Chapter 8, Problem T8.5SPT

To determine

To find: The critical value that should be used in this interval

Answer to Problem T8.5SPT

Explanation of Solution

Given:

Population standard deviation is not known.

Sample size ( n ) = 30

Confidence level = 90%

Calculation:

Level of significance is:

  $\begin{array}{c}\text{Level of significance}\left(\alpha \right)=1-\text{Confidence level}\\ =1-0.90\\ =0.10\end{array}$

Here, t -critical value is to be calculated.

Degree of freedom is computed as:

  $\begin{array}{c}\text{Degree of freedom}\left(df\right)=n-1\\ =30-1\\ =29\end{array}$

The critical value at 29 degree of freedom and 10% significance level is computed as:

  $\begin{array}{c}{t}_{\alpha /2,df}=t_{0.10/2,29}\\ =1.699\end{array}$

Hence, the correct option is (b).