MATH SOLVE

2 months ago

Q:
# 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

Accepted Solution

A:

Answer:standard error = 2.11Step-by-step explanation:First we stablish the data that we have for each sample:Population 1 Population 2n₁ = 100 n₂ = 90x¯1= 95 x¯2 = 75σ₁ = 14 σ₂ = 15 To calculate the standard error of each sample we would use the formulas:σ = σ₁/√n₁σx¯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 = 196σ₂² = (15)² = 225Now we can proceed to calculate the standard error of the distribution of differences in sample means: σx¯1 - σx¯2 = √(196/100 + 225/90) = 2.11This gives an estimate about how far is the difference between the sample means from the actual difference between the populations means.