Debate if “failing to reject the null” is the same as “accepting the null.” Support your position with examples of acceptance or rejection of the null. Next, give your opinion on whether or not a failed t test “proves” the null hypothesis.
Take a position on this statement: In setting up a hypothesis test, the claim should always be written in the alternative hypothesis. Provide one (1) example to support your position.
Rejecting and Accepting the Null
The null hypothesis is an indication that there is no significant difference in the measured phenomena. Failing to reject the null is not the same as accepting the null. Failing to reject the null indicates that the researcher did not find conclusive evidence that there exists significant difference between the particular populations. On the other hand, accepting the null hypothesis is an indication that the researcher found conclusive evidence that there is no significant difference in the measured phenomena. For example, the null hypothesis may read “undertaking tutorial classes has no effect on students’ performance”. The evidence gathered by the researcher may not be enough to help in making the decision whether the statement is true or not. On the other hand, the evidence may indicate that there is no relationship between tutorial classes and the students’ performance, hence accepting the null.
A failed t test proves the null hypothesis since it is an indication that there is no significant difference between means of the specified populations.
In setting up a hypothesis test, the claim should actually be written in the alternative hypothesis. This is because the null hypothesis is a statement indicating there is no true difference between means of the population being observed. If there are differences, it could be due to a sampling error. On the other hand, the alternative hypothesis indicates that there is a real difference between the means of the populations under observation. Below is the example.
Null hypothesis: Taking vegetarian diet has no effect on reducing the cholesterol levels among individuals.
Alternative hypothesis: Taking vegetarian diet has a positive effect in reducing the cholesterol levels among individuals.
Related: Normal Distribution