Quantitative methods

In Reading 9: Correlation and regression, Practice Problems, problem no. 11, the solution says the absolute value -2.3017 is greater than the critical value 1.96. How?

I wanna know if that’s right, and if so how exactly is it being interpreted because if it were 2.3017 i.e positive, one can say its greater than 1.96 but this one’s negative and even if we consider -1.96, -2.3017 is still smaller than the critical value.

The absolute value of -2.3017, [-2.3017] is 2.3017, which is greater than 1.96.

Depending the sample value you are assessing (above o below the average), the calculated statistic will be negative or positive. As long as the distribution used is symmetric (like normal, Z, and T distributions), it does not matter the calculated statistic’s sign, so we use the absolute value for decision rules.