Question

In a recent poll, 134 registered voters who planned to vote in the next election were asked if they would vote for a particular candidate and 80 of these people responded that they would. 1. 1. We wish to predict the proportion of people who will vote for this candidate in the election.

a) Find a point estimator of the proportion who would vote for this candidate.

b) Construct a 90% confidence interval for the true proportion who would vote for this candidate.

c) If we wanted the margin of error in the previous problem to be less than 2%, what how many people should we sample?

2. If the candidate receives more than 50% of the votes, a win is guaranteed.

a) Construct the null and alternative hypotheses needed to test the claim that the candidate will have more than 50% of the vote and thus win the election.

b) Calculate the test-statistic and p-value for this hypothesis test.

c) At the .05 level, should the null hypothesis be rejected? Do we have evidence to suggest that the candidate will win the election?

Answer #1

**Solution:-**

**1)**

**a) The point estimator of the proportion who would vote
for this candidate is 0.5970**

**b) 90% confidence interval for the true proportion who
would vote for this candidate is** C.I = (0.5273,
0.6667).

C.I = 0.5970 + 1.645*0.04237

C.I = 0.5970 + 0.0697

**C.I = (0.5273, 0.6667)**

**c) The required sample size is 1628.**

n = 1627.613

**n = 1628**

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