Carol has data on the causes of violent outbursts among kindergarten children. She used a "shot-gun" approach to hypothesis testing by asking the computer to produce p-values for 300 quickly chosen hypothesis tests. She shared her glee with fellow researchers, noting that she had found 15 statistically significant results. She went so far as to brag that she had made some discoveries that defied all previously held notions about the wild behavior of this population of terrifying tots. She used the .05 level of significance. Explain why she actually found nothing.

Carol's approach to hypothesis testing, known as a "shot-gun" approach, is problematic for several reasons. Hypothesis testing involves making a claim or statement about a population based on sample data and determining the likelihood of obtaining such data if the null hypothesis (the statement being tested) is true.

In Carol's case, she conducted 300 hypothesis tests without a clear research question or specific hypotheses. This approach increases the likelihood of finding statistically significant results by chance alone, even when no true effect or relationship exists in the population.

When we conduct multiple hypothesis tests, we need to account for the increased probability of obtaining false positives, also known as Type I errors. This is done by applying appropriate adjustments, such as Bonferroni correction, to the significance level.

In Carol's case, she used a significance level of 0.05 for each individual test without adjusting it for multiple comparisons. This means that, on average, she would expect to find 15 statistically significant results purely by chance even if all the null hypotheses were true.

Therefore, her claim of making groundbreaking discoveries about the causes of violent outbursts among kindergarten children is most likely misleading and unsupported. In reality, she did not find anything significant because her findings were likely due to chance rather than actual relationships or effects in the population.

To avoid such issues in hypothesis testing, it is important to define clear research questions, formulate specific hypotheses, and utilize appropriate statistical techniques that account for multiple comparisons. Adjusting the significance level or employing methods like Bonferroni correction helps maintain the integrity of the results and minimize false discoveries.