Final answer:
In hypothesis testing, the null hypothesis is rejected if the p-value is less than the significance level α. The decision is based on comparing these values, as well as understanding Type I and Type II errors associated with rejecting or not rejecting the null hypothesis.
Step-by-step explanation:
The task involves hypothesis testing concerning the difference between two means or proportions. In the context of hypothesis testing, when we compare α (alpha) and the p-value, we reject the null hypothesis if the p-value is less than α. For example, with an α of 0.05, if the p-value is 0.0175, we would reject the null hypothesis, indicating that there is a statistically significant difference between the two groups being compared. This is supported by evidence from specific test statistics calculated using various functions like 2-PropZTest or 2-SampTTest on a calculator.
Moreover, in hypothesis testing, Type I error occurs when the null hypothesis is rejected when it is actually true, while Type II error happens when the null hypothesis is not rejected when it is false. The seriousness of each error type depends on the context of the hypothesis being tested.