show excel formula for:  You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 95% confidence interval and a margin of error of 2%. A pilot survey reveals that 5 of the 50 sampled hold two or more jobs. How many in the workforce should be interviewed to meet your requirements?

To calculate the sample size required for a 95% confidence interval with a margin of error of 2%, we need to use the formula for sample size in proportion-based surveys. The formula is as follows:

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

Where:
- \(n\) = required sample size
- \(Z\) = Z-score (for 95% confidence level, \(Z\) is 1.96)
- \(p\) = estimated proportion (from the pilot survey, \(p = \frac{5}{50} = 0.10\))
- \(E\) = margin of error (given as 2%, so \(E = 0.02\))

### Excel Formula:
Here’s the Excel formula you can use to calculate the required sample size:

```excel
= (1.96^2 * 0.1 * (1 - 0.1)) / (0.02^2)
```

### Step-by-Step Explanation:
1. **Z-score**: For a 95% confidence level, the Z-score is 1.96.
2. **Proportion (p)**: From the pilot survey, the proportion of people with two or more jobs is \( p = \frac{5}{50} = 0.10 \).
3. **Margin of error (E)**: The margin of error is 2%, or \(E = 0.02\).

In Excel, this formula will give you the minimum sample size required to meet your confidence interval and margin of error requirements.

### Result:
When you run this formula in Excel, the result will be approximately **865.88**. Therefore, you should interview at least **866** people in the workforce to meet your survey requirements.

Would you like further clarification or more details on this calculation?

---

### Related Questions:
1. What happens if the confidence interval is changed from 95% to 99%?
2. How does increasing the margin of error impact the sample size?
3. What would happen if the pilot survey revealed a higher proportion (say, 15%) of people holding two or more jobs?
4. How does the sample size change if the workforce population is known to be finite (e.g., 10,000 people)?
5. What other factors should be considered when conducting a survey of this kind?

**Tip**: Always round up the sample size to the next whole number to ensure the margin of error is met.

You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 95% confidence interval and a margin of error of 2%. A pilot survey reveals that 5 of the 50 sampled hold two or more jobs. How many in the workforce should be interviewed to meet your requirements?

Learn how to calculate the sample size needed for a survey with a 95% confidence interval and 2% margin of error. Using data from a pilot survey where 10% of the sample holds two or more jobs, this example demonstrates statistical concepts like proportions and the normal distribution. Perfect for students or professionals conducting workforce surveys.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation