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There are two types of statistical hypotheses: Null Hypothesis (H0) – a statistical hypothesis that states that there is no difference between a parameter ...
Typology: Schemes and Mind Maps
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In this chapter we will learn ….
To use an inferential method called a hypothesis test To analyze evidence that data provide To make decisions based on data
Major Methods for Making Statistical Inferences about a Population
The traditional Method The p-value Method Confidence Interval
The main goal in many research studies is to check whether the data collected support certain statements or predictions.
Statistical Hypothesis – a conjecture about a population parameter. This conjecture may or may not be true.
Example: The mean income for a resident of Denver is equal to the mean income for a resident of Seattle.
Population parameter is mean income One population consists of residents of Denver while the other consists of residents of Seattle.
We tend to want to reject the null hypothesis so we assume it is true and look for enough evidence to conclude it is incorrect.
We tend to want to accept the alternative hypothesis. If the null hypothesis is rejected then we must accept that the alternative hypothesis is true.
Note: H 0 will ALWAYS have an equal sign (and possibly a less than or greater than symbol, depending on the alternative hypothesis). The alternative hypothesis has a range of values that are alternatives to the one in
The null and alternative hypotheses are stated together. The following are typical hypothesis for means, where k is a specified number.
Note: Right-tailed and left-tailed tests are distinguished by the way the greater than or less than points. It is the direction where are alterative places the true mean.
k
A psychologist feels that playing soft music during a test will change the results of the test. The psychologist is not sure whether the grades will be higher or lower. In the past, the mean of the scores was 73.
H 0 :
When a researcher conducts a study, he or she is generally looking for evidence to support a claim of some type of difference. In this case, the claim should be stated as the alternative hypothesis. Because of this, the alternative hypothesis is sometimes called the research hypothesis.
Keywords help to indicate what the null and/or alternative hypotheses should be.
H 0 is True
H 0 is False
Reject
Type I Error
Correct Decision
Do not Reject
^ H 0 Correct Decision
Type II Error
Example: Decision Errors in a Legal Trial. What are
H 0 and
H 0 : Defendant is innocent. H 1 : Defendant is not innocent, i.e., guilty
Significance level - is the maximum probability of committing a Type I error. This probability is symbolized by
Critical or Rejection Region – the range of values for the test value that indicate a significant difference and that the null hypothesis should be rejected.
Non-critical or Non-rejection Region – the range of values for the test value that indicates that the difference was probably due to chance and that the null hypothesis should not be rejected.
To obtain the critical value, the researcher must choose the significance level,
, and know the distribution of the test value.
The distribution of the test value indicates the shape of the distribution curve for the test value. This will have a shape that we know (like the standard normal or t distribution). Let’s assume that the test value has a standard normal distribution. We should use Table E (the standard normal table) or Table F (using the bottom row of the t distribution, which is equivalent to a standard normal distribution) to find the critical value.
Finding the Critical Values for Specific α Values, Using Table E
Step 1: Draw a figure for the distribution of the test values and indicate the appropriate area for the rejection region.
If the test is left-tailed, the critical region, with area equal to α, will be on the left side of the distribution curve. If the test is right-tailed, the critical region, with area equal to α, will be on the right side of the distribution curve. If the test is two-tailed, α must be divided by 2; the critical regions will be in each end of the distribution curve - half the area in the left part of the distribution and half of the area in the right part of the distribution.
0.0-4 -2 0 2 4
0.^ 0.^ 0.^
Z
P(Z)
Example: Find the critical value(s) for each situation and draw the appropriate figure, showing the critical region.
Left-tailed test with α = 0.
Looking up 0.005 in the Z table We have Z = -2.575.
Right-tailed test with α = 0.
0.0-4 -2 0 2 4
0.^ 0.^ 0.^
Z
P(Z)
Two-tailed test with α = 0.
Left-tailed test with α = 0.
0.0-4 -2 0 2 4
0.^ 0.^ 0.^
Z
P(Z)
0.0-4 -2 0 2 4
0.^ 0.^ 0.^
Z
P(Z)
