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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.

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