Question

Determine zα for the following. (Round your answers to two decimal places.)

(a)    α = 0.0089

(b)    α = 0.09

(c)    α = 0.707

Please explain where and how you got the answer.

Thank you.

Answer 1

Concepts and reason

The concept of standard normal variate is used to solve this problem.

The standard normal variate is a normal distribution which has a mean equal to zero and a standard deviation equal to one, and the curve of this variate is bell-shaped.

Fundamentals

The confidence level and the level of significance are related with the following relationship:

${\rm{Confidence level}} = {\rm{ }}1 - {\rm{ level of significance}}$

The confidence level shows the area to the left of the corresponding z-value, whereas the level of significance shows the area to the right of the corresponding z-value.

(a)

To find the value of ${Z_\alpha }$ at the significance level 0.0089, the confidence level would be;

$1 - 0.0089 = 0.9911$

Then use Excel function ${\rm{normsinv}}\left( {0.9911} \right)$ to get the corresponding z- value. The Excel formula used is as shown:

(b)

To find the value of ${Z_\alpha }$ at the significance level 0.09, the confidence level would be;

$1 - 0.09 = 0.91$

Use the Excel function ${\rm{normsinv}}\left( {0.91} \right)$ to get the Z value as shown:

(c)

To find the value of ${Z_\alpha }$ at the significance level 0.707, the confidence level would be:

$1 - 0.707 = 0.293$

Use the Excel function ${\rm{normsinv}}\left( {0.293} \right)$ to get the Z value as shown:

Ans: Part a

The Z-value for a significance level of 0.0089 is $2.37$ .

Part b

The Z-value for a significance level of 0.91 is $1.34$ .

Part c

The Z-value for a significance level of 0.293 is $- 0.545$ .