A candidate for an election takes a poll to determine if she will win a certain
ID: 3182847 • Letter: A
Question
A candidate for an election takes a poll to determine if she will win a certain election. In a poll of 1100 likely voters (chosen at random) 580 favor the candidate. Find a 96% confidence interval for the proportion of all likely voters that favor the candidate. Based on this information, do you think the candidate will win? Explain. Perform a one tailed hypothesis test to test the null hypothesis that the proportion of all likely voters who favor the candidate is equal to 0.5 against the hypothesis that it is greater than 0.5. Calculate the p-value, and give a conclusion at the 4% level of significance. Based on this information, do you think the candidate will win? Were the results in parts a and b consistent? Explain.Explanation / Answer
(A)
pcap = 580/1100 = 0.5273
sigma = sqrt(pcap * (1-pcap)/n) = sqrt(0.5273 * (1-0.5273)/1100) = 0.0151
For 96% CI, z-value = 2.05
lower limit = 0.5273 - 2.05*0.0151 = 0.4964
upper limit = 0.5273 + 2.05*0.0151 = 0.5583
From this CI, it is evident that contenstent will win an election.
(B)
Here null and alternate hypothesis are
H0: p = 0.5
H1: p > 0.5
value of test statistics,
z = (0.5273 - 0.5)/sqrt(0.5*0.5/1100) = 1.8109
p-value = 0.0351
Significance level = 0.04
As p-value is less than significance level, we reject the null hypothesis. This means there is significant evidence that she will get more than 50% of votes.
(c)
Results in parts a and b are consistent
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