To estimate the proportion of the voting population that prefers Candidate A, we can use a point estimate and a confidence interval. The point estimate is the sample proportion, which is:
p-hat = 160/400 = 0.4
To construct a confidence interval for the true proportion p, we can use the following formula:
p-hat ± z*sqrt(p-hat*(1-p-hat)/n)
where z is the critical value for the desired confidence level, sqrt is the square root function, and n is the sample size.
At a 90% confidence level, the critical z-value is 1.645. Substituting the given values, we get:
0.4 ± 1.645*sqrt(0.4*(1-0.4)/400)
Simplifying this expression, we get:
0.4 ± 0.052
Therefore, the 90% confidence interval for the true proportion p is (0.348, 0.452).
This means that we can be 90% confident that the proportion of the voting population that prefers Candidate A is between 0.348 and 0.452.