM 1: 95% Confidence Level
A sample of size n = 64 is drawn from a population whose standard deviation is \(\sigma\) = 10.0. Find the margin of error for a 95% confidence interval for \(\mu\).
A 2.45
B 1.56
C 3.12
D 0.98
Show Your Calculations Below
PROBLEM 2: 99% Confidence Level
A sample of size n = 45 is drawn from a population whose standard deviation is \(\sigma\) = 8.2. Find the margin of error for a 99% confidence interval for \(\mu\). Round your final answer to two decimal places.
A 1.96
B 3.15
C 5.28
D 2.41
Show Your Calculations Below
Margin Mastery Answer Key
Answer Key
Margin Mastery: Confidence Calculations
PROBLEM 1 SOLUTION (95% CL) Correct Answer: A
The Given Data
- n 64 (Sample Size)
- σ 10.0 (Std. Deviation)
- z* 1.96 (for 95% Confidence)
Step-by-Step Calculation
\[ E = z^* \cdot \frac{\sigma}{\sqrt{n}} \]
\[ E = 1.96 \cdot \frac{10}{\sqrt{64}} \]
\[ E = 1.96 \cdot \frac{10}{8} \]
\[ E = 1.96 \cdot 1.25 \]
\[ E = 2.45 \]
PROBLEM 2 SOLUTION (99% CL) Correct Answer: B
The Given Data
- n 45 (Sample Size)
- σ 8.2 (Std. Deviation)
- z* 2.576 (for 99% Confidence)
Step-by-Step Calculation
\[ E = z^* \cdot \frac{\sigma}{\sqrt{n}} \]
\[ E = 2.576 \cdot \frac{8.2}{\sqrt{45}} \]
\[ E \approx 2.576 \cdot \frac{8.2}{6.7082} \]
\[ E \approx 2.576 \cdot 1.2224 \]
\[ E \approx 3.1489 \rightarrow 3.15 \]
Teacher Tip
Remind students that as the confidence level increases (from 95% to 99%), the margin of error also increases because the critical value \(z^*\) is larger.
