The following are the heights (in inches) of five starters in a basketball team. Player A B C D E Height 76 78 79 81 86 In this discussion you will compare and talk about the mean of smaller samples and will compare these sample means with the population mean of those five players. So, first compute and mention the population mean of these five players. That is, compute the mean of these five players. Next, create samples of size two (all possible pairs among all five players, there are ten total pairs that you can come up). Compute the mean of each sample of size two (each pair, again you will compute ten means in this step). Compare all these ten sample means with the actual population mean of all five players. Next, create all possible samples of size four (they are five groups where you will have four players in each group). Compute the mean of each of these groups which contain four players and compare these sample means with the actual population mean that you computed at the beginning.

Respuesta :

Solution :

Given :

Player    A     B    C   D    E

Height   [tex]$76$[/tex]    [tex]$78$[/tex]    [tex]$79$[/tex]  [tex]$81$[/tex]  86

The population mean = [tex]$\frac{76+78+79+81+86}{5}$[/tex]

                                    = 80

The sample of the size two :

Pair     Heights     [tex]$\text{Sample Mean}$[/tex]      [tex]$\text{Difference}$[/tex] from population mean

(A,B)    [tex]$(76,78)$[/tex]            [tex]$77$[/tex]                            [tex]$-3$[/tex]

(A,C)    (76,79)           77.5                        -2.5

(A,D)    (76,81)            78.5                        -1.5

(A,E)    (76,86)           81                              1

(B,C)    (78,79)           78.5                         -1.5

(B,D)    (78,81)            79.5                        -0.5

(B,E)     (78,86)           82                            2

(C,D)    (79,81)             80                           0

(C,E)     (79,86)           82.5                       2.5

(D,E)     (81,86)           83.5                        3.5

The sample mean are arranged between (77, 83.5)

The standard deviation of the sample means = STDEV.P(C10:C19) = 2.09

We can thus see that the sample means are spread ± 3.5 inches from the population mean.

Sample size of four

Group        Heights            Sample mean    Difference from population mean

(A,B,C,D)   (76,78,79,81)           78.5                   -1.5

(A,B,C,E)   (76,78,79,86)          79.75                 -0.25

(A,B,D,E)   (76,78,81,86)           80.25                0.25

(A,C,D,E)   (76,79,81,86)          80.5                   0.5

(B,C,D,E)   (78,79,81,86)           81                       1

The sample mean are ranged between the (78.5, 81).

The standard deviation of the sample means = STDEV.P(H15:H19) = 0.85

Thus we can see that sample mean are spread ± 1.5 inches from the population mean.