Question 1 Foundation
What does the null hypothesis state?
Answer. The status quo value being tested — it always contains an equality.
It must be specific enough to calculate with. "" describes infinitely many possibilities and cannot serve as .
Hypothesis Testing
Original questions written at exam standard. Work each one before you open the solution.
Difficulty
Question 2 Foundation
State the critical values for a two-tailed test at the 5% level.
Answer.
2.5% sits in each tail, and .
Question 3 Standard
State the critical value for a one-tailed test at the 5% level.
Answer.
All 5% is in one tail, and . Using 1.96 here would be too strict.
Question 4 Standard
A sample of 64 has mean 52; the claim is with . Find the test statistic.
Answer.
SE , so .
Question 5 Stretch
Explain why lowering increases the risk of a Type II error.
Answer. More evidence is demanded before rejecting, so genuine effects are missed more often.
The critical region shrinks, making rejection harder in every case — including when really is false. Only a larger sample reduces both risks.
Question 6 Stretch
Why is it wrong to say a test has "proved true"?
Answer. Failing to find evidence against a claim does not establish it.
A small sample may simply lack the power to detect a real effect. The correct wording is "insufficient evidence to reject ".