From here we moved to the t-model. This is typically what you end up working with because you don't know the mean nor the standard deviation of the population. It is natural to replace the population standard deviation with the sample standard deviation. However, this introduces more variability into the model, specifically, every sample size results in a slightly different standardized model. This family of models is know as t-models and the specific family member used is determined by the sample size. Specifically, the degrees of freedom (df) is one less than the sample size, i.e. df = n - 1.
We worked through the same examples we used before but no longer assumed the population standard deviation and and sample standard deviation were the same. In this case, since we are using the sample standard deviation, sx, to estimate the standard deviation, we distinguish this by calling the t-model's standard deviation a standard error. Otherwise, t-models behave and are used similar to a normal model.
We were in the computer lab today, so I was able to show students how to conduct their analyses using the Minitab software. Although we won't cover hypothesis testing until next class, there was enough foundational pieces in place that students could follow the general idea and how they could proceed with their projects.
Below is an outline of the lesson along with italicized comments enclosed in square brackets [like this].
·
Margin of error
o
Length of ci/2 or value of what is being added
and subtracted to mean [actually looked at value being added/subtracted first and then mentioned the interval length divided by 2 gives same value]
o
Calculate margin of error for two practice
confidence intervals
·
Estimate sample size needed
o
Solve algebraically starting with ME value [worked through a couple of problems using different confidence levels and margin of errors]
·
Typically don’t
know the population standard deviation, just like we don’t know the
population mean – what can we do
o
Use sample standard deviation for population
standard deviation
o
This introduces more error
§
No longer have standard deviation have standard
error
·
t-model
o
looks like normal model, same basic properties
o
as sample size increase looks more and more like
a normal model
·
t-table
o
in book and handout [book did not include a t-table that provides df and t-score and then shows percentage in upper tail]
·
Confidence intervals
o
Same as before except use t-score and t-table
instead of z-score and normal table
o
Practice problem as before but assume don’t know
population standard deviation
o
Use calculator [introduced this after making use of tables on several intervals]
·
Sample size for t-model – worst case is to use
z-score since don’t know sample size
o
Can get a better estimate after by recalculating [didn't get into this, just have them estimate using z-score]
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