Question

5. Political Science, Inc (PSI) specializes in voter polls and surveys designed to keep political office-seekers informed of their position in a race. Using telephone surveys (yuck!), PSI interviewers ask registered voters who they would vote for if the election were held that day. In a current election campaign, PSI has just found that 260 registered voters out of 500 contacted would favor a particular candidate. At a 90% confidence level, can the candidate conclude from this data that he currently has more than 50% of the registered voters on his side?6. Develop a 90% confidence interval estimate for the proportion of registered voters who favor this candidate at this time.

6. Develop a 90% confidence interval estimate for the proportion of registered voters who favor

this candidate at this time.

Answer 1

5)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.5
Alternative Hypothesis, Ha: p > 0.5

Rejection Region
This is right tailed test, for α = 0.1
Critical value of z is 1.28.
Hence reject H0 if z > 1.28

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.52 - 0.5)/sqrt(0.5*(1-0.5)/500)
z = 0.89

P-value Approach
P-value = 0.1867
As P-value >= 0.1, fail to reject null hypothesis.

No, candidate conclude from this data that he currently has more than 50% of the registered voters on his side

6)

sample proportion, = 0.52
sample size, n = 500
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.52 * (1 - 0.52)/500) = 0.0223

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.64

Margin of Error, ME = zc * SE
ME = 1.64 * 0.0223
ME = 0.0366

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.52 - 1.64 * 0.0223 , 0.52 + 1.64 * 0.0223)
CI = (0.4834 , 0.5566)