Question

A population consists of the five numbers 3, 4, 7, 8, 11. Consider all possible samples of size two which can be drawn with replacement from this population. Find
1. the mean of the population,
2. the standard deviation of the population,
3. the mean of the sampling distribution,
4. the standard deviation of the sampling distribution of means, i.e., the standard error of means.A population consists of the five numbers 3, 4, 7, 8, 11. Consider all possible samples of size two which can be drawn with replacement from this population. Find
1. the mean of the population,
2. the standard deviation of the population,
3. the mean of the sampling distribution,
4. the standard deviation of the sampling distribution of means, i.e., the standard error of means.A population consists of the five numbers 3, 4, 7, 8, 11. Consider all possible samples of size two which can be drawn with replacement from this population. Find
1. the mean of the population,
2. the standard deviation of the population,
3. the mean of the sampling distribution,
4. the standard deviation of the sampling distribution of means, i.e., the standard error of means.A population consists of the five numbers 3, 4, 7, 8, 11. Consider all possible samples of size two which can be drawn with replacement from this population. Find
1. the mean of the population,
2. the standard deviation of the population,
3. the mean of the sampling distribution,
4. the standard deviation of the sampling distribution of means, i.e., the standard error of means.

Answer 1

Answer:

I have only like few, but hope can help...

Explanation:

Answer 2

1. The mean of the population is 6.6

2. The standard deviation of the population is 3.286335345

3. The mean of the sampling distribution is 6

4. The standard deviation of the sampling distribution is 3.674234614

Explanation:

1. Mean = $\frac{3 + 4 + 7 + 8 + 11}{5}$

             = $\frac{33}{5}$

             = 6.6

2.  Variance of population =  $\frac{[(2-6)²+(3-6)²+(6-6)²+(8-6)²+(11-6)²] }{5}$

                                            = 10.8

      Standard deviation = $\sqrt{variance}$ = $\sqrt{10.8}$

                                       = 3.286335345

3.  [2,2]  mean = 2       var =  0

 [2,3]  mean = 2.5       var =  0.25

 [2,6]  mean = 4          var =  4

 [2,8]  mean = 5          var =  9

[2,11]  mean = 6.5       var = 20.25

 [3,3]  mean = 3          var =  0

 [3,6]  mean = 4.5       var =  2.25

 [3,8]  mean = 5.5       var =  6.25

[3,11]  mean = 7           var = 16

 [6,6]  mean = 6          var =  0

 [6,8]  mean = 7           var =  1

[6,11]  mean = 8.5        var =  6.25

 [8,8]  mean = 8           var =  0

[8,11]  mean = 9.5        var =  2.25

[11,11]  mean = 11            var =  0    

sums               90                 67.5

Mean of sample distribution = $\frac{19}{5}$ = 6

4. Variance of sample  = $\frac{67.5}{5}$ = 13.5

  Standard deviation = $\sqrt{variance}$ = $\sqrt{13.5}$

                                   = 3.674234614