To compute the estimated standard error of the differences for this paired sample t-test, we need to follow these steps:

Step 1: Find the differences between the paired scores

First, calculate the differences between the scores for each participant when they received additional social support and when they did not.

$\text{Difference} = \mu_1 - \mu_2$

Additional Social Support ($\mu_1$)	No Additional Social Support ($\mu_2$)	Difference ($D$)
86	70	$86 - 70 = 16$
81	47	$81 - 47 = 34$
82	83	$82 - 83 = -1$
78	69	$78 - 69 = 9$
22	53	$22 - 53 = -31$
96	79	$96 - 79 = 17$

So the differences are: $D = [16, 34, -1, 9, -31, 17]$.

Step 2: Calculate the mean of the differences ($\overline{D}$)

$\overline{D} = \frac{\sum D}{n} = \frac{16 + 34 - 1 + 9 - 31 + 17}{6} = \frac{44}{6} = 7.3333$

Step 3: Calculate the variance of the differences

The variance of the differences is given by:

$s_D^2 = \frac{\sum (D - \overline{D})^2}{n - 1}$

Now, subtract the mean from each difference and square the result:

$(16 - 7.3333)^2 = 75.1111, \quad (34 - 7.3333)^2 = 711.1111, \quad (-1 - 7.3333)^2 = 69.4444$ $(9 - 7.3333)^2 = 2.7778, \quad (-31 - 7.3333)^2 = 1475.1111, \quad (17 - 7.3333)^2 = 93.4444$

Sum these squared differences:

$75.1111 + 711.1111 + 69.4444 + 2.7778 + 1475.1111 + 93.4444 = 2426.9999$

Now divide by $n - 1 = 6 - 1 = 5$:

$s_D^2 = \frac{2426.9999}{5} = 485.39998$

Step 4: Calculate the standard deviation of the differences

The standard deviation is the square root of the variance:

$s_D = \sqrt{485.39998} = 22.0341$

Step 5: Compute the estimated standard error of the differences ($SE_D$)

The standard error of the differences is given by:

$SE_D = \frac{s_D}{\sqrt{n}} = \frac{22.0341}{\sqrt{6}} = \frac{22.0341}{2.4495} = 9.0000$

Conclusion:

The estimated standard error of the differences is 9.0000 (rounded to four decimal places).

Would you like more details or have any questions?

Here are 5 questions that expand on this information:

1. How is the t-statistic calculated using the standard error of the differences?
2. What assumptions are made in a paired sample t-test?
3. How would you interpret the results if the t-statistic is significant?
4. How does the standard error change with a larger sample size?
5. What are some factors that could affect the life satisfaction scores in this experiment?

Tip: Always check that the data meets the assumptions of the paired t-test (normality, independence, etc.) before running the test.