Explain how to calculate margin of error.

What effect does increasing your sample size have on the margin of error?

What effect does it have on the confidence level?

What effect does it have on the confidence interval?

Calculating the margin of error involves several steps:

1. Determine the desired confidence level: This is typically expressed as a percentage (e.g., 95%, 99%).

2. Determine the sample size (n): This is the number of observations or participants in your study. The larger the sample size, the more accurate your estimate will be.

3. Calculate the standard error (SE): The standard error is a measure of the variability or dispersion of the sample estimate. It is calculated by dividing the standard deviation of the population by the square root of the sample size.

4. Determine the critical value (Z-score): This value corresponds to the desired confidence level. It can be obtained from a standard normal distribution table or using statistical software.

5. Calculate the margin of error (ME): The margin of error is the product of the standard error and the critical value. It represents the maximum amount of error you should expect in your estimate.

Increasing the sample size has a direct effect on the margin of error. As the sample size increases, the variability or dispersion of the estimate decreases. This leads to a smaller standard error and, consequently, a smaller margin of error. Therefore, increasing the sample size improves the precision of the estimate.

The confidence level represents the level of certainty or probability that the true population parameter falls within the calculated interval. It is typically expressed as a percentage. Increasing the sample size does not have a direct effect on the confidence level. The confidence level depends on the chosen critical value and remains unchanged regardless of the sample size.

The confidence interval is a range of values that likely contains the true population parameter. It is calculated by adding and subtracting the margin of error from the sample estimate. Increasing the sample size narrows the confidence interval, making it more precise. This means that the estimated range becomes smaller, indicating higher confidence in the estimated parameter.