# ELI5 Confidence Intervals and Margin of Error

Let’s say you are a company that provides a software-as-a-service (SaaS) subscription, and you’re considering investing in a higher engineering budget to improve your product. Before making this investment, you want to gauge whether customers would be willing to pay for an improved product, and whether the potential revenue increase would justify the cost of the investment.

You decide to conduct a survey of potential customers, offering them a discounted rate for a new, improved version of your product that is not yet available. You survey 200 people and find that 120 of them are interested in purchasing the discounted offer, while 80 are not.

To understand how confident you can be in this result, you can calculate a confidence interval and a margin of error.

First, you might calculate a 95% confidence interval for the proportion of potential customers who are interested in purchasing the discounted offer. This might give you a range of 55% to 71%, for example. This means that if you conducted the same survey many times, you’d expect the true proportion of potential customers who are interested in purchasing the discounted offer to fall within this range 95% of the time.

Next, you might calculate a margin of error for your survey results. This would give you an idea of how much your results might have varied if you had surveyed a different group of 200 potential customers. If your margin of error is +/- 7%, for example, this means that if you conducted the survey again with a different group of 200 potential customers, you’d expect the results to be within 7 percentage points of what you got the first time.

So, you could report your survey results by saying something like: “Based on our survey of 200 potential customers, we can be 95% confident that between 55% and 71% of potential customers are interested in purchasing our improved product at a discounted rate. Our margin of error is +/- 7%, so if we conducted the survey again with a different group of 200 potential customers, we’d expect the results to be within 7 percentage points of what we got the first time.”

This information would help you make an informed decision about whether to invest in a higher engineering budget. If the potential revenue increase from the improved product is higher than the cost of the investment, then it might make sense to move forward. If not, then you might need to reconsider your plans or find other ways to increase revenue.