www.jjw3.com > Math1431 OR Math1431H > Math1431 Notes > Sullivan Chapter 9 Notes

Chapter 9: Estimating the Value of a Parameter

Section 9.1: Estimating 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
  2. procedural knowledge
    1. Chapter 6:
      • all
    2. Chapter 7:
      • all
    3. Section 8.2:
      • all
  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

Learning Goals

  1. declarative knowledge (definitions)
    1. point estimate
    2. confidence level (C-level)
    3. confidence interval (CI)
    4. critical value, zα/2
    5. z-interval (CI)
    6. margin of error (E or ME)
  2. procedural knowledge
    1. calculate α for a given C-Level
    2. calculate the critical value, zα/2, that corresponds to a given C-level using the TI83/84: http://stats.jjw3.com/math1431/ti83invNorm.htm
    3. find the CI for population proportion, p, using the TI83/84: http://stats.jjw3.com/math1431/ti83zpCI.htm
    4. calculate the point estimate using the TI83/84 [using formula given below]
    5. calculate the ME for a CI [using formula given below]: http://stats.jjw3.com/math1431/ti83m.htm
    6. calculate the sample size needed CI for population proportion using previous estimates [using formula given below]
    7. calculate the sample size needed CI for population proportion without using previous estimates [using formula given below]
  3. conditional knowledge
    1. describe how α, C-Level, and n affect ME and CI
    2. identify the conditions needed to construct a CI using the z-statistic
    3. know exactly how to express a CI
    4. know how to interpret a CI
    5. explain why results of a survey must include a margin of error
    6. explain why the calculation for n needs to be rounded up

Section 9.2: Estimating 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 9.1:
      • all
  2. procedural knowledge
    1. Chapter 7:
      • all
    2. Section 8.1:
      • all
    3. 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 7:
      • all
    4. Section 8.1:
      • all
    5. 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. degrees of freedom (df)
    2. Student's t-distribution
    3. properties of t-distribution
    4. t-interval (i.e., CI using the t-statistic)
  2. procedural knowledge
    1. calculate the degrees of freedom from sample size, n
    2. calculate α for a given C-Level
    3. calculate the critical value, tα/2, that corresponds to a given C-level using the TI83/84: http://stats.jjw3.com/math1431/ti83invt.htm
    4. find the t-interval for given statistics using the TI83/84: http://stats.jjw3.com/math1431/ti83tCI.htm
    5. find the t-interval for given data using the TI83/84: http://stats.jjw3.com/math1431/ti83tCId.htm
    6. calculate the point estimate using the TI83/84 [using formula given below]
    7. calculate the ME for a t-interval [using formula given below]
    8. calculate the sample size needed for a given ME, σ, and zα/2 [using formula given below]
    9. explain why the calculation for n needs to be rounded up
  3. conditional knowledge
    1. explain why the t-interval is robust
    2. identify the similarities and differences between the normal distribution and the t-distribution
    3. identify the conditions needed to construct a CI using the t-statistic
    4. know exactly how to express a t-interval
    5. know how to interpret a t-interval
    6. describe how α, C-Level, n, and n affect ME and CI

Section 9.3: Putting It All Together: Which Procedure Do I Use?

Knowledge Prerequisites

  1. declarative knowledge (definitions)
    1. Section 9.1:
      • all
    2. Section 9.2:
      • all
  2. procedural knowledge
    1. Section 9.1:
      • all
    2. Section 9.2:
      • all
  3. conditional knowledge
    1. Section 9.1:
      • all
    2. Section 9.2:
      • all

Learning Goals

  1. declarative knowledge (definitions)
    1. none
  2. procedural knowledge
    1. none
  3. conditional knowledge
    1. identify the correct statistic to construct the CI
    2. identify that the required conditions are met
    3. know how to state and interpret a CI

Chapter 9: Required Formulas – Need to Know for Tests

  1. df = n – 1
  2. Point-Estimate for a Population Proportion: Sample Proportion
  3. Relationship Between α and Confidence Level: α = 1 – C-Level
  4. Confidence Interval (CI): Point Estimate ± Margin of Error, i.e., (Point Estimate – Margin of Error, Point Estimate + Margin of Error)
  5. Point Estimate for a given Confidence Interval (CI): Point Estimate
  6. Margin of Error (ME or E) for a given Confidence Interval (CI): Margin of Error
  7. t-Distribution: t-Distribution, with n – 1 degrees of freedom

Chapter 9: 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
  3. Sample Size Required for a given Confidence Interval (CI) for p given E using Prior Estimate: Sample Size Required for a given Confidence Interval (CI) given E using Prior Estimate, rounded up to next integer
  4. Sample Size Required for a given Confidence Interval (CI) for p given E: Sample Size Required for a given Confidence Interval (CI) given E, rounded up to next integer
  5. Sample Size Required for a given Confidence Interval (CI) for μ given E: Sample Size Required for a given Confidence Interval (CI) given E, rounded up to next integer