Chapter 8.3, Problem 57E

(a)

To determine

To calculate: The critical value $t^{*}$ when the confidence level is 95% and the population mean is 10.

Answer to Problem 57E

The critical value is 2.262.

Explanation of Solution

Given information:

Confidence level $c=95\%$

Population mean $n=10$

Formula used:

Degree of freedom $df=n-1$

Calculation:

Find the degree of freedom, use the formula $df=n-1$ .

  $\begin{array}{l}df=n-1\\ =10-1\\ =9\end{array}$

Degree of freedom $df$ represent the row in table B.

Confidence level is 95%.

Convert 95% into decimal.

  $\frac{95}{100}=0.95$

Find the column.

  $\begin{array}{c}\frac{1-c}{2}=\frac{1-0.95}{2}\\ =0.025\end{array}$

Find the critical value $t^{*}$ , for row 9 and the column 0.025 from the table B.

  $t^{*}=2.262$

Hence, the critical value is 2.262.

(b)

To determine

To calculate: The critical value $t^{*}$ when the confidence level is 99% and the population mean is 20.

Answer to Problem 57E

The critical value is 2.861.

Explanation of Solution

Given information:

Confidence level $c=99\%$

Population mean $n=20$

Formula used:

Degree of freedom $df=n-1$

Calculation:

Find the degree of freedom, use the formula $df=n-1$ .

  $\begin{array}{l}df=n-1\\ =20-1\\ =19\end{array}$

Confidence level is 99%.

Convert 99% into decimal.

  $\frac{99}{100}=0.99$

Find the column.

  $\begin{array}{c}\frac{1-c}{2}=\frac{1-0.99}{2}\\ =0.005\end{array}$

Find the critical value $t^{*}$ , for row 19 and the column 0.005 from table B.

  $t^{*}=2.861$

Hence, the critical value is 2.861.