# Thread: Quick! How do I find this test statistic?

1. ## Quick! How do I find this test statistic?

Consider the following summarized results of 18 pairs of data: SXX = 10, SYY = 160, SXY = -32. What is the value of test statistic for testing the following hypotheses? H0: ρ = 0 vs. H1: ρ ≠ 0

How can I find the test statistic from this info? I've broken it down into:
10=(Sum)X^2 - (Sum X)^2 / 18...etc. But I have no idea to find these initial values so I can work through the problem. Or am I totally off base?

2. Originally Posted by helpwithstats09
Consider the following summarized results of 18 pairs of data: SXX = 10, SYY = 160, SXY = -32. What is the value of test statistic for testing the following hypotheses? H0: ρ = 0 vs. H1: ρ ≠ 0

How can I find the test statistic from this info? I've broken it down into:
10=(Sum)X^2 - (Sum X)^2 / 18...etc. But I have no idea to find these initial values so I can work through the problem. Or am I totally off base?
The test statistic is $\displaystyle t = \frac{r}{\sqrt{1 - r^2}} \cdot \sqrt{n - 2}$ which follows Student's t-distribution with (n - 2) degrees of freedom.

So your task is to first calculate the sample correlation coefficient $\displaystyle r$.