Download Section 9.2 Significance Test for a Mean

Section 9.2 A Significance Test for a Mean DISCUSSION
Statistics
In section 8.2 we looked at a significance test for a proportion. We computed a
test statistic (z value) to determine if a hypothesized population proportion
_____ is compatible with a sample proportion ______. The test statistic value
was:
In this section we are going to compute a test statistic to determine if a
hypothesized mean value for a population, _______, is compatible with a
sample mean, ______.
It would be nice if we could just use a z-distribution like we did in Section 7.2
(Sampling Distribution of a Sample Mean), where :
However, in this case we do not know ______, the population standard
deviation, so we must use the standard deviation of our sample, _____.
Remember, though, that if we use ____ the ______ values must be adjusted, and
we compute a ______ value instead, and use a t-table when working with
probabilities. Recall that the probability values associated with a t-table refer to
tail probabilities, or _____ values.
Since there are so many parallels between sections 8.2 and 9.2, this discussion
will just highlight the characteristics for a Significance Test for a Mean. You
are encouraged to read through the section itself for more details. Here we will
just mention the characteristics of using a P-value in a test of a mean, the
components of a Significance Test for a Mean, and we will look at an example
problem.
Using a P-value in a Test of a Mean
The ____________ is the probability of getting a random sample, from a
distribution with the ________ given in the _______ hypothesis, ______, that
has a value of ______ that is as _____________ or even more extreme than the
_____________ value of ______ computed from the _____________.
When the _____ value is close to ______, you have convincing evidence
____________ the null hypothesis. When the _____ value is large, the result
from the ___________ is consistent with the hypothesized mean and you do not
have enough evidence to ____________ the null.
The test of ___________ for the ________ is called a ____________.
Components of a Significance Test for a Mean
1.) Name the test and check conditions. Three conditions must be tested for:
 _____________________.
 For a ______________, the sample
must have been randomly selected.
 For an ________________, the
________________ must have been
________________ assigned to the
_________________ units.
(1. Name the test and check conditions, continued)
 ____________________.
 The sample must look like it is
reasonable to assume it came
from a __________________
distributed population OR
 the sample ___________ must
be ____________ enough for
the sampling distribution of the
sample mean to be
approximately normal (there is
no set rule for approximately
normal)
2.) State your hypotheses.
 The _______ hypothesis is that the population mean, ______, has a
particular value ______. This is typically abbreviated as
________ = _______.
 The _____________ hypothesis, _______, has one of three forms:
3.) Compute the test statistic, find the ____value, and draw a sketch.
 The ________ statistic is the distance from the sample mean, _____,
to the hypothesized value, ______, measured in standard errors:
(the P-value is the probability of getting a value of t that is as extreme or more extreme than the one
computed form the actual sample if the null hypothesis is true).
4.) Write your _______________ linked to your computations and in the
context of the problem.
 Reject the _______ hypothesis, ______, if your _____value is less
than the level of significance, ______.
 If the _____value is greater than or equal to _______, do not reject
the _______ hypothesis, _____.
 If you are not given a value of ______, assume that _____ = ______.
Example (from pages 590 – 591 of text)
McDonald’s “target value” for the mass of a large order of French Fries is 171
g. 30 bags of French Fries at a McDonald’s Restaurant were purchased. When
plotted, the mass distribution has a reasonably normal distribution shape. The
mean of this sample was ______ = 144.07 grams with a sample standard error
of _____ = 12.28 grams. Based on your sample, you want to determine if
McDonald’s “target value” is reasonable.
Step 1.) The problem states that the shape of the sample looks approximately
normal, so we assume we are OK to do the analysis.
Step 2.) State the null hypothesis and alternative hypothesis.
Step 3.) Compute the test statistic, find the P-value, and draw a sketch.
Step 4.) Write your conclusion lined to the computations and in context of the
problem.