To calculate the estimated standard error of the differences ($SE_d$) between the two conditions, we follow these steps:

Step 1: Calculate the Differences ($d$)

Since we have repeated measures, we will find the difference for each student between their scores under the two conditions: $\text{Additional social support}$ ($X_1$) and $\text{No additional social support}$ ($X_2$):

$d_i = X_{1i} - X_{2i}$

Step 2: Compute the Mean of the Differences ($\bar{d}$)

The mean difference $\bar{d}$ is calculated as:

$\bar{d} = \frac{\sum d_i}{n}$

where $n$ is the number of pairs (which is 6 in this case).

Step 3: Calculate the Sum of Squared Differences ($\sum (d_i - \bar{d})^2$)

To compute the standard error, we first need the sum of squared deviations of the differences from their mean.

Step 4: Calculate the Estimated Standard Error of the Differences ($SE_d$)

The formula for the estimated standard error of the differences is:

$SE_d = \sqrt{\frac{\sum (d_i - \bar{d})^2}{n (n-1)}}$

Now, let’s calculate each step:

1. Calculate the differences ($d$) between the two sets of scores.
2. Compute the mean of these differences.
3. Find the sum of squared deviations.
4. Calculate the standard error using the formula.

Let's compute this.The estimated standard error of the differences ($SE_d$) is approximately 8.9839 when rounded to four decimal places.

Would you like a detailed breakdown of these calculations or have any other questions?

Here are 5 related questions that could help deepen your understanding:

1. How do you interpret the result of a t-test using the standard error?
2. What are the assumptions of a paired t-test in this experimental design?
3. How does the standard error influence the t-statistic value?
4. Why is it important to use paired data when comparing conditions like this?
5. How would the calculation change if there were more participants?

Tip: The standard error measures how much the sample mean differences are expected to vary due to random sampling, which is crucial for determining if observed differences are statistically significant.