Chapter 7. Hypothesis Testing: Introduction to Hypothesis Testing (Critical Region Approach
Connection between Hypothesis Testing and Confidence Intervals
Recall that a population mean can be estimated using a confidence interval .
Reinterpreting C
The number can be reinterpreted as for some number .
For example, if , then , or if , then .
Connecting Hypothesis Testing and Confidence Intervals
Thus a for can be reinterpreted as a for .
This enables us to establish a direct connection between a two-sided hypothesis test for and a confidence interval for :
- If falls inside the , then should not be rejected at the level of significance.
- If falls outside of the , then should be rejected at the level of significance.
Do not reject .
Since the confidence interval contains the value , we would not reject at the level of significance.
Since the confidence interval contains the value , we would not reject at the level of significance.
Unlock full access
Teacher access
Request a demo account. We will help you get started with our digital learning environment.
Student access
Is your university not a partner?
Get access to our courses via Pass Your Math independent of your university. See pricing and more.
Or visit omptest.org if jou are taking an OMPT exam.
Or visit omptest.org if jou are taking an OMPT exam.