V Similar to the previous exercise, let's assume that 50% of the population voted for Scott (p=0.50). V If this is the case, then the mean of the sampling distribution will be 0.5. Calculate the standard error of the sampling distribution of the sample proportion using the formula P(1 – p) Round your answer to 4 decimal places. n v Calculate the z-score for the proportion from the exit poll that voted for Scott (0.505). Round to 2 decimal places. V This time we've asked ourselves the question, "Suppose only half the population voted for Scott; would it then be surprising that 50.5% of the sampled individuals voted for him?" Based on your answers above, should you call the race for Scott? Explain your thoughts.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Question

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In an exit poll of 2,696 voters in the 2014 gubernatorial election in Florida, 50.5% said they voted for Rick Scott and 49.5% said they voted for Charlie Crist. Suppose you are at the “decision desk” and you need to decide if you are comfortable calling the race for Scott. To make this decision, do the following:

- **Assumptions:**
  - Similar to the previous exercise, let’s assume that 50% of the population voted for Scott (\(p=0.50\)).
  - If this is the case, then the mean of the sampling distribution will be 0.5.

- **Calculate** the standard error of the sampling distribution of the sample proportion using the formula:
  \[
  \sqrt{\frac{p(1-p)}{n}}
  \]
  - Round your answer to four decimal places.

- **Calculate** the z-score for the proportion from the exit poll that voted for Scott (0.505). Round to two decimal places.

- **Considerations:**
  - This time we’ve asked ourselves the question, “Suppose only half the population voted for Scott; would it then be surprising that 50.5% of the sampled individuals voted for him?” Based on your answers above, should you call the race for Scott? Explain your thoughts.

Note: This exercise involves doing calculations to explore whether the sample proportion significantly differs from the assumed population proportion, utilizing statistical tools such as standard error and z-scores to inform decision-making in an electoral context.
Transcribed Image Text:In an exit poll of 2,696 voters in the 2014 gubernatorial election in Florida, 50.5% said they voted for Rick Scott and 49.5% said they voted for Charlie Crist. Suppose you are at the “decision desk” and you need to decide if you are comfortable calling the race for Scott. To make this decision, do the following: - **Assumptions:** - Similar to the previous exercise, let’s assume that 50% of the population voted for Scott (\(p=0.50\)). - If this is the case, then the mean of the sampling distribution will be 0.5. - **Calculate** the standard error of the sampling distribution of the sample proportion using the formula: \[ \sqrt{\frac{p(1-p)}{n}} \] - Round your answer to four decimal places. - **Calculate** the z-score for the proportion from the exit poll that voted for Scott (0.505). Round to two decimal places. - **Considerations:** - This time we’ve asked ourselves the question, “Suppose only half the population voted for Scott; would it then be surprising that 50.5% of the sampled individuals voted for him?” Based on your answers above, should you call the race for Scott? Explain your thoughts. Note: This exercise involves doing calculations to explore whether the sample proportion significantly differs from the assumed population proportion, utilizing statistical tools such as standard error and z-scores to inform decision-making in an electoral context.
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