A political pollster is conducting an analysis of sample results to make predict

Question

A political pollster is conducting an analysis of sample results to make predictions on election night. Assuming a two-candidate election, if a specific candidate receives at least 55% of the vote in the sample, then that candidate will be forecast as the winner of the election. As the election results start to be received you will assume that each candidate will receive 50% of the votes.

1. Determine the box model.

2. Compute the average and SD for the box.

3. If a sample of 100 voters is taken, what is the chance that they will receive more than 55% of the vote?

4. If a sample of 400 voters is taken, what is the chance that they will receive more than 55% of the vote?

5. If a sample of 1600 voters is taken, what is the chance that they will receive more than 55% of the vote?

6. You take a sample of 100 voters and one candidate receives 55 votes. Compute a 95% confidence interval based on this data.

7. You take a sample of 400 voters and one candidate receives 220 votes. Compute a 95% confidence interval based on this data.

8. You take a sample of 1600 voters and one candidate receives 880 votes. Compute a 95% confidence interval based on this data.

9. Summarize the results of your analysis as the sample size increases. What did you observe about the chances and the confidence intervals

Explanation / Answer

Z = (p^ - p)/sqrt(pq/n)

here p = 0.5 , q = 0.5

3)

P(p^ > 0.55)

= P(Z > (0.55 - 0.5)/sqrt(0.5*0.5/100))

=P(Z> 1)

= 0.1587

4)

P(p^ > 0.55)

= P(Z > (0.55 - 0.5)/sqrt(0.5*0.5/400))

=P(Z> 2)

=0.0228

5)

P(p^ > 0.55)

= P(Z > (0.55 - 0.5)/sqrt(0.5*0.5/1600))

=P(Z> 4)

=0.0000316

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