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.
Note:
We can NEVER, EVER, accept the Null Hypothesis. We can either reject it, or fail to reject it. Failing to reject the Null
Hypothesis is NOT the same thing as accepting it.
•

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 5
:
In this step we either list the data we need in Step 6 or calculate it if necessary. In this example we don't need to calculate it.
Basically we need to gather the appropriate data from the information we have to plug into the formula in Step 6.
In Step 2, we determined that this is the appropriate formula for this experiment: Z =
Therefore we need ,
, s, and n. From the text of the problem we see that:
= 11.65
s = 1
n = 30
= 12
(This is obtained from the Null Hypothesis)
•

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 6
:
In this step we plug the data from Step 5 into the formula we identified in Step 2:
Z =
= Z =
= -1.9170
Step 7:
Here we compare the observed Z Statistic we calculated in Step 6 to our Decision Rule in Step 4:
[Reject the Null Hypothesis is Z < -1.96 of if Z > 1.96]
-1.9170 is NOT less than -1.96
and -1.9170 is NOT greater than 1.96
Therefore we
Fail to Reject
the Null Hypothesis
•

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

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- DebraACasto
- Null hypothesis, Statistical hypothesis testing