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Sagot :
Answer:
The correct value of the Z-statistic is z = -1.56
Step-by-step explanation:
A company manufacturing computer chips finds that 8% of all chips manufactured are defective.
This means that the null hypothesis is:
[tex]H_{0}: p = 0.08[/tex]
A hypothesis test is performed to determine if the additional training was effective in lowering the defect rate.
This means that the alternate hypothesis is:
[tex]H_{a}: p < 0.08[/tex]
z-statistic:
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
0.08 is tested at the null hypothesis:
This means that [tex]\mu = 0.08, \sigma = \sqrt{0.08*0.92}[/tex]
After training was implemented, a sample of 450 chips revealed only 27 defects.
This means that [tex]n = 450, X = \frac{27}{450} = 0.06[/tex]
The correct value of the Z-statistic is
[tex]z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{0.06 - 0.08}{\frac{\sqrt{0.08*0.92}}{\sqrt{450}}}[/tex]
[tex]z = -1.56[/tex]
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