Could someone have some insights?

Suppose that based on one measurement X, a sample size of N will be
enough to give me sufficient precision of the population mean with a
certain power.  Now, suppose we can only measure Y, but Y is highly
correlated with X, say with .9 correlation, is there any easy way to
compute the needed sample size based on Y to give similar precision of
the mean at the same power?

Thanks!




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