Mathematics · Testing of Hypothesis
A sample of size 10 is selected at random from a lot containing 20 items of a manufactured product. Suppose the total number of defectives D in the lot is unknown. Let X be the number of defectives in the sample. We wish to test H 0 : D = 7 against the alternative H 1 : D > 7. Consider the test: Reject H 0 if X ≥ k where k is determined such that P H 0 (X ≥ k) ≤ 0.05 H 0 (X ≥ k - 1). Which of the following statements are true? I. The test is the Uniformly Most Powerful (UMP) test of its size. II. The power function of the test is increasing in D. III. The power function of the test is decreasing in D. IV. The test is unbiased.
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1Only I, III and IV
- 2Only II and IV
- 3Only I and III
- 4Only I, II and IV✓
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Only I, II and IV
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