Question

The 2000 election fiasco in Florida has raised some serious questions regarding election reform. One poll specifically asked voters if they favor doing away with the Electoral College and choosing the president using a strictly popular vote (in which each vote is counted) of the people. The sample of 1,200 voters was taken and the results are given below. Please note that the results shown are for the proportion of those sampled that favored doing away with the Electoral College and favored using a popular vote.

Hypothesis Test - One Proportion

Sample Size 1200

Successes 675

Proportion 0.56250

Null Hypothesis: P = 0.54

Alternative Hyp: P > 0.54

Difference 0.02250

Standard Error 0.01432

Z (uncorrected) 1.56

Method 95% Confidence Interval

Simple Asymptotic (0.53443, 0.59057)

Based on the confidence interval information presented in the print out, do you believe that 50% of the population favored doing away with the Electoral College?

I am 95% confident that more than 50% of the population favor doing away with the Electoral College

I am 95% confident that less than 50% of the population favor doing away with the Electoral College

I am 95% confident that exactly 50% of the population favor doing away with the Electoral College

Is the sample size of n=1200 large enough to use this inferential procedure?

No

Yes, since n ≥ 30

Yes, since the central limit theorem works whenever proportions are used.

Yes, since both np and nq are greater than or equal to 15.

Answer 1

(a)

Correct option:

I am 95% confident that more than 50% of the population favor doing away with the Electoral College

Explanation:

Since all the values of the 95% Confidence Interval: (0.53443, 0.59057) are greater than 0.5, we conclude that I am 95% confident that more than 50% of the population favor doing away with the Electoral College

(b)

Correct option:

Yes, since n ≥ 30

Explanation:

By Central Limit Theorem, for Large Sample: n 30, the sampling distribution of sample proportion is Normal Distribution irrespective of the shape of the population.