Answer to Question #309764 in Statistics and Probability for Ali de austria

Question

A population consists of the values (6, 9, 5, 3). Consider samples of size 2 that can be

drawn from this population.

a. List down all the possible samples and corresponding sample mean

Sample

Sample Means

b. Construct the sampling distribution of the sample means.

Answer 1

Solution

Population $N=4$

Sample $n=2$

Possible samples

$=C_4^2= \binom{4}{2}=6$ combinations

(a) Possible samples and their means

$\def\arraystretch{1.5}\begin{array}{c:c:c}no.& sample & sample mean\\\hline1&3,5&4.0\\\hdashline2&3,6&4.5\\\hdashline3&3,9&6.0\\\hdashline4&5,6&5.5\\\hdashline4&5,6&5.5\\\hdashline5&5,9&7.0\\\hdashline6&6,9&7.5\\\hline\end{array}$

(b) Probability distribution

$\def\arraystretch{2.0}\begin{array}{c:c}Mean& Probability\\\hline4.0&\dfrac{1}{6}\\\hdashline4.5&\dfrac{1}{6}\\\hdashline5.5&\dfrac{1}{6}\\\hdashline6.0&\dfrac{1}{6}\\\hdashline7.0&\dfrac{1}{6}\\\hdashline7.5&\dfrac{1}{6}\\\hline\end{array}$