Question

A population consists of 6 students were given the allotted time for studying and making tasks.

The number of hours are 2, 3, 4, 5, 6 and 7.

A. Find the mean and variance of the population. (10 points)

B. Using a sample size of 5, calculate the mean (𝜇𝑥̅) of the sampling distribution of the

sample means. Compare the result to the mean of the population.

Answer 1

Solution

A.     Mean E(X)= (2+3+4+5+6+7)/6

          =4.5

Variance= ∑[(X- E(X))²]/N

= 6.25+2.25+0.25+0.25+2.25+6.25/6

Var =2.9167

B.     Sample sizes n=5

6C5=6

(2,3,4,5,6)   (2,3,4,5,7) (3,4,2,6,7)  (2,3,5,6,7)  (2,4,5,6,7)   (3,4,5,6,7)

E(x)= 4+4.2+4.4+4.6+4.8+5/6

=4.5

The sample and population mean are equal