Chapter 8.3, Problem 58E

(a)

To determine

To calculate: The critical value $t^{*}$ when the confidence level is 90% and the population mean is 12.

Answer to Problem 58E

The critical value is 1.796.

Explanation of Solution

Given information:

Confidence level $c=90\%$

Population mean $n=12$

Formula used:

Degree of freedom $df=n-1$

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

  $\begin{array}{l}df=n-1\\ =12-1\\ =11\end{array}$

Confidence level is 90%.

Convert 90% into decimal.

  $\frac{90}{100}=0.90$

Find the column.

  $\begin{array}{c}\frac{1-c}{2}=\frac{1-0.90}{2}\\ =0.05\end{array}$

Find the critical value $t^{*}$ , for row 11 and the column 0.05 from table B.

  $t^{*}=1.796$

Hence, the critical value is 1.796.

(b)

To determine

To calculate: The critical value $t^{*}$ when the confidence level is 95% and the population mean is 30.

Answer to Problem 58E

The critical value is 2.045.

Explanation of Solution

Given information:

Confidence level $c=95\%$

Population mean $n=30$

Formula used:

Degree of freedom $df=n-1$

Calculation:

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

  $\begin{array}{l}df=n-1\\ =30-1\\ =29\end{array}$

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.

  $t^{*}=2.045$

Hence, the critical value is 2.045.