Question

if P represent unknown population proportion then variance of sample proportion is?

1) p(1-p) /n
2) p/n
3) (1-p)/n
4) p(1-p)
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Answer 1

Answer:

4) p(1-p)

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Step-by-step explanation:

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Answer 2

Var(p) = p(1-p) /n (option a)

Given:

P represents an unknown population proportion.

To Find:

The variance of the sample proportion.

Solution:

The representation of sample proportion (p) is,

$p = \frac{X}{n}$

where,

X =  number of yes respondents in the sample. (where X is a binomial random variable)

n = total number of people.

Now, the variance stands as,

Var(X)=npq

[where q = 1−p ]

Thus,

The variance of sample proportion p is,

Var(p)

=Var(X/n)

= $\frac{1}{n^{2} } Var(X)$

= $\frac{1}{n^{2} } * npq$

=  $\frac{pq}{n}$

= $\frac{p*(1-p)}{n}$

Thus,

Var(p) = p(1-p) /n (option a)

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