Question

Based on a sample of 178 residents in the United States, we found 95 of them support Joe Biden for the presidential election of 2020.
a) Suppose a statistician wants to construct a confidence interval for the proportion of all residents in the United States who support Joe Biden for the presidential election of 2020, what are the preliminary conditions that need to be verified, and what can we assume once the conditions are satisfied?
b) Construct a 88% confidence interval for the proportion of all residents in the United States who support Joe Biden for the presidential election of 2020, and state the confidence statement

Answer 1

a) We first check for randomness and independence. Once the conditions are satisfied we assume normality.

b) 88% CI= $\hat p±z^*\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$\hat p=\frac {95}{178}$ =0.5337

$=0.5337±1.55\sqrt{\frac{0.5337*(1-0.5337)}{178}}$

=(0. 4758,0.5916)

We are 88% Confident that the population proportion range between 0.4758 and 0.5916.