Let $ x_1, x_2, x_3, x_4 $ be the observed values from a random sample drawn from a $ N(\mu, \sigma^2) $ distribution, where $ \mu \in \mathbb{R} $ and $ \sigma \in (0, \infty) $ are unknown parameters. Let $ \bar{x} $ and $ s = \sqrt{\frac{1}{3} \sum_{i=1}^{4} (x_i - \bar{x})^2} $ be the observed be the observed sample mean sample standard deviation,repectively. For testing the hypotheses $ H_0: \mu = 0 $ against $ H_1: \mu \neq 0 $, the likelihood ratio test of size $ \alpha = 0.05 $ rejects $ H_0 $ if and only if $$\frac{|\bar{x}|}{s} k.$$ Then the value of $ k $ is given by:

Question

Let $ x_1, x_2, x_3, x_4 $ be the observed values from a random sample drawn from a $ N(\mu, \sigma^2) $ distribution, where $ \mu \in \mathbb{R} $ and $ \sigma \in (0, \infty) $ are unknown parameters. Let $ \bar{x} $ and $ s = \sqrt{\frac{1}{3} \sum_{i=1}^{4} (x_i - \bar{x})^2} $ be the observed be the observed sample mean sample standard deviation,repectively. For testing the hypotheses $ H_0: \mu = 0 $ against $ H_1: \mu \neq 0 $, the likelihood ratio test of size $ \alpha = 0.05 $ rejects $ H_0 $ if and only if $$\frac{|\bar{x}|}{s} > k.$$ Then the value of $ k $ is given by:

cdquestions Admin · Accepted Answer

The correct option is (A): $ \frac{1}{2} t_{3,0.025} $

Answer

$ \frac{1}{2} t_{3,0.025} $

Answer

$ t_{3,0.025} $

Answer

$ 2 t_{3,0.05} $

Answer

$ \frac{1}{2} t_{3,0.05} $

The Correct Option is A

Solution and Explanation

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