Friday, February 15, 2008

Lecture 6 - Ch 8b - Confidence Interval for the Mean with *Known* Std Dev

A more realistic example of confidence intervals for the mean would be the case in which the standard deviation of the population is unknown. I mean, how often would you know the standard deviation of the population but not know the mean??

But as a reminder, we did an example where the population std dev is known.

A sample of 11 circuits from a large normal population has a mean resistance of 2.20 ohms. We know from past testing that the population standard deviation is 0.35 ohms. Determine a 95% confidence interval for the true mean resistance of the population.
As in any scenario (what we used to call "story problems"), the key is to pull out the key pieces of information and identify how they should be used. In this case:
sigma(i.e. population std dev)=0.35
and we want a 95% confidence interval

Our confidence interval is xbar +/- zalpha/2(sigma/sqrt(n))
= 2.20 +/- 1.96(0.35/sqrt(11))
= 2.20 +/- 0.2088

Note 1: Some textbooks leave out the alpha/2 subscript from z. It's really more precise to leave it in there. It will become important when we start looking at one-tail hypothesis testing in Chapter 9.

Note 2: On an exam, the +/- notation is enough. You don't need to actually calculate the endpoints of the interval.

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