UGC NET Questions (Paper – 1)

Statement C is wrong because statistical significance does not automatically imply practical importance; a small effect can be statistically significant in a large sample yet practically trivial. Statements A, B, D and E correctly describe the roles and potential misuses of statistics, including summarising data, the risk of misleading presentations, the need to report methods and the importance of understanding assumptions. Therefore, C alone is the incorrect statement in the list.

Option A:
Option A is correct because it isolates C as the sole misleading statement and acknowledges that the remaining statements align with good statistical practice. It emphasises the distinction between statistical and practical significance, which is crucial for sound interpretation.

Option B:
Option B is incorrect because it also labels A as wrong, even though A correctly explains that statistics help reveal patterns and relationships in data. Treating A as wrong underestimates the central purpose of statistical analysis.

Option C:
Option C is also wrong because it groups D with C, despite D rightly stressing transparency in reporting methods. Misclassifying D as wrong contradicts the principle of reproducible research.

Option D:
Option D is incorrect because it adds B and E to the set of wrong statements. Both B and E accurately warn about misleading presentations and the need to understand test assumptions, so including them with C misrepresents statistical best practices.

A Type I error occurs when the null hypothesis is actually true but the sample data lead the researcher to reject it, suggesting an effect that does not exist in the population. It is also called an alpha error or false positive. The chosen significance level, such as 0.05, represents the maximum probability of committing this kind of error under repeated sampling. Therefore, incorrectly rejecting a true null hypothesis is known as a Type I error.

Option A:
Option A clearly labels this error as Type I, which is central to decisions about the significance level and interpretation of p-values. Researchers aim to keep the probability of such false alarms low, consistent with the description in the stem.

Option B:
A Type II error, by contrast, occurs when a false null hypothesis is not rejected, leading to a failure to detect a real effect; this is a false negative situation, not the false positive described. Hence, Type II is not the correct answer.

Option C:
Sampling error refers more broadly to the natural differences between sample statistics and population parameters due to using a subset of the population. While related to hypothesis testing, it is not the specific decision error of rejecting a true null.

Option D:
Measurement error involves inaccuracies in data due to instrument flaws or respondent factors and is different from the inferential decision errors in hypothesis testing, so it is not appropriate here.

A Type I error occurs when a researcher concludes that an effect or difference exists in the population when in fact the null hypothesis is true. It is analogous to a false positive decision. The probability of committing a Type I error is controlled by the significance level alpha, such as 0.05. Therefore, the error of rejecting a true null hypothesis described in the stem is called a Type I error.

Option A:
Type II errors occur in the opposite situation, when a false null hypothesis is not rejected, corresponding to a false negative; this is not the scenario given.

Option B:
Random error refers broadly to unpredictable fluctuations in data due to chance influences, not specifically to the decision error of rejecting a true null hypothesis.

Option C:
Systematic error involves consistent bias in measurement or procedure, which affects estimates but does not directly define the statistical decision about hypotheses.

Option D:
Type I errors are a central concern in hypothesis testing because setting a low alpha reduces their likelihood, though it may increase Type II errors. This link with rejecting true null hypotheses fits the stem exactly, making this option correct.

Statement D is wrong because a p-value does not directly give the probability that the null hypothesis is true; it is the probability of obtaining results as extreme as those observed, assuming the null is true. Statements A, B, C and E are correct: inferential methods generalise from samples, significance depends on several factors, confidence intervals express plausible parameter ranges and context plus effect size are vital for interpretation. Thus, only D is the incorrect statement.

Option A:
Option A is incorrect because it also labels A as wrong, despite A correctly explaining the purpose of inferential statistics. Disputing A blurs the distinction between sample-level and population-level reasoning.

Option B:
Option B is correct because it isolates D as the single misinterpretation, while implicitly confirming the other statements as accurate. It emphasises that the p-value is often misunderstood and must be interpreted cautiously.

Option C:
Option C is wrong because it treats C, which accurately describes confidence intervals, as wrong along with D. This misrepresents a core concept in inferential statistics.

Option D:
Option D is incorrect because it declares B and E wrong along with D, even though both B and E reflect best practice for interpreting statistical results by considering multiple determinants and substantive meaning.

Statements A, B, D, E and F correctly explain aspects of significance testing, while C is wrong. Statement A is true because the null hypothesis typically asserts no difference or relationship, and statement B is correct that a small p-value suggests the data are unlikely under the null. Statement D rightly notes that not rejecting the null does not prove it true, and statement E is correct in pointing out that large samples can make small effects significant. Statement F is also true because practical interpretation requires attention to effect size and context, whereas C is false because statistical significance does not guarantee practical importance.

Option A:
Option A labels C and D as wrong, but D is actually a correct caution about interpreting non-rejection of the null. Misclassifying D as wrong makes this combination conceptually flawed.

Option B:
Option B treats A and C as wrong, but A is a standard definition of the null hypothesis and is therefore correct. By grouping A with the incorrect C, this option confuses fundamental concepts.

Option C:
Option C considers B and C wrong, but B is a correct interpretation of a small p-value in relation to the null hypothesis. Including B among wrong statements therefore invalidates this choice.

Option D:
Option D correctly isolates C as the only wrong statement and leaves all other statements intact as true. It distinguishes between statistical and practical significance, emphasising that significance alone does not ensure usefulness. Hence this combination is the correct answer.