Hypothesis Testing

Could chance alone explain this?

12 problems · about 23 minutes · TEKS P.S.4.E, S-IC.B.5

What this lesson teaches

The student states hypotheses, interprets a p-value, and draws a conclusion in context.

The null hypothesis says nothing is happening; the alternative is the claim under investigation.
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.

Straightforward practice. Get the method working first.

5 problems

p-value 0.002 at the 0.05 level. Significant? 1 yes, 0 no.
Answer 1
Why Yes.
What exactly does a p-value measure?
Answer The chance of a result 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 the threshold.
p-value 0.20 at the 0.05 level. Significant? 1 yes, 0 no.
Answer 0
Why Above the threshold.
Which hypothesis states no effect? 1 null, 2 alternative.
Answer 1
Why The boring one.

The same ideas with more to keep track of.

3 problems

A fair coin, 100 tosses. Expected heads?
Answer 50
Why np.
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 Small means unlikely by chance.

Mixed problems. Work out what kind of question it is before you start.

4 problems

Put a hypothesis 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 it to the threshold and conclude in context.
Why The 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 Threshold: p-value 0.03 at the 0.05 level. Is the result significant? 1 yes, 0 no.
Answer 1
Why Yes.
The Large p: p-value 0.40. Does this prove the null hypothesis is true? 1 yes, 0 no.
Answer 0
Why No.