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Determine z_{α} 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.

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Concepts and ReasonThis problem can be solved using the concept of standard normal variate.

The standard normal variate refers to a normal distribution with a mean equal or zero and a standard variance equal to one. The curve of this variate has a bell-shaped shape.

FundamentalsThe following relationship links the confidence level and the significance level:

Confidencelevel = 1–levelofsignificance

The confidence level indicates the area left of the

z-value. While the level of significance indicates the area right of thez-value.(a)To determine the value ofZ_{α}1 – 0.0089 = 0.99111–0.0089 = 0.9911

Then use Excel function normsinv (0.9911)

(b)To determine the value ofZ_{α}1 – 0.09 = 0.911–0.09 = 0.91

Use the Excel function normsinv (0.91)

(c)To determine the value ofZ_{α}1 – 0.707 = 0.2931–0.707 = 0.293

Use the Excel function normsinv (0.293)

Ans:Part AThe Z-value to indicate a significance level at 0.0089 is 2.37

Part B

For a significance level 0.91, the Z-value is 1.34

Part C

For significance levels of 0.293, the Z-value is – 0.545

This problem can be solved using the concept of standard normal variate.

The standard normal variate refers to a normal distribution with a mean equal or zero and a standard variance equal to one. The curve of this variate has a bell-shaped shape.

The following relationship links the confidence level and the significance level:

[katex]{\rm{Confidence level}} = {\rm{ }}1 – {\rm{ level of significance}}[/katex]

The confidence level indicates the area left of the

z-value. While the level of significance indicates the area right of thez-value.(a)To determine the value of [katex]{Z_\alpha }[/katex]

[katex]1 – 0.0089 = 0.9911[/katex]

Then use Excel function [katex]{\rm{normsinv}}\left( {0.9911} \right)[/katex]

(b)To determine the value of [katex]{Z_\alpha }[/katex]

[katex]1 – 0.09 = 0.91[/katex]

Use the Excel function [katex]{\rm{normsinv}}\left( {0.91} \right)[/katex]

(c)To determine the value of [katex]{Z_\alpha }[/katex]

[katex]1 – 0.707 = 0.293[/katex]

Use the Excel function [katex]{\rm{normsinv}}\left( {0.293} \right)[/katex]

Ans: Part A

The Z-value to indicate a significance level at 0.0089 is [katex]2.37[/katex]Part B

For a significance level 0.91, the Z-value is [katex]1.34[/katex]Part C

For significance levels of 0.293, the Z-value is [katex] – 0.545[/katex].