Question

A group of students got the following scores in a test: 6, 9, 12, 15, 18, and 21. Consider sample of size 4 that can be drawn from this population.

How many possible samples of size 4 can be drawn?

List all the possible samples and compute the sample mean.

Sample

Sample Mean

Construct the sampling distribution of the sample mean.

Sample Mean

Frequency

Probability P(x)

Draw a histogram corresponding to the sampling distribution of the sample mean.

Answer 1

 The number of possible samples of size 4 can be calculated as: $_nC_r=\frac{n!}{r!\left(n-r\right)!}$ where n = population size, r = sample size.

$_nC_r=\frac{720}{48}=15\:$

Number of possible samples of size 4 is 15.

To calculate the mean of the possible outcomes we use the formula:$Mean=\frac{sum\:of\:values\:of\:a\:possible\:otcome}{sample\:size}$

To calculate the Probability P (X) we use the formula: $Probability\:P\left(X\right)=\frac{Frequency}{Number\:of\:possible\:outcomes}$

A histogram corresponding to the sampling distribution of the sample mean.