Chapter 10.2, Problem 10.52E

(a)

To determine

To Explain: the parameter in this problem and the sample statistic.

Answer to Problem 10.52E

Parameter, mean of all students in the room

Explanation of Solution

Given:

  $\begin{array}{l}n=9\\ \overline{x}=64\\ s=3\end{array}$

DEFINITIONS

The population having all individuals/subjects about which require to assemble information. A sample is the part of population of which information was actually assembled.

A parameter is a descriptive measure for a population, while a statistic is a descriptive measure for a sample. The parameters are the mean height $\mu$ of all students in the room. The statistic is the mean height $\overline{x}=64$ of the 9 students in the sample.

(b)

To determine

To Explain: about the appropriate to use the normal distribution and make a confidence statement about the average height on the basis of given information.

Answer to Problem 10.52E

No

Explanation of Solution

It will not be proper to use the normal distribution, because the sample size of $n=9$ is not enough large and do not know if the population distribution is about normal.

If would be about to use the Student’s $t$ -distribution, if the sample does not having any neither outliers nor shows strong curvature.