What happens to the estimated standard error as the sample variance increases?
Answer:
The standard error increases as the sample variance increases. The intuition is that one is less confident in the estimate of the standard deviation of the sampling distribution of a statistic the greater the variance in the sample.
the expected value of the error should not change or you have a whole set of problems. As the variance of the error increases Hypothesis testing or confidence in a prediction becomes more problematic. It becomes more difficult to reject in hypo testing; and, a your prediction confidence interval becomes wider making it more difficult to really predict a true value
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