Having developed a construction technique for confidence intervals for mean with σ known, we now drop our simplifying assumption and address the common case when we do not know much about the populat...Having developed a construction technique for confidence intervals for mean with σ known, we now drop our simplifying assumption and address the common case when we do not know much about the population; i.e. we do not know the population mean or population standard deviation. We must know that the sampling distribution of sample means has either a normal parent population or the sample size n is greater than 30. Now we create our confidence intervals when population parameters are unknown.
We begin with testing hypotheses about the population mean. Just like our considerations of confidence intervals for means, we will have two cases to consider based on whether the population standard ...We begin with testing hypotheses about the population mean. Just like our considerations of confidence intervals for means, we will have two cases to consider based on whether the population standard deviation is known or unknown. The latter case is the more frequently occurring case as we discussed in the chapter on confidence intervals, but we again begin with the case that the population standard deviation is known because of pedagogical considerations.
