a sample of n=25 scores has a mean of M=65 and an estimated standard error of 2 points. What is the sample variance
SEm = SD/√n
Variance = SD^2
kbk
The sample variance can be calculated using the estimated standard error as follows:
Sample Variance = (Estimated Standard Error)^2 * (sample size)
Given that the estimated standard error is 2 points and the sample size is 25, we can substitute these values into the formula to find the sample variance:
Sample Variance = (2)^2 * 25
= 4 * 25
= 100
Therefore, the sample variance is 100.
To find the sample variance, we can use the formula:
Sample Variance = (Σ(x - M)²) / (n - 1)
Where:
- Σ refers to the sum of the values
- x represents each individual score in the sample
- M is the mean of the sample
- n is the number of scores in the sample
- (n - 1) is the degrees of freedom correction factor
In this case, we are given that the mean (M) is 65, and the number of scores (n) is 25. However, we do not have the individual scores of the sample.
The estimated standard error (SE) of 2 points can be used to calculate the standard deviation of the sample, assuming the distribution is approximately normal. The standard deviation (SD) is related to the standard error as follows:
SD = SE * √n
In this case, SD = 2 * √25 = 2 * 5 = 10.
Now that we have the standard deviation (SD), we can calculate the sample variance using the formula mentioned earlier:
Sample Variance = (Σ(x - M)²) / (n - 1)
However, without knowing the individual scores of the sample, we cannot calculate the sample variance exactly. We need the actual data to compute the deviations from the mean and then complete the calculation.