Survey Margin of Error Calculator (Sample Proportion)

Find the standard error and 95% confidence interval margin from a sample size and a proportion such as a TV rating.

Input

Enter a sample size and a proportion such as a TV rating to compute the standard error and the 95% confidence interval margin.

Sample size n

people

Number of people surveyed (sample count)

Rating (sample proportion)

Enter a value from 0 to 100

95% margin of error

±2.86%

Sample proportion plus or minus 1.96 times the standard error

95% confidence interval

12.14% to 17.86%

Standard error

1.46 %

z value (95%)

1.96

Calculation steps

Convert the rating 15.00% to a proportion and use the sample size n = 600.

Compute the standard error SE = sqrt(p(1 minus p)/n) = 1.46%.

Compute the 95% margin = 1.96 times 1.46% = 2.86%.

The confidence interval is 12.14% to 17.86%.

The standard error of a sample proportion is SE = sqrt(p times (1 minus p) divided by n), where p is the proportion from 0 to 1 and n is the sample size.
The 95% margin of error uses a z value of 1.96, so margin = 1.96 times SE.
The confidence interval is p plus or minus the margin. The interval is clamped to the 0 to 100 percent range for display.
Example: with a sample of 600 people and a rating of 15 percent, the standard error is about 1.46 percent and the 95% margin is about plus or minus 2.86 percent.
A larger sample size n gives a smaller error, shrinking in proportion to the square root of n.
The error is largest when the proportion is near 50 percent and smallest near 0 or 100 percent.
This is an approximation that assumes simple random sampling. Real surveys may differ due to the sampling design or a finite population correction.

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