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Questions › DSE › DSE 2015 › Q47
2 marks, −0.666666666666667Statistics › Hypothesis testing › Type I and type II errors and powerModerateabout 3 min

DSE 2015 Question 47: Hypothesis testing

In Y=a+b1X1+b2X2+uY=a+b_1X_1+b_2X_2+uY=a+b1​X1​+b2​X2​+u (large sample), let t1,t2t_1,t_2t1​,t2​ test b1=0b_1=0b1​=0 and b2=0b_2=0b2​=0; treat them as independent. Testing the joint null b1=b2=0b_1=b_2=0b1​=b2​=0 by the rule 'reject if either ∣t1∣|t_1|∣t1​∣ or ∣t2∣|t_2|∣t2​∣ exceeds 1.961.961.96' gives a Type I error probability that is

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In Y=a+b₁X₁+b₂X₂+u (large sample), let t₁,t₂ test b₁=0 and b₂=0; treat them as independent. Testing the joint null b₁=b₂=0 by the rule 'reject if either |t₁| or |t₂| exceeds 1.96 ' gives a Type I error probability that is (A) 5 percent (B) less than 5 percent (C) more than 5 percent (D) either 5 percent or less than 5 percent

Also written as: In Y=a+b_1X_1+b_2X_2+u (large sample), let t_1,t_2 test b_1=0 and b_2=0; treat them as independent. Testing the joint null b_1=b_2=0 by the rule 'reject if either |t_1| or |t_2| exceeds 1.96 ' gives a Type I error probability that is

Hypothesis testing has come up 47 times in 7 exams since 2007.

What this question tests

This question is on Type I and type II errors and power, part of Hypothesis testing in Statistics.

The two ways a test can be wrong and the probability of detecting a real effect.

TestStop has 15 past-paper questions on this subtopic; the nearest in year are below.

  • IIT JAM 2021 · Q15Let X be uniform on [0, b]. Testing H₀: b = 2 against H_A: b ≠ 2 uses the critical region {x ≤ 0.1 or x ≥…
  • IIT JAM 2022 · Q8In hypothesis testing, which of the following defines the size of the power of the test?
Practise Hypothesis testingMore on Type I and type II errors and power

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Question from the DSE 2015 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.