may seem like always choosing W r i t i n g
Does not need to be elaborate. Straight and to the point. Keep it simple
Assume that you are interested in doing a statistical survey and using confidence intervals for your conclusion. Describe a possible scenario and indicate what the population is, and what measure of the population you would try to estimate (proportion or mean) by using a sample.
- What is your estimate of the population size?
- What sample size will you use? Why?
- How will you gather information for your sample? Describe your process.
- What confidence percentage will you use? Why?
Assume that you have completed the survey and now state your results using a confidence interval statement. You can make up the numbers based on a reasonable result.
Here is an example of the instructor below:
Feel free to follow the format of my example below as you come up with your own example. I may end up being a little more wordy because I’ll try to explain any new concepts as they come up, and I’ll try to provide some reasoning behind it all too.
First, a confidence interval is simply an estimate. I could say that I estimate that the high temperature tomorrow will be between 20 and 30 degrees. That is a confidence interval. It starts with a point estimate which is a single value, and then you use a margin of error to create a buffer, or a range of values, for your estimate. In my temperature example, I was using 25 degrees as my point estimate (or best guess) for the high temperature tomorrow, and then came up with 5 degrees as my margin of error. Your final example should be set up in this same way.
Now let’s say I am interested in finding out the proportion of americans who prefer pepperonni on their pizzas. Let’s walk throguh the bullet points to set up my estimate for finding a confidence interval to esimate the actual proportion of americans who prefer pepperonni.
- My population will be roughly 300 million. This is nearly the size of the entire populaiton of america. There is no need to go so big in your own example, you could restrict to a smaller geographic region like a state, county, or your home town, or to a sub-population like all college students or all employees at a certain company. I didn’t use the entire population of america because for the most part babies probably don’t eat much pizza (silly babies!) and then there are people who don’t like pizza (they exist!)
- I will use a sample size of 200. It is realistic for me to be able to survey 200 people and collect that data, and I can actually come up with a fairly decent estimate using a sample that is only a tiny fraction of the entire population.
- I will use my live classroom questions to determine people’s favorite style of pizza and record that data over the course of the term (because I do anyway!).
- I will use the confidece percentage of 95%. Typical choices are either 95% or 99%. If I choose a confidence level of 95% it means that my estimate has a 95% chance of being good, but a 5% chance of being bad. In other words, my estimate will have a 95% chance of correctly estimating the true proportion of americans who prefer pepperonni. We are free to choose whatever confidence level we want. It may seem like always choosing a bigger confidence level is better, but increasing your confidence level actually makes for a bigger margin of error. Consider my weather example again. I may be 95% confident that the high temperature will be between 20 and 30 degrees tomorrow, but I could also be 99% confident that it will be between 10 and 40 degrees tomorrow. The 99% interval is bigger and so it has a bigger chance of being correct and capturing the actual high temperature, but the 95% interval is better at telling me what to wear when I go outside tomorrow even if it has a slightly higher chance of being wrong.
Now let’s pretend I competed my survey and have gathered the data and my sample found that 110 of the 200 people I surveyed stated they prefer pepperonni pizza. My point estimate is then 55% of all americans prefer pepperonni. If we assume I do the calculations and come up with a margin of error of 3.5% my confidence interval would become from 51.5% to 58.5%. I interpret this by saying that I am 95% confident that between 51.5% and 58.5% of americans prefer pepperoni on their pizza.
I hope this helps, but we’ll work on any mistakes your own examples have as we go through the week. You can actually find a few flaws with my own example here if you think about it for awhile.
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