Calculating Margin of Error for a 95% Confidence Interval

How to calculate the margin of error for a 95% confidence interval?

Answer:

The margin of error for a 95% confidence interval can be calculated using the formula M = 1.96 × (s) / (√(N)), where M is the margin of error, s is the standard deviation, and N is the sample size.

Explanation:

Margin of Error Formula: M = 1.96 × (s) / (√(N))

To calculate the margin of error for a 95% confidence interval, you need to know the standard deviation of the sample and the sample size. The value 1.96 corresponds to a 95% confidence level.

Let's consider an example where the standard deviation is $10 and the sample size is 100:

Plug these values into the formula:

M = 1.96 × 10 / (√(100))

M = 1.96 × 10 / 10

M = 1.96

Therefore, the margin of error for a 95% confidence interval is approximately ± $1.96.

By calculating the margin of error, you can assess the precision of your sample data and determine the range in which the true population parameter is likely to fall.

For further information on margin of error, you can explore additional resources or seek more examples to deepen your understanding.