Session 14, Sections 8-1 and 8-2
Hypothesis Testing
Statistical hypothesis testing is a decision-making process for evaluating
claims about a population. In hypothesis testing, the researcher must define the
population under study, state the particular hypotheses that will be
investigated, give the significance level, select a sample from the population,
collect the data, perform the calculations required for the statistical test,
and reach a conclusion. Researchers are interested in answering many types
of questions. For example: “Will a new drug lower blood pressure?” or “Will seat
belts reduce the severity of injuries caused by accidents?”. These types
of questions can be addressed through statistical hypothesis testing, which is a
decision-making process for evaluating claims about a population.
At the end of this chapter you will be able to:
If you have learned all of these objectives, then close this window to
return to where you were.
- Hypotheses concerning parameters such as means and proportions can be
investigated.
- The z test and the t test are used for hypothesis testing concerning
means.
- The three methods used to test hypotheses are:
- The traditional method.
- The P-value method.
- The confidence interval
method.
- A statistical hypothesis is a conjecture about a population parameter
which may or may not be true.
- There are two types of statistical hypotheses for each situation:
- the null hypothesis
- The null hypothesis represents the status quo or the hypothesis that
is to be disproved. The null hypothesis includes an equal sign in its
definition of a parameter of interest.
- the alternative hypothesis
- The alternative hypothesis is the opposite of the null hypothesis, and
usually represents taking an action. The alternative hypothesis includes
either a less than sign, a not equal sign, or a greater than sign in its
definition of a parameter of interest.
- A type I error occurs if one rejects the null hypothesis when it is
true.
- A type II error occurs if one does not reject the null hypothesis when
it is false.
- The critical value(s) separates the critical region from the
noncritical region. The symbol for critical value is C.V. The
critical or rejection region is the range of values of the test value that
indicates that there is a significant difference and that the null
hypothesis should be rejected.
- The noncritical or nonrejection region is the range of values of the
test value that indicates that the difference was probably due to chance
and that the null hypothesis should not be rejected.
- A one-tailed test indicates that the null hypothesis should be
rejected when the test value is in the critical region on one side of the
mean.
- In a two-tailed test, the null hypothesis should be rejected when the
test value is in either of the two critical regions.
-
Return to objectives
-
The null hypothesis,
- symbolized by H0, is a statistical hypothesis that states
that there is no difference between a parameter and a specific value, or
that there is no difference between two parameters.
-
The alternative hypothesis,
- symbolized by H1, is a statistical hypothesis that states
the existence of a difference between a parameter and a specific value, or
states that there is a difference between two parameters.
-
Hypothesis-Testing Common Phrases
- Table 8-1 on page 368 gives mathematical expressions, equalities
and inequalties, associated with common English language phrases.
-
Design the study:
After stating the hypotheses, the researcher’s next step is to design
the study. The researcher
- selects the correct statistical test,
- chooses an appropriate level of significance,
- and formulates a plan for conducting the study
- If living beings are involved, several levels of permission are
required.
-
Possible Outcomes of a Hypothesis Test
- Null hypothesis is true.
- Null hypothesis is false.
-
Possible Errors with a Hypothesis Test
- A type I error occurs if one rejects the null hypothesis when it is
true.
- A type II error occurs if one does not reject the null hypothesis when
it is false.
-
Error Probabilities
- The level of significance is the maximum probability of committing a
Type I error. This probability is symbolized by alpha
α. We will
primarily concern ourselves with Type I errors.
- The probability of a Type II error is symbolized by Beta
β.
-
α and β
Probabilities
- In most hypothesis testing situations, β
cannot easily be computed; however,
- α and
β are related in that decreasing one
increases the other.
-
Hypothesis Testing
- In a hypothesis testing situation, the researcher decides what level
of significance to use.
- After a significance level is chosen, a critical value is selected
from a table for the appropriate test.
Return to objectives
State the null and alternative hypotheses
The average income of the nurses is 36,250
Return to objectives
State the null and alternative hypotheses
the average cost of a VCR is $297.75
Return to objectives
State the null and alternative hypotheses
The average electric bill for residents of White
Pine Estates exceeds $52.98 per month
Return to objectives
- In a hypothesis testing situation,
the researcher decides what level of
significance to use.
- After a significance level is
chosen, a critical value is selected
from a table for the appropriate test.
- Critical Values
- The critical value(s) separates
the critical region from the
noncritical region.
- The symbol for critical value is
C.V.
- The critical or rejection region
is the range of values of the test
value that indicates that there is a
significant difference and that the
null hypothesis should be rejected.
- The noncritical or nonrejection
region is the range of values of the
test value that indicates that the
difference was probably due to chance
and that the null hypothesis should
not be rejected.
- One-Tailed Test
- A one-tailed test indicates that
the null hypothesis should be rejected
when the test value is in the critical
region on one side of the mean.
- A one-tailed test is either
right-tailed or left-tailed, depending
on the direction of the inequality of
the alternative hypothesis.
- Left-Tailed Test
- Right-Tailed Test
- Two-Tailed Test
- In a two-tailed test, the null
hypothesis should be rejected when the
test value is in either of the two
critical regions.
Return to objectives
Explain the difference between a one tailed and two tailed test
Return to objectives
Explain the difference between a right tailed and left tailed test
Return to objectives
- Step 1 State the hypothesis, and identify the claim.
- Step 2 Find the critical value from the appropriate table.
- Step 3 Compute the test value.
- Step 4 Make the decision to reject or not reject the null hypothesis.
- Step 5 Summarize the results.
Return to objectives
- A statistical hypothesis is a conjecture about a
population.
- There are two types of statistical hypotheses: the null
hypothesis states that there is no difference, and the
alternative hypothesis specifies a difference.
- Researchers compute a test value from the sample
data in order to decide whether the null hypothesis should or
should not be rejected.
- Statistical tests can be one-tailed or two-tailed,
depending on the hypotheses.
- The null hypothesis is rejected when the difference
between the population parameter and the sample statistic is
said to be significant.
- The difference is significant when the test value falls in
the critical region of the distribution.
- The critical region is determined by
α, the level of
significance of the test.
- The significance level of a test is the probability of
committing a type I error.
- A type I error occurs when the null hypothesis is
rejected when it is true.
- The type II error can occur when the null hypothesis is
not rejected when it is false.
Return to objectives
When you finish these notes, then close this window to return to where
you were.