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standard error for proportion is calculated as:

SE = sqrt [(p)(1-p) / n ]

so let us say that "p" is going to represent the decimal proportion of respondents who said YES.... so...

p = 20/25 = 4/5 = 0.8

And... we then are going to say that the complement of "p" which is "1-p" is going to represent the decimal proportion of respondents who said NO ... so... 1-p = 1 - 0.8 = 0.2

Lastly, the "n" in the formula for standard error is equal to 25 because "n" represents the sample size....

So now all you have to do is plug the values you found for "p" and for "1-p"... (remember "p = 0.8" and "1-p = 0.2")... and "n=25"....

Standard Error (SE) = sqrt [(p)(1-p) / n ]

............................ = sqrt [(0.8)(1-0.8) / 25 ]

............................ = sqrt [(0.8)(0.2) / 25 ]

............................ = sqrt [0.16 / 25]

............................ = sqrt (0.0064)

............................ = +/- 0.08

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Q: What is the standard error for the following proportion sample size of 25 and 20 of the respondents said yes?

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The mean of a proportion, p, is X/n; where X is the number of instances & n is the sample size; and its standard deviation is sqrt[p(1-p)]

A small sample size and a large sample variance.

It is 6.1, approx.

3 percent

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A small sample size and a large sample variance.

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