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kristicutie69 · Jul 30, 2009, 09:06 PM

A sample of size n = 20 is selected from a normal population to construct a 95% confidence interval estimate for a population mean. The interval was computed to be (8.20 to 9.80). Determine the sample standard deviation.

galactus · Jul 31, 2009, 05:36 AM

Since n<30, we use a t-distribution with d.f = 19.

Looking this up in the t table we find the rejection regions are t<-2.093 and t>2.093.

${\mu}-E=8.2$

${\mu}+E=9.8$

Solving the system yields $\overline{x}=9, \;\ E=0.8$

Or we could just find the difference in the values and divide by 2. E=(9.8-8.2)/2=0.8

Use the formula $E=t\cdot \frac{s}{\sqrt{n}}$ to find the standard deviation, s, by subbing in your knowns and solving for s.