Calculate the variance version of standard error for each sample in Exercise 10.18—for the liberals (2, 1, 3, 2) and then for the conservatives (4, 3, 3, 5, 2, 4).

Steps to calculate the variance version of standard error:

1. Square the standard error.

2. Multiply the square of the standard error by the sample size.

The result should be the variance of the sample.

To calculate the variance version of the standard error for each sample, we need to follow these steps:

Step 1: Calculate the sample variance for each sample.
Step 2: Divide the sample variance by the square root of the sample size.

Let's calculate it for each sample:

Sample: Liberals (2, 1, 3, 2):

Step 1: Calculate the sample variance:
- Compute the mean of the sample: (2 + 1 + 3 + 2) / 4 = 2
- Calculate the squared difference between each observation and the mean: (2-2)^2 + (1-2)^2 + (3-2)^2 + (2-2)^2 = 2
- Divide the sum of squared differences by the sample size minus 1: 2 / (4-1) = 0.6667

Step 2: Calculate the variance version of the standard error:
- Divide the sample variance by the square root of the sample size: √(0.6667) / √4 = 0.4082

Therefore, the variance version of the standard error for the liberals sample is approximately 0.4082.

Sample: Conservatives (4, 3, 3, 5, 2, 4):

Step 1: Calculate the sample variance:
- Compute the mean of the sample: (4 + 3 + 3 + 5 + 2 + 4) / 6 = 3.5
- Calculate the squared difference between each observation and the mean: (4-3.5)^2 + (3-3.5)^2 + (3-3.5)^2 + (5-3.5)^2 + (2-3.5)^2 + (4-3.5)^2 = 4.5
- Divide the sum of squared differences by the sample size minus 1: 4.5 / (6-1) = 0.9

Step 2: Calculate the variance version of the standard error:
- Divide the sample variance by the square root of the sample size: √(0.9) / √6 = 0.2769

Therefore, the variance version of the standard error for the conservatives sample is approximately 0.2769.