Q. 7.45 - Elementary Statistics

Question

7.45 NBA Champs. Repeat parts (b) and (c) of Exercise $7.41$ for samples of size $5$. For part (b). use your answer to Exercise $7.15\left(b\right)$.

Step-by-Step Solution

Answer

The mean height $\left({\mu }_{\overline{x}}\right)$ for samples of size $5$is $78.6$.

Step 1: Given information

To determine the sample size of $5$. The sample from exercise $7.41$ is:

Step 2: Explanation

For samples of size $5$, calculate the mean height $\left({\mu }_{\overline{x}}\right)$.
As a result, the size $5$ samples and their means are obtained as given in the table below:

Sample size	Height	Mean(x)
B,W,J,C,H	83,76,80,74,80	$\frac{83+76+80+74+80}{5}=78.6$

As a result, the number of possible samples $\left(N\right)$ of size $5$ is one.
The mean of all possible sample means is calculated as follows for samples of size $5$:
$\begin{array}{r}{\mu }_{\overline{x}}=\frac{\sum {\overline{x}}_i}{N}\end{array}$

$=\frac{78.6}{1}$

$=78.6$

As a result, the mean height $\left({\mu }_{\overline{x}}\right)$ for size $5$ samples is $78.6$.

Step 3: 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,
${\mu }_{\overline{x}}=\mu$
$=78.6$
Asa result, the mean height ( $\left({\mu }_{\overline{x}}\right)$ for samples of size $5$ is $78.6$.