Final answer:
In hypothesis testing, comparing the p-value with the significance level determines whether to reject or not reject the null hypothesis. For a significance level of 0.01 and a p-value of 0.12, we fail to reject the null hypothesis. If the significance level is 0.05 and the p-value is 0.015, the null hypothesis is rejected.
Step-by-step explanation:
The question involves making a decision to reject or fail to reject the null hypothesis based on the provided significance level (alpha, α) and the p-value. To compare we shall follow the rule that if the p-value is less than the significance level, we reject the null hypothesis. Conversely, if the p-value is greater than the significance level, we fail to reject the null hypothesis.
With α=0.01 and a p-value=0.12, since the p-value is greater than the significance level (0.12 > 0.01), the decision is to fail to reject the null hypothesis.
For α=0.05 and a p-value=0.015, because the p-value is less than the significance level (0.015 < 0.05), we reject the null hypothesis.
The process to determine these decisions includes a systematic comparison between the alpha value and the observed p-value. This is a fundamental concept in hypothesis testing, relevant to the assessment of statistical evidence against a presumed null hypothesis.