What sample size is required?

Sample proportion is 85%, we want results with 95% confidence and the maximum acceptable error is 0.02.

**Round the number to the nearest whole** Round up

For example, 45.83 is to be reported as 46

a. 

1157

b. 

1225

c. 

999

d. 

1156

e. 

156

To find the required sample size, we use the formula for the sample size for estimating a population proportion:

\[
n = \left( \frac{Z^2 \cdot p \cdot (1 - p)}{E^2} \right)
\]

Where:
- \( Z \) is the Z-score corresponding to the confidence level,
- \( p \) is the sample proportion,
- \( E \) is the margin of error.

Given:
- \( p = 0.85 \),
- Confidence level = 95%, so \( Z = 1.96 \),
- Maximum acceptable error \( E = 0.02 \).

Let's calculate the sample size:

\[
n = \left( \frac{(1.96)^2 \cdot 0.85 \cdot (1 - 0.85)}{(0.02)^2} \right)
\]

First, compute the values inside the formula and round up to the nearest whole number.The required sample size, rounded up to the nearest whole number, is **1225**.

The correct answer is:
**b. 1225**

Do you have any questions or want further details?

Here are 5 related questions:
1. How does increasing the confidence level affect the sample size?
2. What happens to the sample size if the margin of error is increased to 0.05?
3. How would the sample size change if the proportion was closer to 50%?
4. What formula would you use if the population size was small?
5. How does sample size relate to hypothesis testing?

**Tip**: A larger sample size leads to more precise estimates, but it also increases the cost and effort of data collection.

What sample size is required? Sample proportion is 85%, we want results with 95% confidence and the maximum acceptable error is 0.02.

Learn how to calculate the sample size required to estimate a population proportion with 95% confidence and a margin of error of 0.02. This problem uses the sample size formula and covers essential statistical concepts. Suitable for students in Grades 10-12.

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