You can’t always gather data from every member of a population, so you examine a sample. In this video, explore analyzing data using a sample, including estimating your margin of error.
- [Instructor] You can't always gather data from every member of a population, so you examine a sample. In this movie, I'll show you how to analyze data using a sample including estimating your margin of error. The first technique you should follow is to gather as large a sample as you can. Yes, it is certainly possible to reach a situation of diminishing returns where adding more samples doesn't improve the accuracy of your estimate or reduce the margin of error that much, but use your best judgment. Gather as many samples as you can.
Also, you need to estimate the population's standard deviation. This is based on previous surveys and also based on your knowledge of your business. Next, determine your desired confidence level. Do you want to be 90% certain? 95%? 99.7%? I will tell you that reaching a confidence level of 99% or higher can be very expensive because you need to capture a large sample. Typically, 95% is used if possible.
But if not, then 90% will also give you a good estimate. Finally, you need to calculate your margin of error, and I'll show you how to do that later in this movie. So what is your margin of error? Margin of error is often used in political polls to say that candidate A leads candidate B by 48 to 45% of the vote with a plus or minus 3% margin of error. If you want to put that into business terms, then you have say an olive oil company and that says each bottle contains 12 ounces of olive oil with a margin of error of plus or minus 0.03 ounces at a 95% level of confidence.
You rarely see the confidence level stated, but it's always there. In the political poll that I stated earlier, it's very likely that the poll was conducted at the 95% confidence level. So how do you calculate margin of error? Well, the first is that you need to calculate your standard error and that term is calculated as the sigma or standard deviation divided by the square root of your number of samples. So if you have 40 samples, you would take the square root of 40 as the divisor.
The margin of error is your standard error times what's called a z-score. So what's the z-score? Well, that is the number of standard deviations you are away from the mean. A z-score of one includes about 68% of the values. Fortunately, there are quite a few statistical texts out there and online references that allow you to look up commonly used z-scores. I'll show them here, but don't worry about writing them down. You can find them everywhere. For a confidence level of 80%, your z-score should be 1.28.
For 90%, 1.645. 95%, 1.96. 98%, 2.33. And 99%, 2.58. I'll close out with a sample margin of error calculation. Let's go back to our olive oil example and say that we have a standard deviation of 0.1 ounces. So in a 12 ounce bottle, 68% of all bottles will contain between 11.9 and 12.1 ounces. Let's say we want to go for 95% certainty which has a z-score of 1.96 and we're taking 40 measurements.
Our calculation is 1.96 which is our z-score multiplied by 0.1 divided by the square root of 40 and that is equal to about 0.03. That means that our margin of error is plus or minus 0.03 ounces. So each bottle will contain 12 ounces plus or minus 0.03 ounces with 95% confidence.
- Distinguish between the mean, median, and mode.
- Describe the relationship between variance and standard deviation.
- Identify a nondirectional hypothesis.
- Point out the difference between COVARIANCE.P and COVARIANCE.S.
- Explain correlation.
- Analyze Bayes’ rule.