How large a random sample do we need for the sample to be reasonable representative of the population? Most people think that we need a large percentage of the population, but it turns out that all that matters are the number of individuals in the sample

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How large a random sample do we need for the sample to be reasonable representative of the population? Most people think that we need a large percentage of the population, but it turns out that all that matters are the number of individuals in the sample. A random sample of 100 students in a college represents the student body just about as well as a random sample of 100 voters represents the entire electorate of the United States. How can it be that only the size of the sample, and not the population, matters? Imagine you a cooking soup. If you are cooking for a banquet rather than just for a few people, your pot will be bigger, but do you need a bigger spoon to decide how the soup taste? Of course not. The same size spoonful is probably enough to decide about the entire pot, no matter how large the pot. The fraction of the population that you've sampled doesn't matter. It's the sample, the number of individuals in the sample, that is important. In this activity you will start with the Margin of Error formula and use algebraic manipulations to find a formula for the sample size required to estimate a population proportion.

a) Assume that about 16% of people play video games. b) Assume that nothing is known about the worldwide percentage of people who play video games. c) Given that the required sample size is relatively small, could you simply survey the people that you know?