# Standard Error of Two Sample Means Difference for n_{1} = 100 & n_{2} = 150

Calculation summary & work with steps for *sample size* n_{1} = 100, n_{2} = 150, *population standard deviation* σ_{1} = 3 & σ_{2} = 3.5 to estimate the standard error of difference between two sample *means*. The below is the calculation summary for SE of (x̄_{1} - x̄_{2}) for sample size n_{1} = 100 & n_{2} = 150 using standard deviation σ_{1} = 3 & σ_{2} = 3.5.

Calculation Summary | |
---|---|

Population standard deviation (σ_{1}) | 3 |

Population standard deviation (σ_{2}) | 3.5 |

Sample size (n_{1}) | 100 |

Sample size (n_{2}) | 150 |

SE of (x̄_{1} - x̄_{2}) | 0.4144 |

## SE of (x̄_{1} - x̄_{2}) Work with Steps for n_{1} = 100 & n_{2} = 150

The below is the example work with step by step calculation shows how to estimate the standard error of difference between two sample means for sample size n_{1} = 100 & n_{2} = 150 and the population standard deviation σ_{1} = 3 & σ_{2} = 3.5 to help grade school students to solve the similar SE of (x̄_{1} - x̄_{2}) worksheet problems efficiently.

__Workout :__

step 1 Address the formula, input parameters and values

__Input parameters & values__

Population standard deviation σ

_{1}= 3

Population standard deviation σ

_{2}= 3.5

Sample size n

_{1}= 100

Sample size n

_{2}= 150

__Formula__

SD

_{x̄1 - x̄2}= √

σ1²/n1+σ2²/n2

step 2 Apply the values in above formula

= √

(3)²/100+(3.5)²/150

= √

9/100+12.25/150

= √0.09 + 0.0817

= √0.1717

= 0.4144

0.4144 is the standard error for σ

_{1}= 3, σ

_{2}= 3.5, n

_{1}= 100 & n

_{2}= 150.