Q.76 - The Practice of Statistics for AP

Question

You have an SRS of $23$ observations from a Normally distributed population. What critical value would you use to obtain a $98\%$ confidence interval for the mean M of the population if S is unknown? 

(a) $2.508$

(b) $2.500$

(c) $2.326$

(d) $2.183$ 

(e) $2.177$

Step-by-Step Solution

Answer

The correct option is (a).

Step 1: Given Information

Sample size $n=23$,

Confidence interval $c=98\%$,

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

Step 2: Explanation

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

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

 The confidence level is $98\%$.

Convert $98\%$ into decimal.

$\frac{98}{100}=0.98$

Find the column.

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

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

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

Hence, the correct option is (a).