In: Statistics and Probability
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 biased estimator of the population:
From the previous results,
=P
Thus, the sample proportion is an unbiased estimator of the population proportion.