Step 4
: (continued)
a.
Determine if this is a 2-Tail test of a 1-Tail Test. If it's a 1-Tail test, is it a "left-tail" test or a "right-tail" test.
This problem calls for a 2-tail test.
Why?
Because there are two circumstances under which we can "reject" the null
hypothesis. We can reject H
0
if we conclude there are less than12 ounces of soda in the cans, and we can reject H
0
if we
conclude there is more than 12 ounces in the cans. That makes this a 2-tail test. This will hopefully clarify itself when we get
to
the 1-tail tests.
b.
Determine the decision rule which we'll employ in Steps 7 and 8.
We've just concluded that this is a 2-tail test. Now we have to find the Z-Factor against which we'll compare the observed Z
statistic we'll calculate in Step 6. Finding this Z-factor is very similar to what we did in Modules 11 - 13, but it depends on
whether or not we are dealing with a 2-tail or 1-tail test.
This is a 2-tail test so as with confidence intervals, which have 2
sides,
we must divide alpha by 2:
=
=
=
1.96
The table on the next slide should look familiar to you now, but this one has some added information which we'll get into
when we do Example 7B
•

Module 13: Sample Size Determination and Intro to Hypothesis Testing
II. Introduction to Hypothesis testing
Z Factor for 2-Tail Tests
Z Factor for 1-Tail Tests
α
α/2
Z
α/2
Z
α/2
α
Z
α
0.01
0.005
Z
.005
2.5758
=NORMSINV(0.005)*-1
0.01
Z
.01
2.3263
=NORMSINV(0.01)*-1
0.02
0.01
Z
.01
2.3263
=NORMSINV(0.01)*-1
0.02
Z
.02
2.0537
=NORMSINV(0.02)*-1
0.04
0.02
Z
.02
2.0537
=NORMSINV(0.02)*-1
0.04
Z
.04
1.7507
=NORMSINV(0.04)*-1
0.05
0.025
Z
.025
1.9600
=NORMSINV(0.025)*-1
0.05
Z
.05
1.6449
=NORMSINV(0.05)*-1
0.10
0.05
Z
.05
1.6449
=NORMSINV(0.05)*-1
0.10
Z
.10
1.2816
=NORMSINV(0.1)*-1
0.15
0.075
Z
.075
1.4395
=NORMSINV(0.075)*-1
0.15
Z
.15
1.0364
=NORMSINV(0.15)*-1
0.20
0.10
Z
.10
1.2816
=NORMSINV(0.1)*-1
0.20
Z
.20
0.8416
=NORMSINV(0.2)*-1

Module 13: Sample Size Determination and Intro to Hypothesis Testing
II. Introduction to Hypothesis testing
Example 7A
:
Coca Cola sells 12 ounce cans of soda. The presumption is that there are in fact 12 ounces of soda in each can. We
want to conduct a test to verify if that is true. Toward that end, we randomly sample 30 cans of Coke. This results in a sample
mean 11.65 ounces with a sample standard deviation of 1 ounce. At the .05 level of significance, test to determine if there are
there 12 ounces of soda in the cans as Coca Cola claims.
Step 4
: (continued)
On a previous slide we determined that
=
=
= 1.96
The most important component of Step 4 is stating our decision rule. Again, this is a two tail test which means we can reject the
null hypothesis if there is less than 12 ounces, or if there is more than 12 ounces. Thus, our decision rule looks like this:
Decision Rule:
Reject the Null Hypothesis if Z < -1.96 of if Z > 1.96
This means that if the observed Z-Statistic we calculate in Step 6 is less than NEGATVE 1.96 or greater than positive 1.96, we can
reject the Null Hypothesis. If, however, -1.96 Z
1.96, we FAIL to Reject the null.

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- Null hypothesis, Statistical hypothesis testing