A hypothesis test uses sample data to decide whether to reject the null hypothesis, and the null hypothesis is denoted H₀, so this Year 13 sheet opens with the decision being made and its symbol. A 5% value is recorded as the significance level, with rejecting H₀ as a small p-value outcome.
Key Takeaways
A hypothesis test decides whether to reject the null hypothesis (Q1).
The null hypothesis is denoted H₀ (Q2).
Q3 records 5% (0.05) as a standard significance level.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.A hypothesis test uses sample data to
(a) decide whether to reject the null hypothesis(b) prove the alternative hypothesis is true(c) find the mean(d) calculate the variance
2.The null hypothesis is usually denoted by
(a) H₀(b) H₁(c) H₂(d) p
3.The significance level of a test is typically
(a) 5% (0.05)(b) 50%(c) 100%(d) 0%
4.The probability of making a type I error is
(a) the significance level(b) zero(c) 1 − significance level(d) the power of the test
5.In a one-tailed test, the alternative hypothesis states that the parameter is
(a) greater than or less than a value, in one direction(b) different in either direction(c) equal to zero(d) equal to the sample value
6.If the p-value is less than the significance level, you
(a) reject the null hypothesis(b) accept the null hypothesis(c) accept the alternative hypothesis without evidence(d) cannot decide
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Define the null hypothesis.
8.Define the alternative hypothesis.
9.What is a significance level?
10.What is a p-value?
11.What is the difference between a one-tailed and a two-tailed test?
12.When do you reject the null hypothesis?
13.What is a type I error?
14.Give an example of a hypothesis test that could be run.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.A test gives a p-value of 0.03 with a significance level of 5%. Do you reject H₀?
16.A test gives a p-value of 0.08 with a significance level of 5%. Do you reject H₀?
17.The significance level of a test is 0.05. What is the probability of a type I error?
18.A two-tailed test is run at a 5% significance level. How much probability lies in each tail?
19.For X ~ B(10, 0.5), find the mean using np.
20.A one-tailed test at a 5% significance level gives p = 0.04. Do you reject H₀?
Answer Key
1. a) decide whether to reject the null hypothesis
2. a) H₀
3. a) 5% (0.05)
4. a) the significance level
5. a) greater than or less than a value, in one direction
6. a) reject the null hypothesis
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What does a hypothesis test use sample data for?
To decide whether to reject the null hypothesis, option (a) in this worksheet (Q1).
What is the null hypothesis denoted by?
H₀, option (a) in this worksheet (Q2).
What significance level is recorded?
5% (0.05), option (a) in this worksheet (Q3).
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