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Questions › CUET-PG › CUET-PG 2018 › Q29
4 marks, −1Statistics › Sampling distributions and limit theorems › Chi-square, t and F distributionsModerateabout 1 min

CUET-PG 2018 Question 29: Sampling distributions and limit theorems

Let x1,…,xnx_1,\dots,x_nx1​,…,xn​ be a random sample from N(μ,σ2)N(\mu,\sigma^2)N(μ,σ2). What is the sampling distribution of xˉ−μs/n\dfrac{\bar{x}-\mu}{s/\sqrt{n}}s/n​xˉ−μ​?

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Let x₁,…,xₙ be a random sample from N(μ,σ²). What is the sampling distribution of (x̄-μ)/(s/√n)? (A) F-distribution (B) t-distribution (C) z-distribution (D) Normal distribution

Also written as: Let x_1,...,x_n be a random sample from N(mu,sigma^2). What is the sampling distribution of (x_bar-mu)/(s/sqrt(n))?

Sampling distributions and limit theorems has come up 25 times in 7 exams since 2007.

What this question tests

This question is on Chi-square, t and F distributions, part of Sampling distributions and limit theorems in Statistics.

The distributions that arise from normal samples and the degrees of freedom they carry.

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