Answer to Question #309068 in Statistics and Probability for Italia

Question

1.   The weight of Group 1:Jay - 43 kg, Stella - 42 kg, Tilly - 44 kg, Joanna - 53 kg. Consider samples of size 3 that can be drawn from this population.

a.   How many possible samples can be drawn?

b.   List all the possible samples and the corresponding means.  

c.    Construct the sampling distribution of the sample means. 

Answer 1

Given N $=4$ and sample size $n=3$

(a) Possible samples

$=(_n^N)=(_3^4)=4$ samples

(b) Possible samples and their means

$\def\arraystretch{1.5}\begin{array}{c:c:c} no.& Sample &Mean\\\hline1.&42,43,44&43\\\hdashline2.&42,43,53&46\\\hdashline3.&42,44,53&46.333\\\hdashline4.&43,44,53&46.667\\\hline\end{array}$

(c) Sampling distribution of the sample means

$\def\arraystretch{1.5}\begin{array}{c:c:c:c} \bar{X}&f&f(\bar{X})&\bar{X}f(\bar{X})\\\hline43&1&\frac{1}{4}&\frac{43}{4}\\\hdashline46&1&\frac{1}{4}&\frac{46}{4}\\\hdashline\frac{139}{3}&1&\frac{1}{4}&\frac{139}{12}\\\hdashline\frac{140}{3}&1&\frac{1}{4}&\frac{140}{12}\\\hline\end{array}$