##### Question

In: Statistics and Probability

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

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. b) construct a table for sampling distribution of the sample proportion of odd numbers. c) find the mean of sampling distribution of the sample proportion of odd numbers. d) is the sample proportion and unbiased estmator or. biased estimator of the population? Why?

## Solutions

##### Expert Solution

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 biased estimator of the population: From the previous results, =P

Thus, the sample proportion is an unbiased estimator of the population proportion.

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