Chapter 8.3, Problem 76E

To determine

To calculate: For the confidence interval of 98% the critical value $t^{*}$ is (a) 2.508, (b) 2.500, (c) 2.326, (d) 2.183, (e) 2.177.

Answer to Problem 76E

The correct option is (a).

Explanation of Solution

Given Information:

Sample size $n=23$

Confidence interval $c=98\%$

Formula Used Degree of freedom $df=n-1$

Calculation:

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

  $\begin{array}{c}df=n-1\\ =23-1\\ =22\end{array}$

The confidence level is 98%.

Convert 98% into decimal.

  $\frac{98}{100}=0.98$

Find the column.

  $\begin{array}{c}\frac{1-c}{2}=\frac{1-0.98}{2}\\ =0.01\end{array}$

From table B find critical value $t^{*}$ , use the row and column.

Thus, the critical value $t^{*}\text{is}2.508$ .

Hence, the correct option is (a)