Final answer:
In a two-tailed hypothesis test evaluating a Pearson correlation, the null hypothesis states that the population correlation is zero, signifying no significant linear relationship between the variables in the general population. Option 2 is the correct answer.
Step-by-step explanation:
In conducting a two-tailed hypothesis test for a Pearson correlation, the null hypothesis asserts that there is no linear relationship between the two variables being examined in the general population. Specifically, the null hypothesis states that the population correlation coefficient (ρ) is zero. This implies that any observed correlation in the sample data is due to random variation and is not reflective of a true relationship in the broader population. The alternative hypothesis, on the other hand, posits that there is a non-zero correlation, meaning that a significant linear relationship does exist between the two variables in the population.
If the test concludes the correlation coefficient is not significantly different from zero, it supports the null hypothesis, indicating no significant relationship. However, if the coefficient is significantly different from zero, it supports the alternative hypothesis, indicating a significant correlation.
The correct statement by the null hypothesis for a two-tailed test evaluating a Pearson correlation is: The population correlation is zero.