In the field of probability and statistics, a survey serves as a valuable tool for assessment. In a survey, a certain sample is collected and the information gained from the said sample is used for generalizing to large population. A good analogy to surveying would be that of taste-testing soup. The idea of how an entire pot of soup tastes like is gained from just a few spoons of the soup.
Randomness of survey is important
For any survey to be valid, randomness is very crucial. Coming back to the analogy, for a few spoons of the soup to represent the entire pot, the soup has to be stirred properly. Just like that, when a population is sampled, some stirring must be done before selecting the respondents. Choosing the respondents randomly is crucial for the results of the survey to generalize an entire population.
Confidence level and margin of error: two important statistics
Confidence level and margin of error are two vital statistics for determining how well a population is represented by the sample. They show how well a few spoons of soup represent the whole pot of it. For example, the pew research poll described in exercise 1 found that 49 percent of a certain sample of teens misrepresent their age when accessing online websites. For this question, you can determine the margin of error if the confidence level is given.
What do these statistics signify?
If the confidence level is 95, it means that if the survey was conducted 100 times, the percentage of teens who would misrepresent their age would remain around 49 percent 95 times out of 100. If the margin of error is 3 percent, it would remain within the range of 46 to 52 percent.
Thus, a margin of error signifies how many percentage points will the results differ from actual population value. Therefore, it shows the imprecision that is inherent in a survey data. A data from a survey never provides a certain number, it provides a range.
If a pew research poll is conducted every six months and the poll result decreases from 45 percent to 42 percent, the result is still accurate. This is because the result falls within the margin of error. At the same time, if the pew research poll described in exercise 1 found that 49 percent is the result, a conclusion can be made that there has been an increase in percentage, although a small one.
Statistics data isn’t always precise
The main idea behind margin of error and confidence level for any poll or survey is that the result will differ from the actual population by a certain percentage. Margin of error and confidence interval signifies the fact that there is room for error in a survey result.
For a survey, a confidence level of 95% and a margin of error of 2% might sound like a good statistic. However, with these statistics, a room for error is inferred, which means that statistics can be wrong sometimes.

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