Answer to Question #194547 in Statistics and Probability for FaynuseD

Question

Suppose we would like to gauge voters’ preferences for the President of Mars’ election. In an exit poll with a random sample of 120 voters, 30 voted for Mark Zuckerberg and 90 voted for Elon Musk. For the following, report your answers in 3 decimal places.

(a) Construct a 98% Wilson score confidence interval for Mars’ population proportion p supporting Elon Musk.

(b) Construct a 98% Wald confidence interval for p.

(c) Explain why Wald confidence intervals can have lower coverage in practice when compared to Wilson score confidence intervals

Answer 1

We have given that,

With a random sample of 120 voters, 30 voted for Mark Zuckerberg and 90 voted for Elon Musk

$p_1 = \dfrac{30}{120} = 0.25$

$p_2 = \dfrac{90}{120} = 0.75$

a.) $CI= p_1 \pm z\sqrt{\dfrac{p_1(1-p_1)}{n}}$

$CI = 0.25 \pm2.33 \sqrt{\dfrac{0.25 \times 0.75}{120}}$

$CI = 0.25 \pm 0.092$

b.) $CI= p_2 \pm z\sqrt{\dfrac{p_2(1-p_2)}{n}}$

$CI = 0.75 \pm2.33 \sqrt{\dfrac{0.25 \times 0.75}{120}}$

$CI = 0.75 \pm 0.092$

c.) We can clearly see that wald confidence interval have lower average coverage because the proportion for the wald's score is more as compared to wilson.