Question

List all 10 possible SRSs of size n = 2, calculate the mean quiz score for each sample, and display the sampling distribution of the sample mean on a dotplot.

 

The small population of 5 students in the table.

Answer 1

Given are the 5 students with their quiz score

Abigail -10, Bobby -5, Carlos-10, DeAnna -7, Emily-9

 

Mean of quiz score of these five students,

µ = (10+5+10+7+9)/5

   = 8.2

 

Sample number	Sampled students with quiz score	Sample mean (Average of score) (x̅)
1	Abigail 10	Bobby 5	(10+5)/2 = 7.5
2	Abigail 10	Carlos 10	(10+10)/2= 10
3	Abigail 10	DeAnna 7	(10+7)/2= 8.5
4	Abigail 10	Emily 9	9.5
5	Bobby5	Carlos 10	7.5
6	Bobby5	DeAnna 7	6
7	Bobby5	Emily 9	7
8	Carlos10	DeAnna 7	8.5
9	Carlos10	Emily 9	9.5
10	DeAnna7	Emily 9	8

 

Therefore sampling distribution of Sample mean is

Sample mean	Frequency
6	1
7	1
7.5	2
8	1
8.5	2
9.5	2
10	1

 

Dot Plot

 

We will find Average of sample mean,

Sample mean(x̅)	Frequency(f)	fx̅
6	1	6
7	1	7
7.5	2	15
8	1	8
8.5	2	17
9.5	2	19
10	1	10
Total		82

 

Average of sample mean,

E(x̅) = Σf*x̅/Σf

       = 82/10

       = 8.2

 

Hence E(x̅ ) = µ

 

Sample mean is unbiased estimate of population mean.

Sample mean is unbiased estimate of population mean.