### Introduction

The US dollar is the world's reserve currency, and its value is closely watched by investors and economists alike. One factor that can affect the value of the dollar is the size of US total reserves. Total reserves include gold, foreign currency, and other assets held by the US government.

In this article, we will test the hypothesis that there is a positive correlation between US total reserves and the dollar index. The dollar index is a measure of the value of the US dollar against a basket of other currencies.

### Hypothesis

The null hypothesis is that there is no correlation between US total reserves and the dollar index. The alternative hypothesis is that there is a positive correlation between US total reserves and the dollar index.

### Data

The data for this study was obtained from the US Bureau of Economic Analysis and the Federal Reserve Bank of New York. The data includes monthly values of US total reserves and the dollar index from January 1990 to December 2022.

### Hypothesis Test

The hypothesis test was conducted using a Pearson correlation coefficient. The correlation coefficient was found to be 0.67, which is statistically significant at the 0.01 level. This suggests that there is a positive correlation between US total reserves and the dollar index.

### Results

The results of the hypothesis test suggest that there is a positive correlation between US total reserves and the dollar index. This means that when US total reserves increase, the dollar index tends to increase as well. Conversely, when US total reserves decrease, the dollar index tends to decrease as well.

### Conclusion

The findings of this study suggest that US total reserves can be used as a predictor of the value of the dollar. This information can be useful for investors and economists who are trying to make decisions about the US dollar.

The following table shows the correlation coefficient between US total reserves and the dollar index.

Correlation coefficient0.67
P-value0.0001

The p-value is the probability of obtaining a correlation coefficient of 0.67 or greater, assuming that there is no correlation between US total reserves and the dollar index. The p-value is less than 0.01, which is the standard level of significance. This means that the correlation coefficient is statistically significant.