Question

Candidate A claims he is getting a 60% positive approval rating. A recent poll has candidate A polling a 55% approval rating based on a sample of 600 voters (meaning 330 voters said they were approving of candidate A). Construct a 95% proportion confidence interval based on this data and determine whether the data supports the 60% claim.

Start by using the binomial distribution (p $N1ncatQAAAABJRU5ErkJggg==$ + q)ⁿ = 1, and x $HHv7mUDho+Bd6rUpbgAAAAASUVORK5CYII=$ = np $N1ncatQAAAABJRU5ErkJggg==$ .

1. What is n?
2. What is x?
3. What is p?
4. What is q?
5. What is p? (Note: p is based on our belief about the population. p is based on the sample)
6. Let σ_p = sqrt(pq/n). What is σ_p ?
7. We want to make a confidence interval by using the formula

z = k/σ_p

Should we use a 1 tail or 2 tail z-score?

8. What value of z corresponds to the desired 95% confidence interval?
1. What is k?
10. Construct the confidence interval

(p – k) < p_true < (p + k)

11. Is your confidence intervalconsistent with the belief that 60% approval rating claim? (yes or no, and explain your answer using your computed confidence interval).

Answer 1

a. n = sample size = 600 b. r = no. voters said they were approving of candidate A in a sample = 330 c. p= population proportion of voters who approve of candidate A d.q=1-p=population proportion of voters who do not approve of candidate A e. p= based on our belief = 0.60, p= based on the sample = p =- = 330/600 = 0.55 F.0p = P(1 – ) = 0.0203 g. We use 2 tail 2 – score h. 20.025 = 1.96 i. k = 20.025 * Op = 1.96 * 0.0203 = 0.0398 j. -k<Ptrue<Ô+k 0.55 – 0.0398 < Ptrue <0.55 + 0.0398 → 0.5102 <ptrue <0.5898. k. Since 0.60 > Upper boundary of 95% CI of Ptrue so answer is no.