Question
Download Solution PDFN इकाइयों वाली जनसंख्या से आकार n के SRSWOR में यदि p किसी दिए गए गुण वाली नमूना इकाइयों का अनुपात है, तो V(p) का निष्पक्ष अनुमानक क्या है?
Answer (Detailed Solution Below)
Detailed Solution
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व्याख्या
मान लीजिए कि n आकार का एक साधारण यादृच्छिक नमूना चुना गया है और इस नमूने में n1 इकाई वर्ग C से संबंधित है।
मान लीजिये कि p = n1/n वर्ग C में इकाइयों का नमूना समानुपात हैI
⇒ y̅ = n1/n = p
⇒ S2y = npq/(n – 1)
हमारे पास दो स्थिति हैं
(i)- SRSWOR
जब p, P का एक निष्पक्ष अनुमानक है
⇒ Var(p) = [(N – n)/(N – 1)] × PQ/n
⇒ Est. Var(p) = [(N – n)/N] × pq/(n – 1)
⇒ rse(p) = √Var(p)/P
⇒ √[(N – n)/(N – 1)] × √)Q/Pn
∴ Var(p) = [(N – n)/(N – 1)] × PQ/n
Important Points
SRSWR के लिए
p, P का निष्पक्ष अनुमानक है
(ii) - Var (p) = PQ/n
Est Var(p) = PQ/(n - 1)
rse(p) = √Var(p)/P = √Q/Pn
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