Chapter 20, Problem 20.17CYS

To determine

To identify: The correct reason for given statement.

Answer to Problem 20.17CYS

Option (b)

Explanation of Solution

Reason for the correct option:

Prefer the t procedures to the z procedures for inference about a population mean because z procedures require that the population standard deviation is known but the t procedures are not required.

Reason for the incorrect answer:

For both test procedures, the data or observations considered as simple random sample from the population and the observations are from a normal population. Therefore,

Option (a) and Option (c) are incorrect.

Therefore, the correct option is (b), “z requires that you know the population standard deviation $\sigma$”.

Statistics Concept Introduction

Introduction:

Conditions for inference about a one-sample t test:

• Simple random sample from the population.
• Observations are from a normal population.

Conditions for inference about a one-sample z test:

• Simple random sample from the population.
• Observations are from a normal population.
• Population standard deviation is known.