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by **zorro** on Fri Jul 02, 2010 2:29 am

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}

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by **Martingale** on Fri Jul 02, 2010 2:58 am

zorro wrote: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?

by **zorro** on Sat Jul 03, 2010 6:10 am

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

by **Martingale** on Sat Jul 03, 2010 2:34 pm

zorro wrote: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 $\hat{p}=\frac{X}{n}$

by **zorro** on Sat Jul 03, 2010 6:36 pm

Martingale wrote: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 ?? :confused:

by **Martingale** on Sat Jul 03, 2010 8:08 pm

zorro wrote:Could u please tell what is the name of the formula ??

It's the $(1-\alpha)100\%$ confidence interval for population proportions (assuming normality)

by **zorro** on Sun Jul 04, 2010 5:40 am

Thanks All :mrgreen:

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