2. STATISTICAL
HYPOTHESIS
TESTING ERRORS
|RECALL
Null Hypothesis
Two sided-Alternate Hypothesis
Testing the hypothesis involves taking a
random sample, computing a test statistic from
the sample data and then using the test statistic
to make a decision about the NULL hypothesis.
7. TESTS ON THE MEAN OF A
NORMAL DISTRIBUTION,
VARIANCE KNOWN
8. TESTS ON THE MEAN OF A NORMAL
DISTRIBUTION, VARIANCE KNOWN |
BURNING PROPELLANT EXAMPLE
9. TESTS ON THE MEAN OF A
NORMAL DISTRIBUTION,
VARIANCE UNKNOWN
10. TESTS ON THE MEAN OF A
NORMAL DISTRIBUTION,
VARIANCE UNKNOWN | EXAMPLE
A public health official claims that the mean home water use
is 350 gallons a day.
To verify this claim, a study of 20 randomly selected homes
was instigated with the result that the average daily water uses
of these 20 homes were as follows:
340 344 362 375 356 386 354 364 332 402 340 355 362 322
372 324 318 360 338 370
Do the data contradict the official’s claim?
11. GENERAL PROCEDURE FOR
HYPOTHESIS TESTS
In practice, such a formal and (seemingly) rigid procedure is
not always necessary.
Generally, once the experimenter (or decision maker) has
decided on the question of interest and has determined the
design of the experiment (that is, how the data are to be
collected, how the measurements are to be made, and how
many observations are required), only three steps are really
required:
1. Specify the test statistic to be used.
2. Specify the location of the critical region (two-tailed,
upper-tailed, or lower-tailed).
3. Specify the criteria for rejection (typically, the value of
α, or the P-value at which rejection should occur).
