GENERATE WORK

GENERATE WORK

**Input Data : **

Sample Size(n) = 6

Probability = 0.8

Population size(N) = 8

**Objective : **

Find what is margin of error for given data?

**Formula **

Margin of error = 1.96 x √((N - n)/(n-1)) x √(p(1-p)/n)

**Solution :**

Margin of error = 1.96 x √((8 - 6)/(6-1)) x √((0.8 x (1 - 0.8))/6) x 100

= 1.96 x √(2/5) x √((0.8 x (0.2))/6) x 100

= 1.96 x √(0.4) x √(0.16/6) x 100

= 1.96 x √(0.4) x √(0.0267) x 100

= 1.96 x 0.6325 x 0.1634 x 100

Margin of error = 17.1083 %

** Margin of Error (ME) Calculator** - step by step calculation, formula & solved example problems online to determine the amount of random sampling error in experiments or survey results, from the input values of sample size, probability & population size. In statistics & probability, the larger & lower ME provides lower & higher confidence intervals.

It's a widespread abstract of sampling error, which measures an uncertainty about an experiment or test result. Generally, margin of error (ME) is 1.96 times of Standard Error. The *standard error calculation* can be done by the mathematical formula SE = (√((p(1-p)/n) )). Therefore **ME = 1.96 x √((p(1-p)/n) )**. 1.96 is the *z-score* for 95% confidence (commonly used), 1.64 is the z-score for 90% confidence level and 2.58 is the z-score for 99% confidence level. Margin of error arises whenever a population is incompletely sampled. The higher value provides lower confidence interval & the lower value provides higher confidence interval.

The below mathematical formula is used in this calculator to determine the uncertainty of an experiment result based on the input values of *sample size n*, probability p & population size N.

The below solved example may be useful to understand how the values are being used in the mathematical formulas to estimate the margin of error in statistical & probability experiment or survey results. The z-score 1.96 is commonly used value in this formula and it may gets changed sometimes based on the other confidence levels 90% & 99%, so please carefully select the z-score for the expected confidence level.

**Example Problem :**

Estimate the margin of error (ME) for the experiment having the probability expectation p = 0.3, confidence interval 95% & the sample size n = 1000?**Solution :**

Data given

probability p = 0.3

confidence level = 95%

so the z-score is 1.96 for 95% confidence interval

z = 1.96

sample size n = 1000

**Step by step calculation**

formula to find ME = z √(p(1-p)/n)

substitute the values in the above formula

= 1.96 x √(0.3 x 0.7/1000)

ME = **0.028**

The ME formulas, step by step calculation & solved example may be useful to understand the complete calculation, but for quick calculations, when it comes to online, this margin of error (ME) calculator may be useful to perform & verify such calculations quick as possible to analyze & summarize the statistical data