Did I calculate this correctly? Thank you. **Estimating the Proportion of U.S. Employees Who "Play Hooky"**A random sample of 4500 U.S. employees was chosen, and each was asked whether they "play hooky" — that is, call in sick at least once a year when they simply need to relax. Out of these, 1080 employees responded “yes”. Using this data, we will set up a 95% confidence interval for the proportion, \( p \), of all U.S. employees who played hooky. ### Step-by-Step Calculation:1. **Sample Proportion (\(\hat{p}\))**: Calculate the sample proportion of employees who answered "yes". \[ \hat{p} = \frac{x}{n} = \frac{1080}{4500} = 0.24 \]2. **Complement of the Sample Proportion (\(\hat{q}\))**: This is obtained by subtracting the sample proportion from 1. \[ \hat{q} = 1 - \hat{p} = 1 - 0.24 = 0.76 \]3. **Critical Value (\(Z_c\))**: For a 95% confidence interval, the critical value is determined from the standard normal distribution (Z-table). \[ Z_c = 1.96 \]4. **Standard Error (SE)**: \[ SE = \sqrt{\frac{\hat{p} \cdot \hat{q}}{n}} = \sqrt{\frac{0.24 \cdot 0.76}{4500}} \]5. **Margin of Error (ME)**: Multiply the critical value by the standard error. \[ ME = Z_c \cdot SE = 1.96 \cdot \sqrt{\frac{0.24 \cdot 0.76}{4500}} \]6. **Confidence Interval**: Add and subtract the margin of error from the sample proportion to obtain the confidence interval. \[ \hat{p} \pm ME \implies 0.24 \pm 0.0125 \]7. The calculated interval is: \[ (0.2275, 0.2525) \]### Interpretation:With 95% confidence, the

Name: Did I calculate this correctly? Thank you. **Estimating the Proportio
Uploaded: 2024-03-05T11:52:21.000Z
Channel: Bartleby
Description: Did I calculate this correctly? Thank you. **Estimating the Proportion of U.S. Employees Who "Play Hooky"**A random sample of 4500 U.S. employees was chosen, and each was asked whether they "play hooky" — that is, call in sick at least once a year w