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GATE 2026 XH5 (Psychology) – Question 56

Research Methods and Statistics · Statistics in Psychology: Central tendency and dispersion, normal probability curve, parametric and non-parametric tests, effect size and power analysis · 2 marks · Multiple select

According to Central Limit Theorem, for a fixed sample size:

  1. Sample means may or may not be normally distributed.
  2. Both Type-I and Type-II errors must be low.
  3. Relative frequency of sample means that are closer to the population mean is higher.
  4. Relative frequency of the sample means that are farther from the population mean is lower.

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Show answer and explanation

Correct answer: (C) Relative frequency of sample means that are closer to the population mean is higher.; (D) Relative frequency of the sample means that are farther from the population mean is lower.

Explanation

The central limit theorem says that sample means pile up around the population mean in a roughly normal shape: means close to the population mean are more frequent, and those far away are less frequent. It says nothing about error rates, and it does not leave normality to chance.