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?

Q: How to calculate Margin Of Error?

Ans: One can determine this amount by using an algebraic formula, a chart or an online calculator. The surveyor only needs three numbers: population size, sample size and standard deviation, a whole number that represents the percentage of time respondents’ answers were evenly split. Once these numbers are determined, the formula is applied and the margin of error is determined. The larger the number, the more room there is for the poll to have error. By using margin of error, readers are able to get a clearer idea of what the numbers actually mean.

To calculate the margin of error, you'll need three pieces of information: the sample size, the standard deviation (or a reasonable estimate), and the desired level of confidence. Here's the step-by-step process:

1. Determine the sample size: This is the number of observations or individuals you have in your sample. A larger sample size generally leads to a more accurate estimate.

2. Estimate the standard deviation: Ideally, you would use the actual standard deviation of the population. However, if this is not available, you can estimate it based on a previous study, a pilot study, or use a standard value for a particular type of data.

3. Determine the desired level of confidence: The level of confidence indicates how sure you want to be that the true population parameter lies within your calculated interval. A common confidence level is 95%, which means you want to be 95% confident that your result represents the population.

4. Calculate the margin of error: The margin of error (ME) is calculated using the formula: ME = Z * (σ / √n), where Z is the Z-score corresponding to the desired confidence level, σ is the standard deviation (or estimated standard deviation), and n is the sample size.

Now, let's address the effects of increasing the sample size:

1. Effect on the margin of error: Increasing the sample size decreases the margin of error. As you collect data from more individuals, you have a larger sample that better represents the population. This increased precision reduces the variability in estimates, resulting in a smaller margin of error.

2. Effect on the confidence level: The confidence level remains the same regardless of the sample size. It is determined before the study and represents the desired level of certainty in your results. Therefore, increasing the sample size does not impact the confidence level.

3. Effect on the confidence interval: The confidence interval width is directly related to the margin of error. As the margin of error decreases with a larger sample size, the width of the confidence interval also decreases. A narrower confidence interval means more precise estimates and a higher level of confidence in the range of values within the interval.