Answer to Question #181778 in Statistics and Probability for matthew

Question

Consider all samples of size 5 from this population. 

3,5,9,11,12,15,26

1. Compute the mean and the standard deviation of the population. 

2. List all samples of size 5 and compute the mean for each sample. 

3. Construct the sampling distribution of the sample means.

4. Calculate the mean of the sampling distribution of the sample means. 

Compare this to mean of the population. 

5. Calculate the standard deviation of the sampling distribution of the 

sample means . Compare this to the standard deviation of the 

population. 

Answer 1

1. Population mean is

$\mu = \frac{3+5+9+11+12+15+26}{7}=11.57 \\ \sigma = \sqrt{ \frac{\sum (x- \mu)^2}{n} } \\ \sigma = \sqrt{ \frac{(3-11.57)^2+...+(26-11.57)^2}{7} } = 7.57$

2. The number of all possible sample = ⁷C₅=21 and the corresponding sample mean = sum of each five values/5

3.

Using the data we make a histogram

4.

The mean of the sampling distribution of the sample means = 11.79

The mean of the population=11.57

5.Excel function

=STDEV()

The standard deviation of the sampling distribution=1.79

The standard deviation of the population=7.57