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Chapter 10: Hypothesis Tests Regarding a Parameter

Section 10.1: The Language of Hypothesis Testing

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. Section 1.1:
      • population
      • sample
      • statistic
      • inferential statistics
      • parameter
    2. Section 1.3:
      • random sampling
    3. Section 5.1:
      • probability
      • random event
      • probability rules
      • unusual event
  2. procedural knowledge
    1. none
  3. conditional knowledge
    1. Section 1.1:
      • how to identify the difference between qualitative data and quantitative data
    2. Section 5.1:
      • know the importance of the concept of randomness or chance in probability
      • interpret value of probability
      • identify when an event is considered unusual

Learning Goals

  1. declarative knowledge (definitions)
    1. hypothesis
    2. hypothesis testing
    3. null hypothesis, H0, i.e., the statement being tested, usually stated as no difference or no effect
    4. alternate hypothesis, H1 or Ha
    5. two-tailed test
    6. one-tailed test
    7. left-tailed test
    8. right-tailed test
    9. Type I error
    10. Type II error
    11. level of significance, α
    12. P(Type I error)
  2. procedural knowledge
    1. none
  3. conditional knowledge
    1. explain the reasons for Type I and Type II errors
    2. explain the relationship between Type I and Type II errors
    3. explain what it means to make Type I and Type II errors in a hypothesis test
    4. distinguish between which hypothesis is being tested and which hypothesis you are trying to find evidence for
    5. identify the parameter being tested
    6. know why you cannot accept H0
    7. identify whether the test is two-tailed, left-tailed, or right-tailed
    8. identify H0 and H1
    9. explain statistical significance
    10. state the conclusion from a hypothesis test

Section 10.2: Hypothesis Tests for a Population Proportion

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. Section 1.1:
      • qualitative data
      • population
      • sample
      • statistic
      • inferential statistics
      • parameter
    2. Section 1.3:
      • random sampling
      • population size, N
      • sample size, n
    3. Section 3.1:
      • sample mean, x bar
      • population mean, μ
    4. Section 3.2:
      • population standard deviation, σ
      • sample standard deviation, s
      • population variance, σ2
      • sample variance, s2
      • Empirical Rule (a.k.a., 68-95-99.7 Rule)
    5. Section 3.4:
      • z-score
      • percentiles
    6. Section 5.1:
      • probability
      • outcome
      • random event
      • probability rules
      • unusual event
    7. Chapter 6:
      • all
    8. Chapter 7:
      • all
    9. Section 8.2:
      • all
    10. Section 9.1:
      • all
  2. procedural knowledge
    1. Chapter 6:
      • all
    2. Chapter 7:
      • all
    3. Section 8.2:
      • all
    4. Section 9.1:
      • calculate α for a given C-Level
      • calculate the critical value, zα/2, that corresponds to a given C-level using the TI83/84: http://stats.jjw3.com/math1431/ti83invNorm.htm
      • calculate the point estimate using the TI83/84
      • calculate the ME for a CI
  3. conditional knowledge
    1. Section 1.1:
      • how to identify the difference between qualitative data and quantitative data
    2. Section 5.1:
      • know the importance of the concept of randomness or chance in probability
      • interpret value of probability
      • identify when an event is considered unusual
    3. Chapter 6:
      • all
    4. Chapter 7:
      • all
    5. Section 8.2:
      • all
    6. Section 9.1:
      • describe how α, C-Level, and n affect ME and CI
      • know exactly how to express a CI
      • know how to interpret a CI
      • explain why results of a survey must include a margin of error

Learning Goals

  1. declarative knowledge (definitions)
    1. statistically significant
    2. P-value
    3. test-statistic
  2. procedural knowledge
    1. six steps to conduct a hypothesis test [P-value Approach is the only required method]
    2. calculate a P-value for a hypothesis test for a population proportion with the z-statistic using the TI83/84: http://stats.jjw3.com/math1431/ti83zpTest.htm
    3. calculate the test-statistic, z0, using the TI83/84
  3. conditional knowledge
    1. identify that the test-statistic is used to measure how far the results are from what would be expected if the H0 is true
    2. identify the conditions needed to conduct a hypothesis test using the z-statistic for proportion
    3. the P-value is the probability of getting outcomes at least as far from what we would expect if the H0 is true
    4. explain the meaning of P-value and α-level
    5. know when to reject H0
    6. explain why you cannot accept H0
    7. P-values are strongly related to sample size. Thus, statistical significance is not the same as practical significance
    8. explain the importance of valid significance test
    9. beware of searching for significance

Section 10.3: Hypothesis Tests for a Population Mean

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. Section 1.1:
      • quantitative data
      • population
      • sample
      • statistic
      • inferential statistics
      • parameter
    2. Section 1.3:
      • random sampling
      • population size, N
      • sample size, n
    3. Section 3.1:
      • sample mean, x bar
      • population mean, μ
    4. Section 3.2:
      • population standard deviation, σ
      • sample standard deviation, s
      • population variance, σ2
      • sample variance, s2
      • Empirical Rule (a.k.a., 68-95-99.7 Rule)
    5. Section 3.4:
      • z-score
      • percentiles
    6. Section 5.1:
      • probability
      • outcome
      • random event
      • probability rules
      • unusual event
    7. Chapter 7:
      • all
    8. Section 8.1:
      • all
    9. Section 9.2:
      • all
  2. procedural knowledge
    1. Chapter 7:
      • all
    2. Section 8.1:
      • all
    3. Section 9.2:
      • calculate α for a given C-Level
      • calculate the critical value, zα/2, that corresponds to a given C-level using the TI83/84: http://stats.jjw3.com/math1431/ti83invNorm.htm
      • calculate the point estimate using the TI83/84
      • calculate the ME for a CI
  3. conditional knowledge
    1. Section 1.1:
      • how to identify the difference between qualitative data and quantitative data
    2. Section 5.1:
      • know the importance of the concept of randomness or chance in probability
      • interpret value of probability
      • identify when an event is considered unusual
    3. Chapter 7:
      • all
    4. Section 8.1:
      • all
    5. Section 9.2:
      • describe how α, C-Level, and n affect ME and CI
      • know exactly how to express a CI
      • know how to interpret a CI
      • explain why results of a survey must include a margin of error

Learning Goals

  1. declarative knowledge (definitions)
    1. practical significance
  2. procedural knowledge
    1. six steps to conduct a hypothesis test [P-value Approach is the only required method]
    2. calculate the critical value, tα,n, that corresponds to a one-tailed test using the TI83/84
    3. calculate the critical value, tα/2,n, that corresponds to a two-tailed test using the TI83/84
    4. calculate a P-value for a hypothesis test for mean using the t-statistic when given statistics using the TI83/84: http://stats.jjw3.com/math1431/ti83tTest.htm
    5. calculate a P-value for a hypothesis test for mean using the t-statistic when given data using the TI83/84: http://stats.jjw3.com/math1431/ti83tTestd.htm
    6. calculate the test-statistic, t0, using the TI83/84
    7. sketch t-distribution showing the critical region
    8. identify the difference between practical significance and statistical significance
  3. conditional knowledge
    1. identify the conditions needed to conduct a hypothesis test using the t-statistic
    2. explain the meaning of P-value and α-level
    3. know when to reject H0
    4. explain why you cannot accept H0
    5. identify the difference between practical significance and statistical significance

Section 10.4: Putting It All Together: Which Method Do I Use?

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. Section 10.1:
      • all
    2. Section 10.2:
      • all
    3. Section 10.3:
      • all
  2. procedural knowledge
    1. Section 10.1:
      • all
    2. Section 10.2:
      • all
    3. Section 10.3:
      • all
  3. conditional knowledge
    1. Section 10.1:
      • all
    2. Section 10.2:
      • all
    3. Section 10.3:
      • all

Learning Goals

  1. declarative knowledge (definitions)
    1. none
  2. procedural knowledge
    1. six steps to conduct a hypothesis test [P-value Approach is the only required method]
  3. conditional knowledge
    1. identify the parameter being testing in the hypothesis test
    2. identify the correct statistic to use for hypothesis test
    3. identify that the required conditions are met
    4. explain the meaning of P-value and α-level
    5. know when to reject H0
    6. explain why you cannot accept H0
    7. identify the difference between practical significance and statistical significance

Chapter 10: Required Formulas – Need to Know for Tests

  1. Relationship Between α and Confidence Level: α = 1 – C-Level
  2. t-Statistic: t-Statistic

Chapter 10: Required Formulas – Will be Given on Tests

  1. One Condition Required to Construct a CI for p: p-hat conditions
  2. Another Condition Required to Construct a CI for p: n ≤ 0.05N OR 20n ≤ N