**Exercise: Confidence Interval Calculation for Voter Support**In a random sample of 400 voters, 208 support the new bonding bill. Find the 98% confidence interval for the true proportion of voters who support the bill. Interpret the interval.**Explanation:**To solve this problem, we'll calculate the confidence interval for the proportion of voters who support the bill using the following steps:1. **Calculate the sample proportion (p̂):** \[ p̂ = \frac{208}{400} = 0.52 \]2. **Choose the confidence level:** The confidence level is 98%, which means we are looking for a z-score associated with this confidence level. For a 98% confidence level, the z-score is approximately 2.33.3. **Calculate the standard error (SE) for the proportion:** \[ SE = \sqrt{\frac{p̂(1 - p̂)}{n}} = \sqrt{\frac{0.52 \times 0.48}{400}} \approx 0.02487 \]4. **Calculate the margin of error (ME):** \[ ME = z \times SE = 2.33 \times 0.02487 \approx 0.05794 \]5. **Determine the confidence interval:** \[ \text{Confidence interval} = p̂ \pm ME = 0.52 \pm 0.05794 \] \[ \text{Lower bound} = 0.46206 \] \[ \text{Upper bound} = 0.57794 \]**Interpretation:**We are 98% confident that the true proportion of voters who support the new bonding bill is between 46.2% and 57.8%.**Visual Representation:**The small diagram on the right is a bell curve, representing the normal distribution. The shaded region under the curve corresponds to the 98% confidence level, showing the range in which the true proportion is likely to fall.

Answered: 8. In a random sample of 400 voters,…

8. In a random sample of 400 voters, 208 support the new bonding bill. Find the 98% confidence interval for the true proportion of voters who support the bill. Interpret the interval.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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