Question

Example # 2:

Find
Za
for the confidence level 90%.
2
Example # 3:
Find 2, for the confidence level 99%.

Answer 1

(a) 1.645

(b) 2.5758

Explanation:

The complete question is: Find Z(
`\alpha`/2) for the confidence level 90% and for the confidence level 99%.

Firstly, as we know that
`\alpha` 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,
`Z_(_(\alpha)/(2)_)` =
`Z_(_(0.10)/(2)_)` =
`Z_(_0_._0_5_)`

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,
`Z_(_(\alpha)/(2)_)` =
`Z_(_(0.01)/(2)_)` =
`Z_(_0_._0_0_5_)`

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.