Introduction to Hypothesis Testing Flashcards
Hypothesis
is a conjecture about a population
parameter. This conjecture may or may
not be true.
Two Types of Hypothesis
- Null Hypothesis
- Alternative Hypothesis
Two Types of Hypothesis
- Null Hypothesis
- Alternative Hypothesis
Null Hypothesis
symbolized by π―π, 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.
Alternative Hypothesis
symbolized by π―π (or π―π ), 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.
Three Methods in Hypothesis Testing
- The traditional method
- The π-value method
- The confidence interval method
Null Hypothesis (π»0)
is the statement being
tested.
Alternative Hypothesis (π»a )
possible values
about the population parameter.
π―πβΆ ππ β π2
(two-tailed test)
π―π βΆ ππ > π2
(one-tailed test)
π―π βΆ ππ < π2
(one-tailed test)
Basic Steps in the Traditional Hypothesis Testing
1.Formulate the Null and Alternative Hypothesis
2. Set the Level of Significance (πΆ)
3. Determining the Statistical Test to be Used
4. Data Computation
5. Determining the Acceptance and Rejection Regions
6. Compare the computed / test value and the
critical / tabular value obtained
7. State your decision and conclusion.
Types of Test Used with the Alternative Hypothesis
a. One-Tailed Test
b. Two-Tailed Test
One-Tailed Test
Used when the rejection region is located at only one extreme of the range value of the test statistic, or it occupies only one side of the normal curve.
One-Tailed Test
It is located only in one tail of the distribution in the rejection region; either in the left tail or the right tail of the distribution of the test statistic with an associated area of πΌ which also indicates a directional hypothesis.
Two-Tailed Test
a test which locates its critical region on both
tails of the distribution which also indicates a
Non-directional Hypothesis.
Level of Confidence
- βbeliefβ
- the degree of assurance that a particular statistical statement is correct under specified conditions
- represents the probability that π»0 is true
Level of Significance
- βdoubtβ
- the degree of uncertainty about the statistical statement under the same conditions used to determine the confidence level
- represents the probability that π»π is false
The most commonly used values of πΌ are 0.01, 0.05 and 0.10. Choosing 0.01 level of significance means that the researcher is 99% confident and has 1% to
commit an error.
The most commonly used values of πΌ are 0.01, 0.05 and 0.10. Choosing 0.01 level of significance means that the researcher is 99% confident and has 1% to
commit an error.
TYPES OF ERROR
Type I
Type II
Type I
Reject π»0 while it is true
Type II
Accept π»0 while it is false
statistical test
uses the data obtained from a
sample to make a decision about whether the null hypothesis should be rejected.
test value or test statistic
The numerical value obtained from a statistical test
Statistical Tests
a. π-Test
b. π-test
π-Test
Basic Assumptions:
- the sample is a random sample
- population standard deviation (π) is known
- either π β₯ 30 or the population is normally
distributed if π < 30
One-sample π βTest
π-test
Basic Assumptions:
- the sample is a random sample
- population standard deviation (π) is unknown (sample standard deviation (π ) is given instead)
- either π β₯ 30 or the population is normally
distributed if π < 30
critical value
separates the critical region from the
noncritical region
critical / 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
noncritical / nonrejection / acceptance 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
If the absolute computed value of the test statistic is less than the absolute critical / tabular value,
accept the null hypothesis and reject the alternative hypothesis.
