Answer to Question #309774 in Statistics and Probability for Ali de austria

Question

Perform what is being asked. Follow the steps indicated in the first column of the table to complete

the activity. In the second column, write your solution on the spaces provided. Situation: A population

of PWD learners in 5 schools in a certain municipality of Quezon Province are (x) 3, 7, 6, 13, and

17. Suppose that two schools were selected as samples, determine the mean and variance of the

sampling distribution of sample mean.

First Step:

Second Step:

a.

Third Step:

Fourth Step:

Fifth Step:

Sixth Step:

Seventh Step:

Answer 1

Solution

Population $N=5$

Sample size $n=2$

Population mean $\mu=\dfrac{\sum X_i}{N}$

$\mu=\dfrac{3+6+7+13+17}{5}=9.2$

Possible number of samples

$=C_5^2= \binom{5}{2}=10$ samples

$\def\arraystretch{1.5}\begin{array}{c:c:c}no &Sample& Sample mean\\\hline1&3,6&4.5\\\hdashline2&3,7&5.0\\\hdashline3&3,13&8.0\\\hdashline4&3,17&10.0\\\hdashline5&6,7&6.5\\\hdashline6&6,13&9.5\\\hdashline7&6,17&11.5\\\hdashline8&7,13&10.0\\\hdashline9&7,17&12.0\\\hdashline10&13,17&15.0\\\hline\end{array}$

Variance

$\sigma^2 =\dfrac{\sum(X_i- \bar X)^2}{N-1}$

$\def\arraystretch{1.5}\begin{array}{c:c:c}\bar X&X_i-\bar X&(X_i-\bar X)^2\\\hline4.5&-4.7&22.09\\\hdashline5.0&-4.2&17.64\\\hdashline6.5&-2.7&7.29\\\hdashline8.0&-1.2&1.44\\\hdashline9.5&0.3&0.09\\\hdashline10.0&0.8&0.64\\\hdashline10.0&0.8&0.64\\\hdashline11.5&2.3&5.29\\\hdashline12.0&2.8&7.84\\\hdashline15.0&5.8&33.64\\\hline\sum &&96.6\\\hline\end{array}$

$\sigma^2 =\dfrac{96.6}{10-1}=\dfrac{96.6}{9}$

$\sigma^2=10.733$