Cogito
AP Statistics · Chapter 4 · Lesson 1
Significance Tests
What a p-value does and does not say.
11 problems · about 26 minutes · AP Statistics 6.7, 7.3
What this lesson teaches
The student states hypotheses, interprets a p-value, and states a conclusion in context.
- The null says nothing is happening; the alternative says something is.
- A p-value is the chance of data this extreme assuming the null is true.
- Failing to reject is never proof of the null.
Warm Up
Straightforward practice. Get the method working first.
4 problemsp = 0.20 at level 0.05. Reject? 1 for yes, 0 for no.
Answer 0
Why Fail to reject.
p = 0.01 at level 0.05. Reject? 1 for yes, 0 for no.
Answer 1
Why Below the level.
p = 0.06 at level 0.05. Reject? 1 for yes, 0 for no.
Answer 0
Why Just above.
Does failing to reject prove the null? 1 for yes, 0 for no.
Answer 0
Why Absence of evidence.
Build It Up
The same ideas with more to keep track of.
3 problemsIs the p-value the probability the null is true? 1 for yes, 0 for no.
Answer 0
Why It assumes the null.
Order the steps of a significance test.
Answer 1. State the hypotheses 2. Check the conditions 3. Compute the test statistic and p-value 4. State a conclusion in context
Why Conditions before computation.
A Type I error rejects a true null. At level 0.05, what is its probability?
Answer 0.05
Why The level is that probability.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsLowering the level from 0.05 to 0.01 makes rejecting which? 1 for easier, 2 for harder.
Answer 2
Why A stricter bar.
p = 0.001 at level 0.05. Reject? 1 for yes, 0 for no.
Answer 1
Why Far below.
The Decision: p = 0.03 at level 0.05. Reject the null? 1 for yes, 0 for no.
Answer 1
Why Reject.
The Other Way: p = 0.30 at level 0.05. Reject the null? 1 for yes, 0 for no.
Answer 0
Why Fail to reject.