Best Answer:
Let me use examples to help explain this:

1) Let's say we have a population of 100 people sitting in a room and you want to know what's the average weight of the people in this room. If you go ask 20 people to tell you their weights, you might be able to get a small idea of the average of the 100 people in front of you. However, let's say you now go and ask 99 of the 100 people how much they weight. Now that your sample size of the population has increased, your margin of error will SURELY decrease. Think logically, what will be closer to the average, knowing only 20% of the population, or knowing 99% of the population? Naturally, when you know more information about the population (increase the sample), you will have a better idea of the mean (average), which in turn means that your error is decreasing. In other words, you now know 99% of the people in that room's weights, so you can get a VERY good idea of the average (because your error will only be as far off as the one person you didn't figure out), but when you only had 20 people, there were 80 people that could easily skew your answer in totally different directions.

2) Let's say I ask you to do a math problem. It's very difficult, but you tell me that you are 90% sure it's right. Thus, you aren't positive, but you think you would be right 9 out of 10 times. If I now asked you, "Do you think that 95% of the time this will be right?", then your answer would naturally be no, because you think only 90% of the time this would be right. Thus, in increasing confidence levels, you are more likely have some error. You can only be so confident in your answer, but as you increase the level that you are asked to be confident to, it is harder to know for sure the truth, and thus the error is increasing.

Another example of this would be to look at the example in problem 1. When you know 20 people's weights, you might calculate hypothetically that your average weight should be within 150 and 250 pounds 80% of the time (thus, I might be wrong 20% of the time). However, if I asked you to be 90% confident, you might have to say, "Well, if I wanted to definitely be right 90% of the time, I should increase the margin from 150-250 to 125-275." Thus, to be 90% confident, you would have to say that 80% of the time, people will weight from 150 to 250 pounds, but 90% of the time, people will weight from 125 to 275 pounds. If you want to be 100% confident, you would have to literally know the person who weighs the least and the most to create the entire interval. Thus, the interval (margin of error) clearly expands when you are asked to be more confident (level increasing).

I hope this helps! Please select as best answer if this helped so I can get credit for my time and effort. I greatly appreciate it. Thanks and good luck!!!

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