Final answer:
The choice of significance level can indeed influence the decision whether to reject or fail to reject the null hypothesis in statistics.
Step-by-step explanation:
The statement in the question is false. The choice of significance level can indeed influence the decision whether to reject or fail to reject the null hypothesis.
The significance level, denoted by alpha (α), is the probability of making a Type I error. If the p-value, which measures the strength of evidence against the null hypothesis, is less than the significance level, we reject the null hypothesis. On the other hand, if the p-value is greater than the significance level, we fail to reject the null hypothesis.
For example, let's say we have a significance level of 0.05. If the p-value is calculated to be 0.03, which is less than 0.05, we would reject the null hypothesis. However, if the p-value is calculated to be 0.07, which is greater than 0.05, we would fail to reject the null hypothesis.