The standard deviation of GPAs (grade point averages) of all male students at a college is .35 and the standard deviation of GPAs of all female students at the same college is .34. Suppose we take one sample of 40 male students and another sample of 50 female students from this college. What is the standard deviation of the sampling distribution of the difference between the mean GPAs of these two samples?
.13
To find the standard deviation of the sampling distribution of the difference between the mean GPAs of these two samples, we can use the formula:
Standard deviation of the difference = square root [(standard deviation of the first sample)^2 / (sample size of the first sample) + (standard deviation of the second sample)^2 / (sample size of the second sample)]
Let's plug in the given values into the formula:
Standard deviation of the difference = square root[(0.35^2 / 40) + (0.34^2 / 50)]
Now, let's calculate the standard deviation of the difference using a calculator or a spreadsheet:
Standard deviation of the difference ≈ √(0.001225 + 0.001156) ≈ √0.002381 ≈ 0.0488
Therefore, the standard deviation of the sampling distribution of the difference between the mean GPAs of these two samples is approximately 0.0488.