The significance level in a hypothesis test corresponds to the maximum probability that

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BlackTom AI · Accepted Answer

The question asks about what the significance level in a hypothesis test represents in terms of error probabilities.
Option 1: 'both a Type I & Type II error will be committed.' This is not accurate. The significance level is fixed as a probability related specifically to Type I errors, not a statement about both error types occurring simultaneously.
Option 2: 'a Type I error will be committed.' This aligns with the standard interpretation: the significance level alpha is the maximum probability of rejecting a true null hypothesis, i.e., committing a Type I error.
Option 3: 'a false null hypothesis will not be rejected.' This describes failing to reject a false null hypothesis (a correct decision under full context), which is not what the significance level quantifies.
Option 4: 'a Type II error will be committed.' A Type II error refers to failing to reject a false null hypothesis, whose probability is beta and is not the definition of the significance level.
Option 5: 'a true null hypothesis will not be rejected.' While this describes a correct decision under a true null, it is not the formal definition of the significance level, which centers on the rate of incorrect rejections of true nulls.
In summary, the core concept is that the significance level bounds the risk of rejecting a true null hypothesis, i.e., a Type I error. The other statements either mix in Type II considerations or describe different aspects of decision accuracy that are not the definition of alpha.

OSC 2030-007 Fall 2025 Exam 2

The significance level in a hypothesis test corresponds to the maximum probability that

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