# Standard Error (SE) of Mean & Proportion Calculator

Calculation summary & work with steps for *sample size* n_{1} = 50, n_{2} = 60, population proportion P_{1} = 0.35 & P_{2} = 0.45 to estimate the standard error of difference between two sample proportions. The below is the calculation summary for SE of (p_{1} - p_{2}) for sample size n_{1} = 50 & n_{2} = 60 using the p values P_{1} = 0.35 & P_{2} = 0.45.

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

Population proportion (P_{1}) | 0.35 |

Population proportion (P_{2}) | 0.45 |

Sample size (n_{1}) | 50 |

Sample size (n_{2}) | 60 |

SE of (p_{1} - p_{2}) | 0.0933 |

## SE of (p_{1} - p_{2}) Work with Steps for n_{1} = 50 & n_{2} = 60

The below is the example work with step by step calculation shows how to estimate the standard error of difference between two sample proportions for sample size n_{1} = 50 & n_{2} = 60 and the population proportions P_{1} = 0.35 & P_{2} = 0.45 to help grade school students to solve the similar SE of (p_{1} - p_{2}) worksheet problems efficiently.

__Workout :__

step 1 Address the formula, input parameters and values

__Input parameters & values__

Population Proportion P1 = 0.35

Population Proportion P2 = 0.45

Sample Size n

_{1}= 50

Sample Size n

_{2}= 60

__Formula__

SE

_{(p1-p2)}= √

P1Q1/n1+P2Q2/n2

step 2 Find Q from P Values

Q

_{1}= 1 - P

_{1}= 1 - 0.35

Q

_{1}= 0.65

Q

_{2}= 1 - P

_{2}= 1 - 0.45

Q

_{2}= 0.55

step 3 Apply the values in below formula

= √

(0.35 x 0.65)/50+(0.45 x 0.55)/60

= √

0.2275/50+0.2475/60

step 4 Simplify the above equation

= √0.0046 + 0.0041

= √0.0087

= 0.0933

0.0933 is the standard error for difference between two sample proprotions.