Outcomes of a Hypothesis Test
There are only two possible results of a hypothesis test:
- Reject the null hypothesis; Conclusion: There is sufficient evidence to support the alternative hypothesis
- Do not reject the null hypothesis; Conclusion: There is not sufficient evidence to support the alternate hypothesis
Notice that we do not ‘accept’ the alternate hypothesis when the null is rejected. This is because here we are making conclusions based on a sample and just one sample test would not be enough to make a bigger decision of changing the null value.
Rejecting the null is only the first step. It gives us something to think about and opens up an opportunity to conduct further research before making concrete decisions about the population.
Rejecting the Null
In order to reject, evidence must exist. This evidence comes from our Test statistic and P–value. We reject the null if P-value is less than Alpha, noted as α. If P-value is less than alpha, then there is enough evidence to support a significant difference in the alternate.
We do not reject the null if P-value is not less than Alpha. If P-value is not less than alpha, then there is not enough evidence to support significant difference in the alternate.
Now you Try! Practice Problems
A hypothesis test was conducted to see if the proportion of children who own kites has decreased in the past ten years. A sample was taken and a hypothesis test conducted. The results are below
H0: p = 0.75
H1: p < 0.75
The following P-value was obtained: P-value =0.0123
- Is there evidence to conclude the average proportion of children who owns kites has changed at a 0.05 α level of significance?
- Is there evidence to conclude the average proportion of children who owns kites has changed at a 0.01 α level of significance?
At a 0.05 Level of Significance, we are testing at a 95% confidence:
Is P-value less than α=0.05?
P-value is 0.0123. This is less than the significance level. Therefore, the null hypothesis can be rejected. There is sufficient evidence to support the alternative hypothesis.
There is evidence level to suggest that the proportion of children who own a kite has decreased at the 0.05 significance.
At a 0.01 Level of Significance, we are testing at a 99% confidence:
Is P-value less than α=0.01?
- P-value is 0.0123. This is not less than the significance level.
- Therefore, the null hypothesis cannot be rejected.
- There is not sufficient evidence to support the alternative hypothesis
- There is no evidence to suggest that the proportion of children who own a kite has decreased at the 0.01 significance level
Need More Help?
Click here to schedule a 1:1 with a tutor, coach, and or sign up for a workshop. *If this link does not bring you directly to our platform, please use our direct link to "Academic Support" from any Brightspace course at the top of the navigation bar.