- In a hypothesis test problem, you may see words such as "the level of significance is
1%." The "1%" is the preconceived or preset αα.
- The statistician setting up the hypothesis test selects the value of αα to use before
collecting the sample data.
- If no level of significance is given, we generally can use α=0.05α=0.05.
- When you calculate the p-value and draw the picture, the p-value is in the left tail,
the right tail, or split evenly between the two tails. For this reason, we call the
hypothesis test left, right, or two tailed.
- The alternate hypothesis, HaHa, tells you if the test is left, right, or two-tailed.
It is the key to conducting the appropriate test.
- HaHa never has a symbol that contains an equal sign.
The following examples illustrate a left, right, and two-tailed test.
H
o
H
o
: μμ
=
5
=5
H
a
H
a
: μμ
<
5
<5
Test of a single population mean. HaHa tells you the test is left-tailed. The picture of the p-value is as follows:
H
o
H
o
: pp
≤
0.2
≤0.2
H
a
H
a
: pp
>
0.2
>0.2
This is a test of a single population proportion. HaHa tells you the test is right-tailed. The picture of the p-value is as follows:
H
o
H
o
: μμ
=
50
=50
H
a
H
a
: μμ
≠
50
≠50
This is a test of a single population mean. HaHa tells you the test is two-tailed. The picture of the p-value is as follows.
- Hypothesis Testing:
Based on sample evidence, a procedure to determine whether the hypothesis stated is a reasonable statement and cannot be rejected, or is unreasonable and should be rejected.
- p-value:
The probability that an event will happen purely by chance assuming the null hypothesis is true. The smaller the p-value, the stronger the evidence is against the null hypothesis.
(What does "Endorsed by" mean?)
"Reviewer's Comments: 'I recommend this book. Overall, the chapters are very readable and the material presented is consistent and appropriate for the course. A wide range of exercises introduces […]"