The standard deviation of a sample taken from population A is 17.6 for a sample of 25. The standard deviation of a sample taken from population B is 21.2 for a sample of 30.
The standard deviation of the sample mean differences is_____. (Round your answer to the nearest hundredth.)
actually both answers are still wrong but i hope this elimination of answers helps
(Standard error of sample means) SEm = SD/√n
Calculate and compare.
.35 is what i got. not sure if its right but seems more realistic to 100
i'm trying .07425
To find the standard deviation of the sample mean differences, we need to use the formula for the standard deviation of the difference between two sample means.
First, we calculate the standard error of the mean (SE) for each sample. The formula for the standard error of the mean is:
SE = σ / √n
where σ is the population standard deviation and n is the sample size.
For population A:
SE_A = 17.6 / √25 = 3.52
For population B:
SE_B = 21.2 / √30 = 3.87
Next, we use the formula for the standard deviation of the difference between two sample means:
SD_diff = √((SE_A)² + (SE_B)²)
Plugging in the values:
SD_diff = √((3.52)² + (3.87)²)
= √(12.38 + 14.98)
= √27.36
≈ 5.23
Therefore, the standard deviation of the sample mean differences is approximately 5.23.