The error of rejecting a true null hypothesis is known as:

Question

Accepted Answer

The correct option is 2:
In the field of hypothesis testing, the error of rejecting the null hypothesis (H0) when it is actually true is formally defined as a **Type I Error**. This is one of the two primary mistakes a researcher can make when drawing conclusions from statistical evidence. Conceptually, it represents a "false positive" outcome, where the test concludes a significant result (e.g., a new drug works, a market change occurred) when no such effect genuinely exists in the population. The probability of committing a Type I Error is denoted by the Greek letter alpha ($\alpha$), and its maximum acceptable risk is typically set beforehand as the level of significance, most commonly at 0.05 or 5%. This level of significance dictates the critical region for the test.

The incorrect option is 1:
**Type II Error** is the complement of the Type I Error, where the researcher *fails to reject* a null hypothesis that is, in fact, false. Essentially, this is a "false negative," meaning a real effect or difference exists but is missed by the statistical test. The probability of a Type II error is denoted by beta ($\beta$). Understanding the difference is crucial, as researchers often try to balance the risks of Type I and Type II errors; reducing the risk of one often increases the risk of the other. The probability of not committing a Type II error (1-$\beta$) is known as the power of the test.

The incorrect option is 3:
The **t-Test** is a statistical *test* or procedure, not an error type. It is a specific method used to compare the means of two groups (e.g., independent samples or paired samples) to see if the observed difference between them is statistically significant. It is a tool utilized *in* the process of hypothesis testing. Based on the calculated t-statistic and its p-value, a researcher makes the decision to either reject or fail to reject the null hypothesis, which is the step where a Type I or Type II error might occur.

The incorrect option is 4:
The **Chi-square Test** is also a statistical *test*, not an error. It is used to examine the distribution of categorical variables, such as testing for independence between two variables or checking how well observed data fits a theoretical distribution (Goodness of Fit). Like the t-Test, it provides a test statistic which is compared against a critical value to reach a decision about the null hypothesis. The test itself is an analytical methodology, not the conceptual mistake of incorrect rejection or acceptance.