Answer :
Final Answer:
(a) Assumption: Sample of 250 voters is randomly selected and representative.
(b) Estimator: Using sample proportion [tex](\(\hat{p}\))[/tex] as estimator for population proportion.
(c) Estimate: With 90% confidence, incumbent support is approximately 36.37% to 43.63%.
(d) Interpretation: We're 90% confident the true proportion lies in this interval.
Explanation:
(a) Assumption: We assume that the sample of 250 voters was randomly selected and that it is representative of the entire voting population. This is crucial for the validity of our estimation.
(b) Estimator: The sample proportion [tex](\(\hat{p}\))[/tex] is a commonly used estimator for the population proportion. In this case, [tex]\(\hat{p} = \dfrac{40}{100} = 0.40\)[/tex].
(c) Estimate: To construct a 90% confidence interval, we use the formula for the confidence interval of a proportion:
[tex]\[CI = \hat{p} \pm z \sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}\][/tex]
Where n is the sample size (250 in this case), and z is the z-score corresponding to a 90% confidence level. The z-score for a 90% confidence level is approximately 1.645.
(d) Interpretation: With 90% confidence, we estimate that the population proportion of voters who support the incumbent candidate lies within the interval calculated in part (c). This means that we are 90% confident that the true proportion falls within this interval.
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