Chapter 8.3, Problem 2.1CYU

a.

To determine

To find: The critical value.

Answer to Problem 2.1CYU

The critical value is 2.518

Explanation of Solution

Given:

  $\begin{array}{l}\text{Confidence level = 98\%}\\ \text{Sample size}\left(n\right)=22\end{array}$

Calculation:

The level of significance is:

  $\begin{array}{c}\text{Level of significance = 1}-\text{ Confidence level}\\ \text{=1-0}\text{.98}\\ \text{=0}\text{.02}\end{array}$

The degree of freedom is 22-1 = 22

The critical value using standard normal table is calculated as:

  $\begin{array}{c}{t}_{{}^{\alpha /2.df}}=t_{0.02/2,21}\\ =2.518\end{array}$

The critical value is 2.518

b.

To determine

To find: The critical value.

Answer to Problem 2.1CYU

The critical value is 1.833.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Confidence level = 90\%}\\ \text{Sample size}\left(n\right)=10\end{array}$

Calculation:

The level of significance is:

  $\begin{array}{c}\text{Level of significance = 1}-\text{ Confidence level}\\ \text{=1-0}\text{.90}\\ \text{=0}\text{.10}\end{array}$

The degree of freedom is 10-1 = 9

The critical value using standard normal table is calculated as:

  $\begin{array}{c}{t}_{{}^{\alpha /2.df}}=t_{0.10/2,9}\\ =1.833\end{array}$

The critical value is 1.833.

c.

To determine

To find: The critical value.

Answer to Problem 2.1CYU

The critical value is 2.447.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Confidence level = 95\%}\\ \text{Sample size}\left(n\right)=7\end{array}$

Calculation:

The level of significance is:

  $\begin{array}{c}\text{Level of significance = 1}-\text{ Confidence level}\\ \text{=1-0}\text{.95}\\ \text{=0}\text{.05}\end{array}$

The degree of freedom is 7-1 = 6

The critical value using standard normal table is calculated as:

  $\begin{array}{c}{t}_{{}^{\alpha /2.df}}=t_{0.05/2,6}\\ =2.447\end{array}$

The critical value is 2.447