Random sample of 120 customers’s spent an average of 9.2 hours on their professional job with a sample standard deviation of 5.1 hours. Calculate the specification hours with confidence of 95%.

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- Dec 15th 2008, 09:46 PMmagentaritaSpecification Hours
Random sample of 120 customers’s spent an average of 9.2 hours on their professional job with a sample standard deviation of 5.1 hours. Calculate the specification hours with confidence of 95%.

- Dec 17th 2008, 03:02 PMmeymathis
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*specification hours*. It looks like you are supposed to calculate the confidence interval with 95% confidence level.

The Central Limit Theorem (which the general rule of thumb says is ok to invoke for $\displaystyle N\geq 30$) tells us that $\displaystyle \frac{\bar{X}-\mu}{S \sqrt{N}}$ is approximately normally distributed with mean 0 and std dev 1.

So then the confidence interval is given by $\displaystyle \bar{X}\pm z_{\alpha/2}S/\sqrt{N}$ where $\displaystyle z_{\alpha/2}$ is defined by $\displaystyle \mathrm{P}(-z_{\alpha/2}\leq Z \leq z_{\alpha/2})=1-\alpha$ (*Z*is from the standard normal distribution). I'm assuming that you have already seen where these formulas came from.

So from a standard normal distribution table $\displaystyle z_{\alpha/2}=1.96$. So just plug away. - Dec 21st 2008, 11:53 AMmagentaritaok...