Introductory Statistics Chapter 9.1
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Questions and Answers

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?

  • 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?

  • 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?

    <p>We do not reject the null hypothesis</p> Signup and view all the answers

    What is the relationship between the null and alternative hypotheses?

    <p>They are contradictory</p> Signup and view all the answers

    What is the purpose of examining evidence in statistical testing?

    <p>To decide if there is enough evidence to reject the null hypothesis</p> Signup and view all the answers

    What is the outcome when we cannot accept the null hypothesis?

    <p>Some action is required</p> Signup and view all the answers

    What is the role of sample data in statistical testing?

    <p>To provide evidence to decide if there is enough evidence to reject the null hypothesis</p> Signup and view all the answers

    What is the purpose of the collaborative exercise mentioned in the content?

    <p>To write null and alternative hypotheses from newspaper articles</p> Signup and view all the answers

    What is the percentage being tested in the null hypothesis?

    <p>40%</p> Signup and view all the answers

    What symbol is used in the null hypothesis to indicate that the population proportion is equal to a certain value?

    <p>=</p> Signup and view all the answers

    What symbol would be used in the null hypothesis?

    <p>=</p> Signup and view all the answers

    What symbol is used in the alternative hypothesis to indicate that the population proportion is greater than a certain value?

    <p>&gt;</p> Signup and view all the answers

    What is the purpose of writing null and alternative hypotheses?

    <p>To test a statistical hypothesis</p> Signup and view all the answers

    In a hypothesis test, which of the following is a correct null hypothesis?

    <p>H0: μ = 2.0</p> Signup and view all the answers

    What type of articles should be brought to class for the collaborative exercise?

    <p>Newspaper, news magazine, and Internet articles</p> Signup and view all the answers

    What is the symbol used in the alternative hypothesis?

    <p>&gt;</p> Signup and view all the answers

    What symbol is used in the alternative hypothesis to indicate that the population mean is not equal to a certain value?

    <p>≠</p> Signup and view all the answers

    In a hypothesis test, which of the following is a correct alternative hypothesis?

    <p>Ha: μ ≠ 2.0</p> Signup and view all the answers

    What is the purpose of a null hypothesis?

    <p>To propose that there is no significant difference between the population parameter and the claimed value</p> Signup and view all the answers

    In a medical trial, the null hypothesis is that a new medicine reduces cholesterol by 25%. What is the correct alternative hypothesis?

    <p>Ha: p &gt; 0.25</p> Signup and view all the answers

    In a hypothesis test, what is the relationship between the null and alternative hypotheses?

    <p>The null and alternative hypotheses are mutually exclusive</p> Signup and view all the answers

    What is the null hypothesis in the example of testing if college students take less than five years to graduate from college?

    <p>H0: μ ≥ 5</p> Signup and view all the answers

    What is the alternative hypothesis in the example of testing if it takes fewer than 45 minutes to teach a lesson plan?

    <p>Ha: μ &lt; 45</p> Signup and view all the answers

    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%?

    <p>H0: p ≤ 0.066</p> Signup and view all the answers

    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%?

    <p>Ha: p &gt; 0.066</p> Signup and view all the answers

    What is the null hypothesis in the example of testing if college students take less than five years to graduate from college?

    <p>H0: μ ≥ 5</p> Signup and view all the answers

    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?

    <p>≥</p> Signup and view all the answers

    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%?

    <p>H0: p ≤ 0.4</p> Signup and view all the answers

    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%?

    <p>Ha: p &gt; 0.4</p> Signup and view all the answers

    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.

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