## Introduction

I was interested in finding out if, during the 2012 election, was the average age of Republican voters greater than 51 years old. The data that I analyzed was collected by The American National Election Study (ANES) from a survey that was administered by Stanford University and the University of Michigan and funded by

the National Science Foundation.

In order to analyze this data and find out if indeed Republican voters were over the age of 51 at the time of the election, a one-sample t-test was conducted using the age data collected from the survey.

## Hypothesis

Null Hypothesis (H₀):

- The mean age of Republican voters is 51 years.

Alternative Hypothesis (H₁):

- The mean age of Republican voters is greater than 51 years.

## Test Type: One-Sample t-Test

The one-sample t-test is appropriate for this analysis because:

- We are comparing the sample mean to a known value (51 years)
- By using a large sample size (in this case, n = 5914), the Central Limit

Theorem ensures the sampling distribution of the mean is approximately normal, despite minor deviations in the distribution of ages.

## Test Results

Statistical Significance:

- The test statistic is -0.11252
- The p-value is 0.5448, which is greater than the significance level (α=0.05)
- We can fail to reject the null hypothesis because there is no statistically

significant evidence available to conclude that the mean age of Republican voters is greater than 51 years.

## Practical Significance

The sample mean age of 50.95639 years is very close to 51 years, suggesting that even if there is a difference, it is not practically significant.

## Conclusion

Overall, I found that the mean age of Republican voters in 2012 was not significantly different from 51 years. This result suggests that the age distribution of Republican voters is centered around this value.

**Mean Age:**The average age of Republican voters in 2012 is approximately

50.95639 years, aligning closely with the hypothesized mean, but not

exactly.**No Significant Difference:**Statistically, there is no significant evidence to

claim that the mean age is greater than 51 years.