Answer :
Based on a random sample, we can estimate the proportion of people in the city who support the incumbent mayor with 95% confidence.
To estimate the proportion of people in the city who support the incumbent mayor, we can use a confidence interval. The formula for calculating the confidence interval for a proportion is given by:
[tex]\[ \text{{Confidence Interval}} = \hat{p} \pm z \cdot \sqrt{\frac{\hat{p} \cdot (1 - \hat{p})}{n}} \][/tex]
where [tex]\(\hat{p}\)[/tex] is the sample proportion, z is the critical value based on the desired confidence level (95% in this case), and n is the sample size.
In this scenario, the sample proportion is [tex]\(\frac{896}{1600} = 0.56\)[/tex]. Since we want a 95% confidence level, the critical value z can be obtained from a standard normal distribution table or a statistical software and is approximately 1.96 for a large sample size.
Calculating the confidence interval:
[tex]\[ \text{{Confidence Interval}} = 0.56 \pm 1.96 \cdot \sqrt{\frac{0.56 \cdot (1 - 0.56)}{1600}} \][/tex]
Simplifying the expression gives us the confidence interval for the proportion of people in the city who support the incumbent mayor.
Learn more about confidence here:
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