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I am severely stumped on this question:

Imagine a study in which a researcher has very low statistical power (<10%), thus a high Type II error rate. Will the point estimate of this study likely be over- or underestimated in comparison to the true population estimate? Provide a short rationale.

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    $\begingroup$ This doesn't have a definite answer, because the bias in a point estimate has no direct (or even strong) relationship to the power of some hypothesis test that might be based on it. You can easily construct examples with low power in which the corresponding point estimate is unbiased, biased low, or biased high: just begin with one unbiased procedure and one biased procedure and contemplate what happens with tiny sample sizes. $\endgroup$ – whuber♦ Oct 23 '20 at 22:00
  • $\begingroup$ To me it feels like this question is maybe missing a few key words. It would make more sense if it included phrasing like "in the case of significant finding within this study, would the estimate be over or under estimated ...". $\endgroup$ – Karolis Koncevičius Oct 23 '20 at 22:16
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Imagine, that we flip a coin in order to determine if it is a fair coin. And in fact it is a fair coin.

We throw only two times and we have one heads one tails. We have exactly right point estimate, which happen in 50% of such test procedures. Also the expected value of possible results is 50%, so our result did not happen accidentally.

We have very low power of the test, however the point estimate is not biased.

Also, we have very high variance of the point estimate. There is 25% chance, that our test will suggest 0% for heads, and same chance to show 100%.

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