Cogito
Integrated Math 3 · Chapter 7 · Lesson 3
Significance Tests
Could chance alone explain this?
12 problems · about 22 minutes · S-IC.B.5, S-IC.B.6
What this lesson teaches
The student interprets a p-value and draws a conclusion in context.
- The null says nothing is happening and is assumed while testing.
- A p-value is the chance of data this extreme if the null were true.
- Below 0.05 is conventionally significant, and a large p-value proves nothing.
Warm Up
Straightforward practice. Get the method working first.
5 problemsp-value 0.30 at the 0.05 level. Significant? 1 yes, 0 no.
Answer 0
Why No.
What exactly does a p-value measure?
Answer The chance of data this extreme, assuming the null is true.
Why It assumes the null and asks how surprising the data is.
p-value 0.01 at the 0.05 level. Significant? 1 yes, 0 no.
Answer 1
Why Below.
p-value 0.20 at the 0.05 level. Significant? 1 yes, 0 no.
Answer 0
Why Above.
Which hypothesis states no effect? 1 null, 2 alternative.
Answer 1
Why The boring one.
Build It Up
The same ideas with more to keep track of.
3 problemsA fair coin, 100 tosses. Expected heads?
Answer 50
Why Half.
The usual significance threshold, as a decimal?
Answer 0.05
Why Five percent.
Does a smaller p-value mean more surprising under the null? 1 yes, 0 no.
Answer 1
Why Less likely by chance.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsPut a significance test in order.
Answer 1. State the null and alternative hypotheses. 2. Collect data and compute the statistic. 3. Find the p-value, assuming the null is true. 4. Compare to the threshold and conclude in context.
Why Hypotheses are stated before the data is seen.
p-value 0.049 at the 0.05 level. Significant? 1 yes, 0 no.
Answer 1
Why Just below.
The Decision: p-value 0.02 at the 0.05 level. Is the result significant? 1 yes, 0 no.
Answer 1
Why Yes.
The Non-Result: p-value 0.40. Does this prove the null is true? 1 yes, 0 no.
Answer 0
Why No.