Q. 7.42 - Elementary Statistics

Question

7.42 NBA Champs. Repeat parts (b) and (c) of Exercise$7.41$ for samples of size 1. For part (b), use your answer to Exercise$7.12$(b).

Step-by-Step Solution

Answer

The mean height $\left({\mu }_{\overline{x}}\right)$ for samples of size $1$ is $78.6$.

Step 1: Given information

The samples from exercise 7.41 is:

Step 2: Explanation

For size $1$ samples, calculate the mean height $\left({\mu }_{\overline{x}}\right)$.
As a result, the size samples and their related means.

Then, the number of possible samples of size $1$is $\left(N\right)$.
The mean of all potential sample means is calculated as follows for samples of size $1$:
${\mu }_{\overline{x}}=\frac{\sum {\overline{x}}_i}{N}$
$=\frac{83+76+80+74+80}{5}$
$=\frac{393}{5}$
$=78.6$
As a result, the mean height $\left({\mu }_{\overline{x}}\right.)$ for samples of size $1$ 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.
It is just to state,
${\mu }_{\overline{x}}=\mu$

$=78.6$

As a result, the mean height $\left({\mu }_{\overline{x}}\right)$ for size$1$ samples is $78.6$.