Q.104
ICAR 2023Shift 1 MCQ (Single Correct) +4 −1
English हिन्दी
Choose the correct answer :
सही उत्तर का चयन कीजिए :
EXPLANATION Testing of Hypotheses: Null and Alternative Hypotheses, Type I and II Errors, Significance Level, Large Sample Tests (Z-test)

Analysis of errors in hypothesis testing:

  • Incorrect: Rejecting $H_0$ when it is false is a correct decision (Power of the test, $1 - \beta$).
  • Incorrect: Rejecting $H_0$ when it is true is Type-I error, not Type-II error.
  • Incorrect: Type-II error occurs when one fails to reject (accepts) $H_0$ when it is false.
  • Correct: By definition, a Type-I error consists of rejecting the null hypothesis $H_0$ when $H_0$ is actually true. Its probability is denoted by $\alpha$ (level of significance).

परिकल्पना परीक्षण में त्रुटियों की परिभाषा:

  • गलत: $H_0$ के असत्य होने पर उसे अस्वीकार करना एक सही निर्णय है (परीक्षण की शक्ति, $1-\beta$)।
  • गलत: $H_0$ के सत्य होने पर उसे अस्वीकार करना टाइप-I त्रुटि कहलाता है, टाइप-II नहीं।
  • गलत: असत्य $H_0$ को स्वीकार करना टाइप-II त्रुटि होता है।
  • सही: मानक परिभाषा के अनुसार, सत्य शून्य परिकल्पना ($H_0$) को अस्वीकार करना टाइप-I त्रुटि (Type-I error) कहलाता है, जिसकी प्रायिकता को सार्थकता स्तर ($\alpha$) कहा जाता है।
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