To calculate the 95 Percent Margin of Error:
\[ E = Z \times \sqrt{\frac{p \times (1 - p)}{n}} \]
Where:
A 95 percent margin of error is a statistical measure that indicates the range within which the true value of a population parameter is likely to fall 95 percent of the time. It is often used in polling or survey data to represent the uncertainty or variability that might be present in the data. The larger the margin of error, the less confidence one has that the poll’s reported percentages are close to the “true” percentages; that is, the percentages in the whole population.
Let's assume the following values:
Step 1: Multiply the sample proportion by 1 minus the sample proportion:
\[ p \times (1 - p) = 0.6 \times (1 - 0.6) = 0.6 \times 0.4 = 0.24 \]
Step 2: Divide the result by the sample size:
\[ \frac{0.24}{100} = 0.0024 \]
Step 3: Take the square root of the result:
\[ \sqrt{0.0024} \approx 0.049 \]
Step 4: Multiply by the Z-score (1.96):
\[ E = 1.96 \times 0.049 \approx 0.096 \]
The 95 Percent Margin of Error is approximately 0.096 or 9.6%.
