Null hypothesis and error types – UGC NET Question

Statements A, B and C correctly describe the null hypothesis and the two basic error types. A explains that the null typically asserts no significant difference or relationship, B is accurate in stating that Type I error means rejecting a true null hypothesis, and C properly defines Type II error as failing to reject a false null hypothesis. Statement E is true because lowering alpha reduces the chance of Type I error, while F is also true since, for a fixed sample size, a lower alpha often increases the probability of Type II error. Only D is wrong because the alternative hypothesis is considered when evidence goes against the null, not when it supports it.

Option A:
Option A omits statement F, thereby failing to acknowledge the trade-off between Type I and Type II errors at a fixed sample size. While A, B, C and E are correct, excluding F means the option does not contain all the true statements in the list. Hence it is incomplete.

Option B:
Option B is correct because it includes A, B, C, E and F, covering definitions of hypotheses, both error types and the effects of changing alpha. It also correctly excludes D, which reverses the relationship between support for the null and acceptance of the alternative. This combination therefore contains all and only the true statements.

Option C:
Option C leaves out statement A, ignoring the basic statement about what a null hypothesis asserts. Although it includes B, C, E and F, missing A makes the description of hypothesis testing incomplete. As a result, this option is not acceptable.

Option D:
Option D omits statement B, which defines Type I error, and thus fails to describe a key component of hypothesis testing. Even though it includes A, C, E and F, missing B leaves a gap in understanding the full error structure. Consequently, this combination cannot be the correct answer.