What is the consequence of a Type II error?

A Type II error occurs when a hypothesis test fails to reject the null hypothesis when in fact it is false. This means that the test concludes that there is not enough evidence to support the alternative hypothesis despite the reality that the alternative hypothesis may be true. Essentially, this type of error reflects a failure to detect an effect or difference that actually exists.

For example, if researchers are testing a new drug's effectiveness compared to a placebo, a Type II error would occur if the researchers conclude that the drug does not work (by failing to reject the null hypothesis) when it actually does provide a benefit. This error can be problematic because it can lead to missed opportunities for significant findings that could have beneficial implications.

In contrast, the other choices describe different scenarios: rejecting a true null hypothesis leads to a Type I error, incorrectly estimating population parameters does not directly relate to Type I or Type II errors, and concluding that a hypothesis has been proven is misleading since hypothesis tests can only provide evidence against the null hypothesis, not prove hypotheses outright.