Could really understand the question

Standard deviation, mean, variance, z-scores, t-tests, etc.
zorro
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Could really understand the question

Question :

A random sample of 500 components was taken from a large consignment and 60 were found to be defective . Obtain the 98% confidence limits for the percentage of defective components in the consignment
(Note that significant value of Z at 2% level of significance is 2.33)

please just point me to the right direction

Martingale
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Joined: Mon Mar 30, 2009 1:30 pm
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Re: Could really understand the question

Question :

A random sample of 500 components was taken from a large consignment and 60 were found to be defective . Obtain the 98% confidence limits for the percentage of defective components in the consignment
(Note that significant value of Z at 2% level of significance is 2.33)

please just point me to the right direction
Where are you stuck?

zorro
Posts: 28
Joined: Sat Jun 12, 2010 9:26 am
Contact:

Re: Could really understand the question

How do i know what is the standard deviation $\sigma$ in this problem

from the question i can figure out that

n = 500
$\bar{X}$ = 60

Martingale
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Re: Could really understand the question

How do i know what is the standard deviation $\sigma$ in this problem

from the question i can figure out that

n = 500
$\bar{X}$ = 60
you need to use

$\left[\hat{p}-Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}},\hat{p}+Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right]$

Where $\hat{p}=\frac{X}{n}$

zorro
Posts: 28
Joined: Sat Jun 12, 2010 9:26 am
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Re: Could really understand the question

you need to use

$\left[\hat{p}-Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}},\hat{p}+Z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\right]$

Where $\hat{p}=\frac{X}{n}$
Could u please tell what is the name of the formula ??

Martingale
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Joined: Mon Mar 30, 2009 1:30 pm
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Re: Could really understand the question

Could u please tell what is the name of the formula ??
It's the $(1-\alpha)100\%$ confidence interval for population proportions (assuming normality)

zorro
Posts: 28
Joined: Sat Jun 12, 2010 9:26 am
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Thanks All