Q. 7.44 - Elementary Statistics

Question

7.44 NBA Champs. Repeat parts (b) and (c) of Exercise $7.41$ for samples of size 4. For part (b), use your answer to Exercise $7.14$.

Step-by-Step Solution

Answer

The mean height $\left({\mu }_{\overline{x}}\right)$ for samples of size $4$ is$78.6$.

Step 1: Given information

To determine the sample for exercise $7.41$ for samples of size$4$. The given sample in exercise 7.41 as:

Step 2: Explanation

For samples of size $4$, calculate the mean height using $\left({\mu }_{\overline{x}}\right)$.
As a result, as indicated in the table below, the samples of size $4$ and their respective means are obtained:

Sample size	Height	Mean(x)
B,W,J,C	83,76,80,74	$\frac{83+76+80+74}{4}=78.25$
B,W,J,H	83,76,80,80	$\frac{83+76+80+80}{4}=79.75$
B,W,C,H	83,76,74,80	$\frac{83+76+74+80}{4}=78.25$
B,J,C,H	83,80,74,80	$\frac{83+80+74+84}{4}=79.25$
W,J,C,H	76,80,74,80	$\frac{76+80+80+74}{4}=77.5$

Step 3: Explanation

As a result, the number of feasible size $4$ samples$\left(N\right)$ is $5$. The mean of all potential sample means is calculated as follows for samples of size $4$:
${\mu }_{\overline{x}}=\frac{\sum {\overline{x}}_i}{N}$
$=\frac{78.25+79.75+78.25+79.25+77.5}{5}$
$=\frac{393}{5}$
$=78.6$
As a result, the mean height $\left({\mu }_{\overline{x}}\right)$ for samples of size 4 is$78.6$.

Step 4: Explanation

Calculate the mean height $\left({\mu }_{\overline{x}}\right)$.
The average height of five players in the population is $78.6$ inches.
The population mean is equal to the mean of the sample mean.
That is to state,
${\mu }_{\overline{x}}=\mu$

$=78.6$

As a result, the mean height $\left({\mu }_{\overline{x}}\right)$ for size $4$ samples is$78.6$.