Answer:
(a) 1.645
(b) 2.5758
Step-by-step explanation:
The complete question is: Find Z([tex]\alpha[/tex]/2) for the confidence level 90% and for the confidence level 99%.
Firstly, as we know that [tex]\alpha[/tex] represent the level of significance, i.e;
Level of significance = 1 - confidence level
(a) We are given the confidence level of 90%, so;
Level of significance = 1 - 90%
= 1 - 0.90 = 0.10 or 10%
Now, [tex]Z_(_\frac{\alpha}{2}_)[/tex] = [tex]Z_(_\frac{0.10}{2}_)[/tex] = [tex]Z_(_0_._0_5_)[/tex]
This means that we have to look for a critical value in the z table at a 5% level of significance which gives us a value of 1.645.
(a) We are given the confidence level of 99%, so;
Level of significance = 1 - 99%
= 1 - 0.99 = 0.01 or 1%
Now, [tex]Z_(_\frac{\alpha}{2}_)[/tex] = [tex]Z_(_\frac{0.01}{2}_)[/tex] = [tex]Z_(_0_._0_0_5_)[/tex]
This means that we have to look for a critical value in the z table at a 0.5% level of significance which gives us a value of 2.5758.
