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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.
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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:
Confidencelevel = 1–levelofsignificance
The confidence level indicates the area left of the z-value. While the level of significance indicates the area right of the z-value.
(a) To determine the value of Zα
1 – 0.0089 = 0.99111–0.0089 = 0.9911
Then use Excel function normsinv (0.9911)
(b) To determine the value of Zα
1 – 0.09 = 0.911–0.09 = 0.91
Use the Excel function normsinv (0.91)
(c) To determine the value of Zα
1 – 0.707 = 0.2931–0.707 = 0.293
Use the Excel function normsinv (0.293)
Ans: Part A
The 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 the z-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].