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Module 4: Clustering, K-means, K-medoids, Density-based Hierarchical, Spectral .

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A hypothesis which defines the population distribution is called ....
(i) Null Hypothesis .
(ii) Positive Hypothesis
(iii) Negative Hypothesis
(iv) Alternative Hypothesis

Worked SolutionAI Assisted

Answer: (i) Null Hypothesis

Explanation:

  • Null Hypothesis (H0H_0): A hypothesis which defines the population distribution / assumes no effect, no difference. It is a statement to be tested and possibly rejected. Example: μ=μ0\mu = \mu_0, distribution is Normal N(μ,σ2)N(\mu,\sigma^2).
  • Alternative Hypothesis (H1H_1 / HaH_a): Complements H0H_0, indicates existence of effect/difference.
  • The term statistical hypothesis which completely specifies the population distribution (parameters) is called simple hypothesis; if H0H_0 does that it defines the distribution. In MCQ context, expected answer is Null Hypothesis.

Positive/Negative hypotheses are not standard statistical terms. Hence (i) Null Hypothesis is correct. If question meant simple hypothesis, null hypothesis is the standard example taught as defining population distribution under assumption.

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