Question: 1. When calculating the sample size for estimating the population mean or the population proportion, is there ever a need to take a preliminary sample?

1. When calculating the sample size for estimating the population mean or the population proportion, is there ever a need to take a preliminary sample? Why?
2. Should we always round up the calculated sample size n for both the population mean and the population proportion? Why or why not?
3. Why is p = 0.5 used to calculate the sample size when estimating the population proportion when an approximate value of the population proportion is unknown?

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