Chapter 16, Problem 16.11CYS

To determine

To find: The critical value for 99.9% confidence interval for a population mean µ.

Answer to Problem 16.11CYS

The correct option is, “(c) $z^{*}=3.291$”.

Explanation of Solution

Reason for the correct answer:

For 99.9% confidence level,

$\begin{array}{c}\frac{1-C}{2}=\frac{1-0.999}{2}\\ =\frac{0.001}{2}\\ =0.0005\end{array}$

Software procedure:

Step-by-step procedure to obtain critical value using the MINITAB software:

• Choose Graph > Probability Distribution Plot and choose View Probability > OK.
• From Distribution, choose ‘Normal’ distribution.
• Click the Shaded Area tab.
• Choose P Value and Two Tail for the region of the curve to shade.
• Enter the data value as 0.0005.
• Click OK.

Output using the MINITAB software is given below:

Thus, the critical value is a 3.291.

The correct option is, “(c) $z^{*}=3.291$”.

Reason for the incorrect answers:

Since, the critical value for the 99.9% confidence level is $z^{*}=3.291$; the other options, “(a) $z^{*}=1.960$” and “(c) $z^{*}=2.576$”are incorrect.

Conclusion:

Thus, the critical value is $z^{*}=3.291$.

Statistics Concept Introduction

Introduction:

Critical value:

The critical value is the area between $-z^{*}\text{and}{z}^{*}$ under the standard normal curve, that is, the confidence level C. The number of standard deviations on both sides of the mean is obtained from the standard normal table by using the central area C under standard normal curve.