Please Note: this handout was created for a different class, so chapter
and page references are not valid.
Example from our first test: Problem 4 can be phrased in this
terminology. We were "testing a conjecture", but we can
formalize the process as a test of hypothesis (see p. 240).
Null hypothesis: specifies the value of a population
parameter. We seek to determine if observed data is contradictory to this
value.
Alternative hypothesis: gives an hypothesis opposing the
null hypothesis. We wonder if the data support the alternative hypothesis.
Test statistic: z-statistic,
Significance level: "the observed significance level, or
p-value, of a test of hypothesis is the probability of obtaining the
observed value of the sampled statistic, or a value of this statistic that is
even more supportive of the alternative hypothesis, under the assumption that
the null hypothesis is true."
Decision rule: specifies when the sampled data provides
sufficient evidence to conclude that we can reject the null hypothesis in favor
of the alternative hypothesis. "We will always phrase the decision rule as:
accept the alternative hypothesis when the p-value of the test is less
than
."
I can never bring myself to say that.... The upshot is, if
, then reject the null
in favor of the alternative.
Compute p-value (value as extreme as Z=-2.08
or more so):
, hence reject the null
in favor of the alternative.
Interpretation of the results: older folks apparantly
don't eat as many eggs as other adults (our estimate is
240 eggs per year).
Examples:
#1, p. 242 (proportion)
Section 7.2: Performing a test of hypothesis about
We'll use a "Z-Test" (see p. 246) when conditions are appropriate
(see p. 245).
In these problems, the final step is interpretation. There are two
guides to interpretation, on pages 252 and 254.