Based on the image you uploaded, the researcher performs a two-tailed test with:

• $n = 8$ pairs (sample size),
• Sample correlation $p = -0.94$,
• Using a t-distribution table to obtain the t-statistic for a two-tailed test.

Steps to solve:

(a) Find $t$ (up to 3 decimal places)

The test statistic $t$ for a correlation test is given by:

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

where:

• $r$ is the sample correlation,
• $n$ is the sample size.

Substitute $r = -0.94$ and $n = 8$:

$t = \frac{-0.94 \sqrt{8 - 2}}{\sqrt{1 - (-0.94)^2}}$

Let's calculate $t$.The calculated $t$-statistic is approximately $t = -6.749$.

(b) If the significance level $\alpha = 0.05$, choose the correct option.

To determine the critical value for $\alpha = 0.05$, look up the degrees of freedom $v = n - 2 = 6$ in the t-distribution table.

From the table provided:

• For $v = 6$ and $\alpha = 0.05$ (two-tailed), the critical value is 2.447.

Since $|t| = 6.749$ is greater than 2.447, we reject the null hypothesis, meaning there is a significant relationship.

Let me know if you need more details or clarifications.

Questions to expand:

1. What is the significance of the two-tailed test?
2. How does the t-distribution change with different degrees of freedom?
3. How do you interpret the critical value in hypothesis testing?
4. What is the null hypothesis in a correlation test?
5. How does the sample size impact the value of the t-statistic?

Tip: The larger the absolute value of $t$, the stronger the evidence against the null hypothesis.