Consider a Sample of N Items Obtained at a Particular $\hat { p } = X / n$

question 59

Multiple Choice

Consider a sample of n items obtained at a particular time, and let X be the number of defectives and $\hat { p } = X / n$ Which of the following statements are not true?

• A) E(X) = np
• B) V(X) = p(1-p)
• C) \(E ( \hat { p } ) = p\)
• D) \(V ( \hat { p } ) = p ( 1 - p ) / n\)
• E) If \(n p \geq 10 \text { and } n ( 1 - p ) \geq 10 , \hat { p }\)
• Has approximately a normal distribution.

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Definitions:

Clay

A fine-grained natural soil material containing clay minerals, known for its plasticity when wet and used in ceramics.

Wallboard

A construction material made from gypsum and used in building for walls and ceilings, known for its fire resistance.

Gypsum

A soft sulfate mineral composed of calcium sulfate dihydrate, used in the construction industry and as a fertilizer.

Granodiorite

A coarse-grained igneous rock similar to granite but containing more plagioclase feldspar than orthoclase feldspar, commonly found in continental crust.