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Questions and Answers
What is the primary purpose of the null hypothesis?
What is the primary purpose of the null hypothesis?
- To establish a claim about the population
- To make a decision without examining evidence
- To provide a statement of no difference between variables (correct)
- To prove a significant difference between variables
What happens when the sample information favors the alternative hypothesis?
What happens when the sample information favors the alternative hypothesis?
- We collect more sample data
- We do not reject the null hypothesis
- We reject the alternative hypothesis
- We reject the null hypothesis (correct)
What is the role of the alternative hypothesis in statistical testing?
What is the role of the alternative hypothesis in statistical testing?
- To provide insufficient evidence to reject the null hypothesis
- To provide a statement of no difference between variables
- To establish a claim about the population that is contradictory to the null hypothesis (correct)
- To make a decision without examining evidence
What is the outcome when the sample information is insufficient to reject the null hypothesis?
What is the outcome when the sample information is insufficient to reject the null hypothesis?
What is the relationship between the null and alternative hypotheses?
What is the relationship between the null and alternative hypotheses?
What is the purpose of examining evidence in statistical testing?
What is the purpose of examining evidence in statistical testing?
What is the outcome when we cannot accept the null hypothesis?
What is the outcome when we cannot accept the null hypothesis?
What is the role of sample data in statistical testing?
What is the role of sample data in statistical testing?
What is the purpose of the collaborative exercise mentioned in the content?
What is the purpose of the collaborative exercise mentioned in the content?
What is the percentage being tested in the null hypothesis?
What is the percentage being tested in the null hypothesis?
What symbol is used in the null hypothesis to indicate that the population proportion is equal to a certain value?
What symbol is used in the null hypothesis to indicate that the population proportion is equal to a certain value?
What symbol would be used in the null hypothesis?
What symbol would be used in the null hypothesis?
What symbol is used in the alternative hypothesis to indicate that the population proportion is greater than a certain value?
What symbol is used in the alternative hypothesis to indicate that the population proportion is greater than a certain value?
What is the purpose of writing null and alternative hypotheses?
What is the purpose of writing null and alternative hypotheses?
In a hypothesis test, which of the following is a correct null hypothesis?
In a hypothesis test, which of the following is a correct null hypothesis?
What type of articles should be brought to class for the collaborative exercise?
What type of articles should be brought to class for the collaborative exercise?
What is the symbol used in the alternative hypothesis?
What is the symbol used in the alternative hypothesis?
What symbol is used in the alternative hypothesis to indicate that the population mean is not equal to a certain value?
What symbol is used in the alternative hypothesis to indicate that the population mean is not equal to a certain value?
In a hypothesis test, which of the following is a correct alternative hypothesis?
In a hypothesis test, which of the following is a correct alternative hypothesis?
What is the purpose of a null hypothesis?
What is the purpose of a null hypothesis?
In a medical trial, the null hypothesis is that a new medicine reduces cholesterol by 25%. What is the correct alternative hypothesis?
In a medical trial, the null hypothesis is that a new medicine reduces cholesterol by 25%. What is the correct alternative hypothesis?
In a hypothesis test, what is the relationship between the null and alternative hypotheses?
In a hypothesis test, what is the relationship between the null and alternative hypotheses?
What is the null hypothesis in the example of testing if college students take less than five years to graduate from college?
What is the null hypothesis in the example of testing if college students take less than five years to graduate from college?
What is the alternative hypothesis in the example of testing if it takes fewer than 45 minutes to teach a lesson plan?
What is the alternative hypothesis in the example of testing if it takes fewer than 45 minutes to teach a lesson plan?
What is the null hypothesis in the example of testing if the percentage of U.S. students who take advanced placement exams is more than 6.6%?
What is the null hypothesis in the example of testing if the percentage of U.S. students who take advanced placement exams is more than 6.6%?
What is the alternative hypothesis in the example of testing if the percentage of U.S. students who take advanced placement exams is more than 6.6%?
What is the alternative hypothesis in the example of testing if the percentage of U.S. students who take advanced placement exams is more than 6.6%?
What is the null hypothesis in the example of testing if college students take less than five years to graduate from college?
What is the null hypothesis in the example of testing if college students take less than five years to graduate from college?
What symbol is used in the null hypothesis in the example of testing if it takes fewer than 45 minutes to teach a lesson plan?
What symbol is used in the null hypothesis in the example of testing if it takes fewer than 45 minutes to teach a lesson plan?
What is the null hypothesis in the example of testing if the percentage of students who pass the state driver’s test on the first try is more than 40%?
What is the null hypothesis in the example of testing if the percentage of students who pass the state driver’s test on the first try is more than 40%?
What is the alternative hypothesis in the example of testing if the percentage of students who pass the state driver’s test on the first try is more than 40%?
What is the alternative hypothesis in the example of testing if the percentage of students who pass the state driver’s test on the first try is more than 40%?
Study Notes
Null and Alternative Hypotheses
- A statistical test begins by considering two hypotheses: the null hypothesis (H0) and the alternative hypothesis (Ha).
- These hypotheses contain opposing viewpoints.
Null Hypothesis (H0)
- A statement of no difference between variables - they are not related.
- Often considered the status quo.
- Requires action if not accepted.
Alternative Hypothesis (Ha)
- A claim about the population that contradicts H0.
- What researchers are trying to prove.
- Rejected if there is enough evidence to reject H0.
Decision Making
- Examine evidence to decide whether to reject H0 or not.
- Two options: "reject H0" or "do not reject H0" (if sample information is insufficient).
Mathematical Symbols Used in H0 and Ha
- H0: equal (=)
- Ha: not equal (≠), greater than (>), or less than (<)
Examples
-
Example 9.1: Testing the percentage of voters in a primary election.
- H0: p ≤ 0.30
- Ha: p > 0.30
-
Example 9.2: Testing the mean GPA of students in American colleges.
- H0: μ = 2.0
- Ha: μ ≠ 2.0
-
Example 9.3: Testing the average time it takes to graduate from college.
- H0: μ ≥ 5
- Ha: μ < 5
-
Example 9.4: Testing the percentage of U.S. students who take advanced placement exams.
- H0: p ≤ 0.066
- Ha: p > 0.066
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Description
Learn about null and alternative hypotheses in introductory statistics. Understand the concepts of hypothesis testing in this chapter.
