Question 1169528
Absolutely! Let's break down how to compute the test statistic for a correlation coefficient.

**Understanding the Problem**

We are given:

* $n = 10$ (sample size)
* $r = 0.24$ (correlation coefficient)
* Significance level ($\alpha$) = 0.01

We need to calculate the test statistic for the correlation coefficient.

**Formula for the Test Statistic**

The test statistic for a correlation coefficient is calculated using the following formula:

$$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$$

**Step-by-Step Calculation**

1.  **Calculate $r^2$:**
    $$r^2 = (0.24)^2 = 0.0576$$

2.  **Calculate $1 - r^2$:**
    $$1 - r^2 = 1 - 0.0576 = 0.9424$$

3.  **Calculate $\sqrt{1 - r^2}$:**
    $$\sqrt{1 - r^2} = \sqrt{0.9424} \approx 0.97077$$

4.  **Calculate $\sqrt{n - 2}$:**
    $$\sqrt{n - 2} = \sqrt{10 - 2} = \sqrt{8} \approx 2.8284$$

5.  **Calculate $r\sqrt{n - 2}$:**
    $$r\sqrt{n - 2} = 0.24 \times 2.8284 \approx 0.6788$$

6.  **Calculate the test statistic $t$:**
    $$t = \frac{0.6788}{0.97077} \approx 0.6992$$

**Result**

Therefore, the test statistic is approximately 0.6992.

**Final Answer**

Test Statistic: n=10 t-test = 0.6992