Chapter 9, Problem 1SE

Ages A study of all the students at a small college showed a mean age of 20.7 and a standard deviation of 2.5 years.

a. Are these numbers statistics or parameters? Explain.

b. Label both numbers with their appropriate symbol (such as $\bar{x},\mu ,s,\text{ or }\sigma$ ).

To determine

Identify if the given numbers are statistics or parameters.

Answer to Problem 1SE

The given numbers are parameters.

Explanation of Solution

It is given that the study of all students in the small college showed mean age of 20.7 years and standard deviation of 2.5 years.

The numerical characteristic of the population and sample are called parameter and statistic, respectively.

The study considered all the students, which can be referred to as the population. Thus, 20.7 years is the population mean and 2.5 years is the population standard deviation. So, the given numbers are characteristics of the population.

Therefore, the given numbers are parameters.

To determine

Identify the appropriate symbols for the given numbers.

Answer to Problem 1SE

The numbers can be labelled as "$\text{\$}$ " $\mu =20.7\text{ years}$ and "$\text{\$}$ " $\sigma =2.5\text{ years}$ .

Explanation of Solution

The given numbers 20.7 years and 2.5 years are population mean and population standard deviation of the ages of students in a small college, respectively.

The population mean is denoted by "$\text{\$}$ " $\mu$ and the population standard deviation is denoted by "$\text{\$}$ " $\sigma$ . Thus, the given numbers can be labelled as "$\text{\$}$ " $\mu =20.7\text{ years}$ and "$\text{\$}$ " $\sigma =2.5\text{ years}$ .