Null hypothesis for a single-sample t-test

1. Null-hypothesis for a Single-
Sample t-test
Conceptual Explanation

2. With hypothesis testing we are setting up a null-hypothesis

3. With hypothesis testing we are setting up a null-hypothesis
– the probability that there is no effect or
relationship –

4. With hypothesis testing we are setting up a null-hypothesis
– the probability that there is no effect or
relationship – and then we collect evidence that leads
us to either accept or reject that null hypothesis.

5. With hypothesis testing we are setting up a null-hypothesis
– the probability that there is no effect or
relationship – and then we collect evidence that leads
us to either accept or reject that null hypothesis.
As you may recall, a single-sample t-test attempts to
determine if a single sample is statistically significantly
different from the population. The hope by
researchers is that they will be similar so as to run
experiments on the single sample that could be
generalized to the population.

6. Example #1

7. Let’s say we collect a sample of 30 teenage ACT scores
in our community and want to know if their ACT scores
are statistically significantly different than the larger
population of ACT scores.

8. Let’s say we collect a sample of 30 teenage ACT scores
in our community and want to know if their ACT scores
are statistically significantly different than the larger
population of ACT scores.
Here’s the null hypothesis:

9. Let’s say we collect a sample of 30 teenage ACT scores
in our community and want to know if their ACT scores
are statistically significantly different than the larger
population of ACT scores.
HeTreh’esr teh ies hnyop sottahtiesstiisc:ally significant difference in ACT
scores between a local sample of 30 teenagers and the
larger population.

10. Let’s say we collect a sample of 30 teenage ACT scores
in our community and want to know if their ACT scores
are statistically significantly different than the larger
population of ACT scores.
HeTreh’esr teh ies hnyop sottahtiesstiisc:ally significant difference in ACT
scores between a local sample of 30 teenagers and the
larger population.
Note – that the single-sample t-test is
one of the few methods where the
researchers are hoping the null-hypothesis
is accepted or retained

11. Let’s say we collect a sample of 30 teenage ACT scores
in our community and want to know if their ACT scores
are statistically significantly different than the larger
population of ACT scores.
HeTreh’esr teh ies hnyop sottahtiesstiisc:ally significant difference in ACT
scores between a local sample of 30 teenagers and the
larger population.
This is because they desire to
conduct experiments on a sample
that will generalize to the population.
For this to happen the sample must
be statistically significantly similar
(not different) from the population.