Answered: Three randomly selected households are…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Three randomly selected households are surveyed. The numbers of people in the households are 3, 5, and 10. Assume that samples of size n=2 are randomly selected with replacement from the population of 3, 5, and 10. Construct a probability distribution table that describes the sampling distribution of the proportion of odd numbers when samples of sizes n=2 are randomly selected. Does the mean of the sample proportions equal the proportion of odd
numbers in the population? Do the sample proportions target the value of the population proportion? Does the sample proportion make a good estimator of the population proportion? Listed below are the nine possible samples.

3,3

3,5

3,10

5,3

5,5

5,10

10,3

10,5

10,10

Construct the probability distribution table then chose the correct answer below

Choose the correct answer below.

The proportion of odd numbers in the population is not equal to the mean of the sample proportions.

The proportion of oddnumbers in the population is equal to the mean of the sample proportions.

The proportion of odd numbers in the population is equal to the mean of the sample proportions of even numbers.

The proportion of even numbers in the population is equal to the mean of the sample proportions of odd numbers.

Expert Solution

Step 1

From the given information,

Sample	Sample proportion for odd number
(3,3)	2/2=1
(3,5)	2/2=1
(3,10)	½=0.5
(5,3)	2/2=1
(5,5)	2/2=1
(5,10)	½=0.5
(10,3)	½=0.5
(10,5)	½=0.5
(10,10)	0/2=0

The sampling distribution is,

Sample proportion	Frequency	Probability
0	1	1/9
0.5	4	4/9
1	4	4/9
	Total=9

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