Question

suppose you get a sample of 12400 people and 6200 people like the product
what is the standard error of the sample proportion

Answer 1

Sol:

step 1: understanding the problem satement

            here we need to find the standard error of the sample proportion .

    sample given is 12400

    people who like the product is 6200

step 2 : converting the statements to mathematical notation

lets take X=   people who like the product ( the number of success ) ie : X= 6200

lets take n= tottal number of observations (sample given) ie: n=12400

step 3: calculation of sample proportion

formula :                                                                                                     ( lets take    P = sample proportion)

                   P = x/n

  

( sample proportion = people who like the product / tottal number of observations ) --> for better understanding for the given problem )

    hence    P = 6200/12400

                      = 0.5

step 4: Now, the standard error of the proportion is need to find:

formula:

standard error = S.E = $\sqrt{(P*(1-P))/n}$

By applying formula ,

S.E = $\sqrt{(0.5*(1-0.5))/12400}$

       =$\sqrt{(0.5*0.5))/12400}$

       =$\sqrt{(0.25)/12400}$

      =

(0.00002016

     =0.00449013255 => 0.00449013 ( 8 digit accuracy)

step 5: solution

the standard error of the sample proportion is 0.00449013                                       

note: ( error value dont have specific unit)