Questions: Two samples, each with n=5 scores, have a pooled variatue of 40. What is the estimated standard error for the sample mean difference? a. 4 b. 8 c. 10 d. 20

Solution Steps

To find the estimated standard error for the sample mean difference, we use the formula for the standard error of the difference between two means with equal sample sizes: \[ SE = \sqrt{\frac{2 \cdot s^2}{n}} \] where \( s^2 \) is the pooled variance and \( n \) is the sample size for each group.

Given:

• Pooled variance (\( s^2 \)) = 40
• Sample size (\( n \)) = 5

We can plug these values into the formula to find the standard error.

We are given the pooled variance \( s^2 = 40 \) and the sample size \( n = 5 \).

The formula for the estimated standard error \( SE \) for the sample mean difference is given by: \[ SE = \sqrt{\frac{2 \cdot s^2}{n}} \]

Substituting the given values into the formula: \[ SE = \sqrt{\frac{2 \cdot 40}{5}} \]

Calculating the expression: \[ SE = \sqrt{\frac{80}{5}} = \sqrt{16} = 4.0 \]

Final Answer