My colleagues and I argued about the point estimate's accuracy. They said that
"The point estimate will tend to be accurate if the sample size exceeds 30."
While I am saying no,
"The point estimate is always a subject to error as we will never know the population value"
Which is the correct one?
Both, really, at least, in some conditions. But also neither, in some conditions.
Your statement is correct, unless we actually do know the population value. This can happen if the population is small and easily defined. E.g "what is the average age of full time professors in NYU's psychology department?" But usually, your statement is right, we have a sample and do not know the population value perfectly.
However, if you have a random sample, then the accuracy goes up as sample size increases, and, for some distributions, 30 is reasonably accurate (for some definition of "reasonably"). How much accuracy you need varies by application.
But it also depends what you are estimating. It's easier to estimate the mean than the 90th percentile (for most distributions, anyway).
EDIT On the other hand, if you do not have a random sample, it doesn't matter how big your sample is. The most infamous example of this is the Literary Digest poll of the 1936 presidential election. They polled tens of millions of people and got millions of response and confidently predicted that Dewey would beat FDR in a landslide. But, FDR actually won one of the biggest landslides of any presidential election. What went wrong? The magazine polled subscribers to the magazine, car owners, and phone owners. In 1936 this was a very biased sample.
