Answer :
The 95% confidence interval for voters not favoring is approximately 16.08% to 23.92%.
How to find confidence interval?
- Calculate the proportion of voters not favoring the incumbent governor:
400 voters - 320 favoring = 80 not favoring
Proportion (p) = 80/400 = 0.2 - Calculate the standard error (SE) using the formula: SE = sqrt(p * (1-p) / n), where n is the sample size.
SE = sqrt(0.2 * (1-0.2) / 400) ≈ 0.020 - Calculate the margin of error (ME) using the formula: ME = 1.96 * SE, where 1.96 is the z-score for a 95% confidence interval.
ME = 1.96 * 0.020 ≈ 0.0392 - Find the 95% confidence interval by subtracting and adding the margin of error from the proportion.
Lower limit: 0.2 - 0.0392 ≈ 0.1608
Upper limit: 0.2 + 0.0392 ≈ 0.2392
The 95% confidence interval for voters not favoring the incumbent governor is approximately 16.08% to 23.92%.
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