grade 12 statistics hypothesis testing exam questions

📚 Quick Study Guide

• 🤔 Hypothesis: A statement about a population parameter that we want to test.
• 📊 Null Hypothesis ($H_0$): The statement we assume to be true initially. It usually states that there is no effect or no difference.
• 📈 Alternative Hypothesis ($H_1$ or $H_a$): The statement we are trying to find evidence to support. It contradicts the null hypothesis.
• significance level, typically 0.05 (5%).
• 🧪 Test Statistic: A value calculated from the sample data used to decide whether to reject the null hypothesis. Examples include z-score, t-statistic, chi-square statistic.
• p-value is less than or equal to $\alpha$, we reject $H_0$. Otherwise, we fail to reject $H_0$.
• 📝 Types of Tests:
  • Z-test: Used when the population standard deviation is known or the sample size is large.
  • T-test: Used when the population standard deviation is unknown and the sample size is small.
  • Chi-square test: Used for categorical data to test for independence or goodness of fit.

Practice Quiz

1. Question 1: Which of the following is the correct definition of the null hypothesis?
   1. A) The hypothesis that the researcher is trying to prove.
   2. B) The hypothesis that there is no effect or no difference.
   3. C) The hypothesis that the sample data is flawed.
2. Question 2: What does the p-value represent in hypothesis testing?
   1. A) The probability of rejecting the null hypothesis when it is true.
   2. B) The probability of observing the test statistic (or a more extreme value) if the null hypothesis is true.
   3. C) The probability of accepting the null hypothesis when it is false.
3. Question 3: What is the typical significance level ($\alpha$) used in hypothesis testing?
   1. A) 0.10
   2. B) 0.05
   3. C) 0.01
4. Question 4: When is a t-test most appropriate to use?
   1. A) When the population standard deviation is known.
   2. B) When the population standard deviation is unknown and the sample size is small.
   3. C) When dealing with categorical data.
5. Question 5: What does it mean to "reject the null hypothesis"?
   1. A) To accept the alternative hypothesis.
   2. B) To conclude that there is not enough evidence to support the alternative hypothesis.
   3. C) To prove that the null hypothesis is false.
6. Question 6: Which test is used for categorical data to test for independence?
   1. A) Z-test
   2. B) T-test
   3. C) Chi-square test
7. Question 7: If the p-value is 0.02 and the significance level is 0.05, what is the correct decision?
   1. A) Reject the null hypothesis.
   2. B) Fail to reject the null hypothesis.
   3. C) Increase the significance level.