Chapter 8, Problem R8.1RE

a.

To determine

To find: The critical value.

Answer to Problem R8.1RE

The critical value is 1.88.

Explanation of Solution

Given:

Confidence level = 94%

Sample size ( n ) = 125

Calculation:

Level of significance $\left(\alpha \right)=1-0.94=0.06$

Using the standard normal, the critical value at 6% level of significance can be calculated as:

  $\begin{array}{c}{z}_{\alpha /2}=z_{0.06/2}\\ =1.88\end{array}$

Thus, the critical value is 1.88.

b.

To determine

To find: The critical value.

Answer to Problem R8.1RE

The critical value is 2.665

Explanation of Solution

Given:

Confidence level = 99%

Sample size ( n ) = 58

Calculation:

Level of significance $\left(\alpha \right)=1-0.99=0.01$

Since, sample standard deviation is known t -critical value is to be calculated.

Degree of freedom can be calculated as:

  $\begin{array}{c}df=n-1\\ =58-1\\ =57\end{array}$

The critical value at 1% level of significance can be calculated as:

  $\begin{array}{c}{t}_{\alpha /2,df}=t_{0.01/2,57}\\ =2.665\end{array}$

Thus, the critical value is 2.665.