- Confidence intervals are based upon a model developed using our sample statistics. We use our sample data to estimate a probable value for the true population mean.
- Hypothesis tests are based upon a hybrid model that is centered on an assumed value for the population mean but making use of our sample standard deviation to create a standard error for the model.
- Confidence intervals are equivalent to a two-tailed hypothesis test, we are excluding extremely small and extremely large values.
- Hypothesis tests can be one-tailed or two-tailed, there is not an equivalent confidence interval for a one-tailed test.
Will get into test errors and their meanings next class. Will also provided project write-up examples so students better understand the end product they need to produce. Ideally I would have a range of samples and have students rank sort the papers and we would discuss if they were A-, B-, C-level or worse. Unfortunately, I only have high quality examples, so I'll have them read through and look for characteristics from the scoring rubric that are demonstrated in the papers.
Below is the outline of today's lesson with italicized comments enclosed in square brackets [like this].
Below is the outline of today's lesson with italicized comments enclosed in square brackets [like this].
—Hypothesis
Test for One Population Mean
·
Compare hypothesis testing to trial
·
Provide hypotheses mentor texts [mentor texts are problem statements along with appropriate hypothesis statements that show what these hypothesis statements look like. Four examples were provided that included one-tail upper, one-tail lower, and two-tailed alternative hypotheses.]
o
Use always, sometimes, never [In the context of the problem statement, what do you always see, sometimes see, and never see in a hypothesis statement.]
o
Discuss what was seen [At this point students have a better sense of what is being tested]
·
Hypotheses are statements about population
parameters
o
Provide examples for H0 and Ha [Examples included commentary on hypothesis statement structure and content.]
·
Significance level and alpha values
o
Discuss picking a probability for which you
would reject your hypothesis—alpha level
o
Connect to critical values and significance
level
·
Usually don’t know the population standard
deviation so use t-test [Just stated this was the case and we were working with t-model]
o
Works the same way
o
Must include degrees of freedom so know which
t-model was used [The degrees of freedom (df) specifies the exact t-model being used from family of all possible t-models]
o
Can use with moderate to large samples, even if
data is not symmetric [The t-test is a robust test that works reasonably well with even relatively small samples that are somewhat skewed. Provided students a rule of thumb for different sample size ranges but basically said unless the sample is small and highly skewed to not worry about it.]
·
Discuss meaning of p-value
o
Conditional probability—given the null
hypothesis is true, what is the probability of seeing the random sample that
was drawn?
o
The more unusual the sample the smaller the
p-value—it’s not likely to be seen
o
Conclusion: either we drew a bad sample or the
null hypothesis is wrong
o
If we followed good data collection procedures
than the conclusion must be the null hypothesis is incorrect
·
Use sibling data and have students calculate a
p-value
o
What if our class is viewed as a sample; does
sample support claim that the mean number of siblings in the US is 1.86?
o
Work through problems in the book
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