Question

the president of the student council wants to survey the student population. she decides to take a random sample of 100 students. she puts every students name on a rectangular slip of paper, each with the same length and width. then she places the slips of paper into a hat and, without looking, selects 100 slips of paper. is this a simple random sample?
yes, because the slips of paper were all the same shape and size.
no, because she did not look into the hat while she was selecting the sample.
yes, because she did not look into the hat while she was selecting the sample.
no, because she did not mix the pieces of paper in the hat before selecting the sample.

Explanation:

A simple random sample requires that each individual in the population has an equal chance of being selected. Just having slips of the same shape and size (Option 1) doesn't guarantee randomness. Not looking into the hat (Option 3) is not the key factor for a simple random sample. The crucial aspect is that if the slips are not mixed, there is a risk of bias (e.g., slips on top are more likely to be selected). So, Option 4 is correct as not mixing the slips violates the randomness requirement.

Answer:

No, because she did not mix the pieces of paper in the hat before selecting the sample.