Which combination of factors will increase the chances of rejecting the null hypothesis?

Question

BlackTom AI · Accepted Answer

To evaluate which combination would raise the likelihood of rejecting the null hypothesis, we need to consider how standard error and the alpha level affect test statistics and decision rules.
Option 1: a small standard error and a small alpha level. A smaller standard error increases precision and can help detect effects, but a smaller alpha makes it harder, not easier, to reject the null, because the threshold for significance is stricter. So this pair has opposing effects: one favorable, one unfavorable.
Option 2: a large standard error and a small alpha level. A large standard error reduces the test statistic's magnitude and makes it harder to achieve significance, and a small alpha further tightens the criterion. Both factors work against rejecting the null, making this the least favorable combination.
Option 3: a small standard error and a large alpha level. Here, the precision is high (small SE), which helps detect true effects, while a large alpha level lowers the bar for declaring significance, increasing the chance of rejection. These factors reinforce each other toward rejecting the null.
Option 4: a large standard error and a large alpha level. The large standard error weakens the signal by broadening the estimate, while a large alpha eases significance criteria. The net effect is mixed: the looser alpha helps, but the imprecision generally undermines ability to detect effects, so this is not as favorable as option 3.
In summary, the combination that both tightens estimation error and relaxes the significance threshold aligns to maximize the chance of rejecting the null, whereas the other options mix opposing influences or introduce weakening factors.

Which combination of factors will increase the chances of rejecting the null hypothesis?Single choice

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