Question

2. Coren was able to sell several pairs of Marikina shoes that have sizes of 9, 7, 11, 3, and

8. Consider samples of size 3 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.

Sample Means

Frequency

Probability P(x)

c. Draw a histogram of the sampling distribution of the sample mean.

Answer 1

Solution

Population $N=5$

Sample size $n=3$

(a) Possible samples

$=C_5^3= \binom{5}{3}=10$ samples

$\def\arraystretch{1.5}\begin{array}{c:c:c}Sample no.&Sample&Sample mean\\\hline1&3,7,8&6.0\\\hdashline2&3,7,9&6.33\\\hdashline3&3,7,9&7.0\\\hdashline4&3,8,9&6.67\\\hdashline5&3,8,11&7.33\\\hdashline6&3,9,11&7.66\\\hdashline7&7,8,9&8.0\\\hdashline8&7,8,11&8.67\\\hdashline9&7,9,11&9.0\\\hdashline10&8,9,11&9.33\\\hline\end{array}$

(b) The sampling distribution

$\def\arraystretch{2.0}\begin{array}{c:c:c}Mean& Frequency &Probability\\\hline6.0&1&\dfrac{1}{10}\\\hdashline6.33&1&\dfrac{1}{10}\\\hdashline7.0&1&\dfrac{1}{10}\\\hdashline6.67&1&\dfrac{1}{10}\\\hdashline7.33&1&\dfrac{1}{10}\\\hdashline7.66&1&\dfrac{1}{10}\\\hdashline8.0&1&\dfrac{1}{10}\\\hdashline8.67&1&\dfrac{1}{10}\\\hdashline9.0&1&\dfrac{1}{10}\\\hdashline9.33&1&\dfrac{1}{10}\\\hline\end{array}$

(c) Histogram