Question

Use the formula to find the standard error of the distribution of differences in sample means, x¯1-x¯2. Samples of size 100 from Population 1 with mean 95 and standard deviation 14 and samples of size 90 from Population 2 with mean 75 and standard deviation 15 Round your answer for the standard error to two decimal places. standard error = Enter your answer in accordance to the question statement

Answer 1

standard error = 2.11

Explanation:

First we stablish the data that we have for each sample:

Population 1 Population 2

n₁ = 100 n₂ = 90

x¯1= 95 x¯2 = 75

σ₁ = 14 σ₂ = 15

To calculate the standard error of each sample we would use the formulas:

σ = σ₁/√n₁

σx¯2 = σ₂/√n₂

Now, in order to obtain the standard error of the differences between the two sample means we combine those two formulas to obtain this:

σx¯1 - σ x¯2 = √(σ₁²/n₁ + σ₂²/n₂ )

So as you can see, we used the square root to simplify and now we require the variance of each sample (σ²):

σ₁² = (14)² = 196

σ₂² = (15)² = 225

Now we can proceed to calculate the standard error of the distribution of differences in sample means:

σx¯1 - σx¯2 = √(196/100 + 225/90) = 2.11

This gives an estimate about how far is the difference between the sample means from the actual difference between the populations means.