Q. 7.16 - Elementary Statistics

Question

7.16 NBA Champs. This exercise requires that you have done Exercises 7.11-7.15.
a. Draw a graph similar to that shown in Fig. 7.3 on page $294$ for sample sizes of $1,2,3,4$, and $5$.
b. What does your graph in part (a) illustrate about the impact of increasing sample size on sampling error?
c. Construct a table similar to Table 7.4 on page $294$ for some values of your choice.

Step-by-Step Solution

Answer

(a) A graph for sample size of 1,2,3,4, and 5 as:

(b) It is clear as the sample size increases; there is decrease in the sampling error.

(c) A table similar to table 7.4 as:

Sample size	Number of samples	Number of samples within 1 of $\mu$	Percentage of samples within 1 of $\mu$	Number of samples within 2 of $\mu$	Percentage of samples within 2 of $\mu$
1	5	0	0	1	20
2	10	4	40	7	70
3	10	5	50	8	80
4	5	3	60	5	100
5	1	1	1	1	100

Part (a) Step 1: Given information

To construct a graph that similar to the sample size of $1,2,3,4$ and $5$.

Part (a) Step 2: Explanation

For the supplied population, use MINITAB to create dot plots for samples of size $1,2,3,4,$ and $5$

 MINITAB's procedure is as follows:

Step 1: Select Graph > Dotplot from the drop-down menu.

Step 2: Select Multiple $Y\text{'}$s from the drop-down menu and click OK.

Step 3: In Graph variables, input columns of $n=1, n=2, n=3, n=4, n=5,$

Step 4: Select OK.

MINITAB's output is as follows:

Part (b) Step 1: Given information

To illustrate the graph in part (a) about the impact of increasing sample size on sampling error.

Part (b) Step 2: Explanation

For five players, the average height$\left(\mu \right)$ is $78.6$ inches.

It is obvious from the MINITAB result in portion (a) that as the sample size grows, the sampling error decreases.
As a result, the sampling error has decreased.

Part (c) Step 1: Given information

To construct a table, that similar to table $7.4$ for some values of own choice.

Part (c) Step 2: Explanation

Create a table with columns for the number of samples, the number of samples within $1$of $\mu$, the percentage of samples within $1$of $\mu$, the number of samples within$2$ of $\mu$, and the percentage of samples within$2$ of $\mu$.

Sample size	Number of samples	Number of samples within 1 of $\mu$	Percentage of samples within 1 of $\mu$	Number of samples within 2 of $\mu$	Percentage of samples within 2 of $\mu$
1	5	0	0	1	20
2	10	4	40	7	70
3	10	5	50	8	80
4	5	3	60	5	100
5	1	1	1	1	100

As a result, the table is generated.