a group of students got the following scores in an achievement test:9,12,15,18,21,and 24.consider sample of size 3 that can be drawn from this population A. determine and laser the possible samples and the corresponding sample means B. Construct a sampling distribution of the resulting sample means C. Draw a histogram of the sampling distribution of the sample means

Solution:

Given population is-9,12,15,18,21,24

Sample size n=3,

Total number of sample formed = 19 and each of the sample mean is shown in the table below.

A. All samples are shown in 2nd column. Corresponding means are in 3rd column.

B. Sampling distribution of the resulting sample means:

Mean $=\dfrac{12+13+14+15+...+19+21}{19}=\dfrac{310}{19}=16.31$

Standard deviation $=\sqrt{\dfrac{\Sigma(x_i-\bar x)^2}{n-1}}$

$=\sqrt{\dfrac{(12-16.31)^2+(13-16.31)^2+...+(21-16.31)^2}{18-1}} \\=\sqrt{5.1169} \\=2.262$

C. Histogram of sample means: