Find the critical value $z _ { \alpha / 2 }$ that corresponds to a 91% confidence level.
A) 1.34
B) 1.645
C) 1.70
D) 1.75

Question

Find the critical value $z _ { \alpha / 2 }$ that corresponds to a  91% confidence level.
A)  1.34 
B)  1.645 
C)  1.70 
D)  1.75

Quizplus · Accepted Answer

For a 91% confidence level, the area in the tails (outside the confidence interval) is 9%, or 0.09. This is split between the two tails, so each tail has an area of 0.045. Looking up 0.045 in the z-table (or using a calculator or software that can invert the normal distribution), we find the z-value that corresponds to the cumulative area of 0.955 (1 - 0.045) is approximately 1.70.

Find the Critical Value zα/2z _ { \alpha / 2 }zα/2​

Find the Critical Value $z _ { \alpha / 2 }$