Null-hypothesis for a Single-Sample t-test

Conceptual Explanation

With hypothesis testing we are setting up a null-hypothesis

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

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.

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.

Example #1

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.

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:

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 hypothesis:There is no statistically significant difference in ACT scores between a local sample of 30 teenagers and the

larger population.

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 hypothesis:There is no statistically 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

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 hypothesis:There is no statistically 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.