The formula to calculate the margin of error is:
\[ \text{MOE} = Z \times \sqrt{\frac{P \times (1 - P)}{n}} \]
Where:
The margin of error is a statistic expressing the amount of random sampling error in a survey's results. It represents the range within which we can expect the true value to lie with a certain level of confidence. The margin of error increases with the level of confidence but decreases with the sample size and the population proportion. It is a crucial concept in statistics and is used to express the precision of an estimate.
Let's assume the following:
Step 1: Calculate the margin of error:
\[ \text{MOE} = 1.96 \times \sqrt{\frac{0.5 \times (1 - 0.5)}{1000}} \approx 0.03098 \]
Therefore, the margin of error is approximately 0.03098 or 3.10%.