The polling company found that 21% of 578 respondents supported the incumbent for re-election. Given this information, construct a 95% confidence interval for the actual percent of the population that supports the incumbent.

A. [tex]0.2012 < p < 0.2188[/tex]
B. [tex]0.1768 < p < 0.4490[/tex]
C. [tex]0.1664 < p < 0.2536[/tex]
D. [tex]0.1924 < p < 0.2276[/tex]

To construct a confidence interval for the actual percentage of the population supporting the incumbent, use the sample proportion and formula for the confidence interval.

Explanation:

To construct a confidence interval for the actual percentage of the population supporting the incumbent, we can use the sample proportion and the formula for the confidence interval. The formula for the confidence interval is:

p ± z √((p(1-p))/n)

Using the provided information, the sample proportion (p) is 0.21 and the sample size (n) is 578. The z-value for a 95% confidence level is 1.96. Plugging these values into the formula gives us:

0.21 ± 1.96 √((0.21(1-0.21))/578)

Simplifying this expression gives us the confidence interval of 0.1924 < p < 0.2276. Therefore, the correct answer is 00. 1924 < p < 0.2276.

Learn more about Confidence Interval here:

https://brainly.com/question/34700241

#SPJ1