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: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.