How do you calculate needed sample size?

How do you calculate needed sample size?



Estimate a population mean:
- General formula is ME=t×Sn√ME=t×Sn or ME=z×sn√ME=z×sn
- MEME is the desired margin of error
- tt is the t score or z score that we need to use to calculate our confidence interval
- ss is the standard deviation

Example: we would like to start a study to estimate the average internet usage of households in one week for our business plan. How many households must we randomly select to be 95% sure that the sample mean is within 1minute from the true mean of the population? A previous survey of household usage has shown a standard deviation of 6.95 minutes.

-Z score corresponding to a 95% interval: 1.96 (97.5%, α2=0.025α2=0.025)
-s=6.95s=6.95
-n=(z×sME)2=(1.96×6.95)2=13.622=186n=(z×sME)2=(1.96×6.95)2=13.622=186

Estimate a proportion:
- Similar: ME=z×p(1−p)n−−−−−√ME=z×p(1−p)n

Example: a professor in Harvard wants to determine the proportion of students who support gay marriage. She asks "how large a sample do I need?"
-She wants a margin of error of less than 2.5%, she has found a previous survey which indicates a proportion of 30%.
n=0.3×0.70.0252

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