In a test of the correlation coefficient, the null hypothesis posits that there is no relationship between the variables in the broader population. This is formalized using the Greek lowercase rho ($\rho$) to represent the population parameter: $\rho = 0$. Conversely, the alternative hypothesis asserts that a relationship does exist in the population: $\rho \neq 0$. Researchers can specify this as a two-tailed test if they do not expect a specific direction, or a one-tailed test if they theoretically predict the relationship will be strictly positive or strictly negative.