**In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job applicant is most important for a good first impression.** 

Construct a confidence interval of the true population proportion of human resource professionals that say the appearance of a job applicant is most important for a good first impression.  **Use a 99% confidence level.** what is the critical value rounded to 4 decimal places?

To construct a **99% confidence interval** for the true population proportion, we need to follow these steps.

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### **Step 1: Identify the given values**
- Sample proportion (\(p\)) = 90% = 0.9  
- Sample size (\(n\)) = 514  
- Confidence level = 99%  
- Critical value (\(z_{\alpha/2}\)) = ?

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### **Step 2: Find the critical value (\(z_{\alpha/2}\))**
For a **99% confidence level**, the significance level \(\alpha = 1 - 0.99 = 0.01\). Since it’s two-tailed, we split \(\alpha\) into two equal parts: \(\alpha/2 = 0.005\). We need the **z-score** corresponding to the upper 0.995 tail in the standard normal distribution.

Using a **Z-table** or a calculator:

\[
z_{\alpha/2} \approx 2.5758
\]

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### **Step 3: Confirm the answer**

- **Critical value** for a 99% confidence interval: **2.5758**

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Let me know if you'd like the **full confidence interval calculation** or further details! Below are 5 related questions to expand your understanding:

1. How do you interpret the meaning of a confidence interval in statistics?
2. How would the confidence interval change if we used a 95% confidence level instead?
3. How does sample size affect the width of the confidence interval?
4. What assumptions are made when calculating a confidence interval for proportions?
5. How can confidence intervals be used in practical decision-making?

**Tip:** Critical values differ for each confidence level; always reference the Z-table or a calculator!

In a Harris poll of 514 human resource professionals, 90% said that the appearance of a job applicant is most important for a good first impression. Construct a confidence interval of the true population proportion of human resource professionals that say the appearance of a job applicant is most important for a good first impression. Use a 99% confidence level. What is the critical value rounded to 4 decimal places?

Learn how to construct a 99% confidence interval for the true population proportion of HR professionals who believe appearance is crucial for a good first impression, based on a sample poll. Detailed steps include calculating the sample proportion and finding the critical value of 2.5758. Ideal for students studying statistics at an undergraduate level.

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