Question

You have an SRS of $23$observations from a large population. The distribution of sample values is roughly symmetric with no outliers. What critical value would you use to obtain a $98\%$confidence interval for the mean of the population?

a. $2.177$

b. $2.183$

c. $2.326$

d. $2.500$

e. $2.508$

Short answer

Option (e) is correct.

Step-by-step solution

Given Information

Confidence level is$98\%$and$n=23$

Calculation

Level of significance is $\alpha =1-0.98=0.02$

Degree is freedom is calculated as $df=n-1=23-1=22$

At $2\%$level of significance, critical value is $t_{\alpha /2,df}=t_{0.02/2,22}$

$=2.508$

Option (e) is correct.