# SE of 2 Sample Means Difference for n1 = 6 & n2 = 5, σ1 = 1.8257 & σ2 = 3.562

Calculation summary & work with steps for n1 = 6 & n2 = 5 with population A 94, 95, 94, 95, 97, . . . . , 93 & 99 and population B 97, 86, 89, 91, 92, 95, 87 & 89 to estimate the standard error of difference between two sample means. The below is the calculation summary for SE of (x̄1 - x̄2) for sample size n1 = 6 and n2 = 5 with polulation standard deviations σ1 = 1.8257 and σ2 = 3.562.

Calculation Summary
Population A94, 95, 94, 95, 97, . . . . , 93 & 99
Sample Size n16
Population B97, 86, 89, 91, 92, 95, 87 & 89
Sample Size n25
population standard deviation1) 1.8257
Population standard deviation (σ2) 3.562
SE of difference between 2 means (x̄1-x̄2)1.7587

## SE of x̄1 - x̄2 Work with Steps for n1 = 6, n2 = 5, σ1 = 1.8257 & σ2 = 3.562

The below is the example work with step by step calculation shows how to estimate the standard error of difference between two means for sample size n1 = 6, sample size n2 = 5 with population dataset A 94, 95, 94, 95, 97, . . . . , 93 & 99 and dataset B 97, 86, 89, 91, 92, 95, 87 & 89 to help grade school students to solve the similar SE of (x̄1-x̄2 worksheet problems efficiently.

Workout :
step 1 Address the input parameters and values
Population Dataset A = 94, 95, 94, 95, 97, . . . . , 93 & 99
Population Dataset B = 97, 86, 89, 91, 92, 95, 87 & 89
Sample size (n1) = 6
Sample size (n2) = 5

step 2 Find the mean for dataset A 94, 95, 94, 95, 97, 93, 95, 93 and 99

µ = n i = 1 Xin

=(94 + 95 + 94 + . . . . + 99)/9

Mean A (μA) = 95

Find the mean for dataset B 97, 86, 89, 91, 92, 95, 87 and 89

=(97 + 86 + 89 + . . . . + 89)/8

Mean B (μB) = 90.75

step 3 Apply the values of μA and dataset A in the below population standard deviation formula

Find the population standard deviation for 94, 95, 94, 95, 97, 93, 95, 93 & 99

=√{ (94 - 95)² + (95 - 95)² + (94 - 95)² + . . . . + (99 - 95)²}/9

= (-1)² + (0)² + (-1)² + . . . . + (4)²/9

= (1 + 0 + 1 + . . . . + 16)/9

= 30/9

= √3.3333

σ1 = 1.8257

Find the population standard deviation for 97, 86, 89, 91, 92, 95, 87 & 89

=√{ (97 - 90.75)² + (86 - 90.75)² + (89 - 90.75)² + . . . . + (89 - 90.75)²}/7

= (6.25)² + (-4.75)² + (-1.75)² + . . . . + (-1.75)²/8

= (39.0625 + 22.5625 + 3.0625 + . . . . + 3.0625)/8

= 101.5/8

= √12.6875

σ2 = 3.562

step 4 Substitute σ1, σ2, n1, n1 the values in below formula

SE(x̄1-x̄2) =
σ1²/n1+σ2²/n2

=
(1.8257)/6+(3.562²/5

=
3.3332/6+12.6878/5

= 0.5555 + 2.5376

= 3.0931

= 1.7587

1.7587 is the standard error of difference between two sample means.