Confidence intervals: When would you ever construct an interval for a sample proportion if the population proportion is known?

#1
Hi everyone,

Looking at the attached text notes outlining confidence intervals, and how to construct confidence intervals for:
  • A sample mean (when the population standard deviation is known)
  • A sample mean (when the population standard deviation is unknown)
  • A sample proportion (when the population proportion is known)
  • A sample proportion (when the population proportion is unknown)
Why would you ever need to construct a confidence interval for a sample proportion when the population proportion is known? Isn't that what you are trying to estimate? If we have the population proportion, wouldn't it be unnecessary to try to estimate the population proportion?

Or is this formula (6.3 in the image) just to demonstrate that the standard deviation of the sampling distribution of proportions is based on what the value of the population proportion is, and so we use the sample proportion as our best estimate (formula 6.4)?

Ultimately, I'm just confused on when formula 6.3 would ever be used - if we're trying to estimate the population proportion, and we already *know* the population proportion, why are we trying to estimate it? Why does it say to use this formula when the population proportion is known?

Thanks,
Frodo
 

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katxt

Well-Known Member
#2
Why would you ever need to construct a confidence interval for a sample proportion when the population proportion is known?
Perhaps to estimate the potential range of a sample. A coin has a known 50% chance for a head. You may be interested in the largest number of heads you are likely to get if you throw 1000 coins.