Sample n = 50 female entrepreneurs, 9 said constrained in their business Find the 95% Cl and the 90% for the propon entrenreneurs are credit constrained in their

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**Understanding Confidence Intervals for Female Entrepreneurs**

**Context:**  
A sample consisting of 50 female entrepreneurs was surveyed, and 9 of them reported that they experience credit constraints in their businesses.

**Objective:**  
Calculate the 95% and 90% confidence intervals (CI) for the proportion of female entrepreneurs who are credit constrained in their businesses.

**Explanation:**  
- **Sample Size (n):** 50
- **Number Reporting Credit Constraints:** 9

Confidence intervals provide a range of values that likely contain the true proportion of a population parameter. In this case, we are estimating the proportion of all female entrepreneurs who might be credit constrained based on our sample.

The calculation involves:
1. Determining the sample proportion (\( \hat{p} \)).
2. Using standard formulas and a Z-distribution to calculate the confidence intervals for different confidence levels.

This exercise helps in understanding how statistical evidence can be used to infer characteristics about a larger population from a sample.
Transcribed Image Text:**Understanding Confidence Intervals for Female Entrepreneurs** **Context:** A sample consisting of 50 female entrepreneurs was surveyed, and 9 of them reported that they experience credit constraints in their businesses. **Objective:** Calculate the 95% and 90% confidence intervals (CI) for the proportion of female entrepreneurs who are credit constrained in their businesses. **Explanation:** - **Sample Size (n):** 50 - **Number Reporting Credit Constraints:** 9 Confidence intervals provide a range of values that likely contain the true proportion of a population parameter. In this case, we are estimating the proportion of all female entrepreneurs who might be credit constrained based on our sample. The calculation involves: 1. Determining the sample proportion (\( \hat{p} \)). 2. Using standard formulas and a Z-distribution to calculate the confidence intervals for different confidence levels. This exercise helps in understanding how statistical evidence can be used to infer characteristics about a larger population from a sample.
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