Hello,
I am currently taking a first course in statistics, and I was hoping that
perhaps someone might be kind enough to answer a question for me. I
understand that, while a quantitative variable may not be normally
distributed, we may calculate the mean of the sample, and use facts about
the Central Limit Theorem, to form a 95% confidence interval for the
population mean. As far as I know, this means that in 95/100 samples, the
interval will contain the true population mean. This seems very useful at
first, but then something begins to confuse me. Yes, we have an interval
that may contain the true population mean, but ... if the distribution is
heavily skewed to the right, say like income, why do we want an interval for
the population mean, when we are taught that the median is a better measure
of central tendency for skewed distributions? This is what confuses me. I
hope that I have phrased my question in such a way that people can
understand what I am saying, and why I am confused. There is just one more
thing I would like to get off my chest. My textbook talks about simple
random sampling, where you can specify the probability of a sample being
selected from the population. Yet, there are examples in the book which deal
with conceptual populations, such as the set of all cars of a particular
model which may be manufactured in the future. Suppose you have a sample of
several of these autos, and you want to find a 95% confidence interval for
mean miles/gallon. How is this an SRS when you can't specify the probability
of a sample being selected, because the population is conceptual? Perhaps I
am simply looking at everything the wrong way, but this is very confusing to
me. Any help would be greatly appreciated.
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