Answer :
The 95% confidence interval for the proportion of voters favoring the incumbent is approximately 0.870 to 0.930. This means we can be 95% confident that the true proportion of voters favoring the incumbent falls within this range based on the given sample.
To calculate the 95% confidence interval for the proportion of voters favoring the incumbent, we can use the formula:
Confidence Interval = Sample Proportion ± (Critical Value * Standard Error)
First, we need to calculate the sample proportion:
Sample Proportion = Number of voters favoring the incumbent / Total sample size
Sample Proportion = 360 / 400
Sample Proportion = 0.9
Next, we need to determine the critical value associated with a 95% confidence level. For a large sample size like this (n > 30), we can use the Z-score corresponding to a 95% confidence level, which is approximately 1.96.
Standard Error = sqrt((Sample Proportion * (1 - Sample Proportion)) / Sample Size)
Standard Error = sqrt((0.9 * (1 - 0.9)) / 400)
Standard Error ≈ 0.015
Now we can calculate the confidence interval:
Confidence Interval = 0.9 ± (1.96 * 0.015)
Confidence Interval = (0.870, 0.930)
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