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?

To calculate the margin of error, you'll need to consider the sample size, the level of confidence, and the standard deviation of the population (if known). Here's a step-by-step explanation of the process:

1. Determine the sample size (n): This refers to the number of individuals or objects in your sample. The larger the sample size, the more accurate your results should be.

2. Choose a confidence level (C): This is the desired level of confidence in your estimate. Commonly used levels are 90%, 95%, and 99%. A higher confidence level means more certainty in the estimate but results in a wider confidence interval.

3. Find the critical value (z): The critical value corresponds to the desired confidence level and accounts for the variability in the population. You can find the critical value from a standard normal distribution table or use a calculator.

4. Calculate the standard deviation (σ) or standard error (SE): If the population standard deviation (σ) is known, then use it directly. Otherwise, estimate the standard error using the sample standard deviation (s) divided by the square root of the sample size (n).

5. Compute the margin of error (ME): Multiply the critical value (z) by the standard deviation (σ) or standard error (SE).

Margin of Error (ME) = z * σ or ME = z * (s / √n)

Now let's move on to how increasing the sample size affects different aspects:

Effect on Margin of Error: Increasing the sample size decreases the margin of error. As the sample size increases, the estimate tends to converge towards the actual population parameter, resulting in a smaller margin of error. The relationship between the sample size and the margin of error is inversely proportional.

Effect on Confidence Level: Increasing the sample size does not directly affect the confidence level. The confidence level is determined before conducting the study and represents the desired level of confidence. However, by increasing the sample size, you improve the precision of your estimate, which means the actual confidence level may be closer to the desired level.

Effect on Confidence Interval: Increasing the sample size decreases the width of the confidence interval. The confidence interval represents the range within which the population parameter is likely to fall. A larger sample size narrows down the range by providing a more accurate estimate, resulting in a shorter confidence interval. The relationship between the sample size and the confidence interval is inversely proportional.