Question

Use the population {3,4,6} and assume that samples of size 2 are randomly selected, with replacement.

?) For the population, find the proportion of odd numbers

?) Construct a table for the sampling distribution of the sample proportions of odd numbers.

?) Find the mean of the sampling distribution of the sample proportion of odd numbers.

?) Is the sample proportion an unbiased estimator or a biased estimator of the population proportion? why?

Answer 1

Answer:

Given that,

Use the population {3,4,6} and assume that samples of size 2 are randomly selected, with replacement.

(a).

For the population, find the proportion of odd numbers:

From the given problem the population is {3,4,6}.

The proportion of odd numbers is,

In the data set {3,4,6} is odd number count is 1.

Therefore, the proportion of odd numbers is 1/3.

(b).

Construct a table for the sampling distribution of the sample proportion of odd numbers:

The table representing the sampling distribution of the sample proportion of odd numbers is,

The data set is {3,4,6}

Sample	Proportion(P)
(3,4)	1/2
(3,6)	1/2
(4,6)	0

c)

Find the mean of the sampling distribution of the sample proportion of odd numbers.

The mean of the sampling proportions ,

Thus , the required mean is 1/3.

d)

Is the sample proportion and unbiased estimator (or) a baised estimator of the population.

From the previous results:

= p

Thus , the sample proportion is an unbaised estimator of the population proportion ,

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