Today:
- Don't forget you have a test next Tuesday!
- Sections 5.2, 6.1-2, 7.1-3, 8.1
- Sampling distribution of the sample proportion
- Estimating means with CI
- Selecting sample size
- Elements of a test of hypothesis
- Performing a test of hypothesis for the mean
- Type I and Type II errors
- Inferences about a population proportion
- Quick hypothesis testing quiz
- Section 8.1: Inferences about a population proportion
- Confidence intervals: Essentially the same as for the sample mean, but
- the standard error formula is different, and
- we don't have a given
, so we estimate it using the computed value
based on the sample proportion p (see p. 273).
- Example:
- The hypothesis testing is essentially the same as for the sample mean,
except that you have a different formula for the z-statistic:
- Additional sample proportion example: #4, p. 285
- Questions on material for the test? If not, we'll start 8.2....
- Section 8.2: Estimating
when
is unknown
- The t-distribution
- similar in shape to the normal
- we estimate
using the sample standard deviation, s:
whereas
- Properties of the t-distribution above:
- symmetric, like the normal
- centered at zero, like the normal
- had n-1 degrees of freedom
- the standard deviation of the distribution is
- Since the standard deviation of the distribution is
greater than 1, it is a little broader than the normal,
a little more variable.
- The major difference between the z- and t-distributions is that
for the normal we have one single table; for the t-distribution, we need to
know the value of n, and then use the table for that value of
df=n-1. (Rats!) Of course, with technology, this is not really much of a
problem.
- How does this affect our strategy? It's basically the same: see
page 290....
- Let's try an example:
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