Chapter 11: Inferences on Two Samples

Section 11.1: Inference about Two Population Proportions

Knowledge Prerequisites

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 1.6:
  - matched-pairs design
4. Section 3.1:
  - sample mean,
  - population mean, μ
5. 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)
6. Section 3.4:
  - z-score
  - percentiles
7. Section 5.1:
  - probability
  - outcome
  - random event
  - probability rules
  - unusual event
8. Chapter 6:
  - all
9. Chapter 7:
  - all
10. Section 8.2:
  - all
11. Section 9.1:
  - all
12. Section 10.1:
  - all
13. Section 10.2:
  - all
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, z_α/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
5. Section 10.1:
  - all
6. Section 10.2:
  - all
conditional knowledge
1. Section 1.1:
  - how to identify the difference between qualitative data and quantitative data
2. Section 1.6:
  - identify matched-pairs experimental design
3. 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
4. Chapter 6:
  - all
5. Chapter 7:
  - all
6. Section 8.2:
  - all
7. 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
8. Section 10.1:
  - all
9. Section 10.2:
  - all

Learning Goals

declarative knowledge (definitions)
1. independent sampling method
2. dependent sampling method (a.k.a., matched-pairs)
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 two-sample hypothesis test for difference in population proportions using the z-statistic for proportion on the TI83/84: http://stats.jjw3.com/math1431/ti83_2szpTest.htm
3. calculate the test-statistic using the TI83/84
4. construct a two-sample CI with the z-statistic for proportion using the TI83/84: http://stats.jjw3.com/math1431/ti83_2szpCI.htm
5. calculate the point estimate using the TI83/84 [using formula given below]
6. calculate the ME for a t-interval [using formula given below]
conditional knowledge
1. identify hypothesis test using one sample and a hypothesis test using two samples
2. identify if the sampling method for two samples is independent or dependent
3. identify the conditions needed to use the two-sample z-statistic for proportion
4. explain the meaning of P-value and α-level
5. know when to reject H₀
6. explain why you cannot accept H₀
7. know exactly how to express a CI
8. know how to interpret a CI
9. interpret the meaning of the two-sample CI for population mean

Section 11.2: Inference about Two Means: Dependent Samples

Knowledge Prerequisites

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 1.6:
  - matched-pairs design
4. Section 3.1:
  - sample mean,
  - population mean, μ
5. 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)
6. Section 3.4:
  - z-score
  - percentiles
7. Section 5.1:
  - probability
  - outcome
  - random event
  - probability rules
  - unusual event
8. Chapter 7:
  - all
9. Section 8.1:
  - all
10. Section 9.2:
  - all
11. Section 10.1:
  - all
12. Section 10.3:
  - all
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, z_α/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
4. Section 10.1:
  - all
5. Section 10.3:
  - all
conditional knowledge
1. Section 1.1:
  - how to identify the difference between qualitative data and quantitative data
2. Section 1.6:
  - identify matched-pairs experimental design
3. 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
4. Chapter 7:
  - all
5. Section 8.1:
  - all
6. 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
7. Section 10.1:
  - all
8. Section 10.3:
  - all

Learning Goals

declarative knowledge (definitions)
1. none
procedural knowledge
1. conduct a hypothesis test for matched-pairs using the TI83/84: http://stats.jjw3.com/math1431/ti83tmp.htm
2. construct a CI for matched-pairs using the TI83/84: http://stats.jjw3.com/math1431/ti83tCId.htm
3. calculate the test-statistic using the TI83/84
conditional knowledge
1. identify the difference between one-sample tests and two-sample tests
2. identify whether two samples are dependent or independent
3. identify the conditions needed to use the t-statistic on the differences, d_i
4. explain the meaning of P-value and α-level
5. know when to reject H₀
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. state the conclusion from a hypothesis test
10. calculate the critical value, t_α/2, that corresponds to a given C-level using the TI83/84: http://stats.jjw3.com/math1431/ti83invt.htm
11. find the t-interval for dependent sample data using the TI83/84: http://stats.jjw3.com/math1431/ti83tCId.htm
12. calculate the point estimate using the TI83/84 [using formula given below]
13. calculate the ME for a t-interval [using formula given below]
14. know exactly how to express a CI
15. know how to interpret a CI
16. interpret the meaning of the CI

Section 11.3: Inference about Two Means: Independent Samples

Knowledge Prerequisites

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,
  - 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
10. Section 10.1:
  - all
11. Section 10.3:
  - all
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, z_α/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
4. Section 10.1:
  - all
5. Section 10.3:
  - all
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
6. Section 10.1:
  - all
7. Section 10.3:
  - all

Learning Goals

declarative knowledge (definitions)
1. none
procedural knowledge
1. conduct a two-[independent] sample hypothesis test with the t-statistic when given statistics using the TI83/84: http://stats.jjw3.com/math1431/ti83_2stTest.htm
2. conduct a two-[independent] sample hypothesis test with the t-statistic when given data using the TI83/84: http://stats.jjw3.com/math1431/ti83_2stTestd.htm
3. calculate the test-statistic using the TI83/84
4. construct a two-[independent] sample CI with the t-statistic when given statistics using the TI83/84: http://stats.jjw3.com/math1431/ti83_2stCI.htm
5. construct a two-[independent] sample CI with the t-statistic when given data using the TI83/84: http://stats.jjw3.com/math1431/ti83_2stCId.htm
conditional knowledge
1. identify the requirements needed to use the two sample t-statistic for hypothesis tests
2. explain the meaning of P-value and α-level
3. know when to reject H₀
4. explain why you cannot accept H₀
5. interpret the meaning of the two-sample CI for population mean

Section 11.4: Putting It All Together: Which Methid Do I Use?

Knowledge Prerequisites

declarative knowledge (definitions)
1. Section 11.1:
  - all
2. Section 11.2:
  - all
3. Section 11.3:
  - all
procedural knowledge
1. Section 11.1:
  - all
2. Section 11.2:
  - all
3. Section 11.3:
  - all
conditional knowledge
1. Section 11.1:
  - all
2. Section 11.2:
  - all
3. Section 11.3:
  - all

Learning Goals

declarative knowledge (definitions)
1. none
procedural knowledge
1. six steps to conduct a hypothesis test [P-value Approach is the only required method]
conditional knowledge
1. identify the difference between one-sample tests and two-sample tests
2. identify whether two samples are dependent or independent
3. identify the correct statistic to construct the CI
4. identify that the required conditions are met
5. know exactly how to express a CI
6. know how to interpret a CI
7. interpret the meaning of the CI

Chapter 11: Required Formulas – Need to Know for Tests

Relationship Between α and Confidence Level: α = 1 – C-Level
Confidence Interval (CI): Point Estimate ± Margin of Error, i.e., (Point Estimate – Margin of Error, Point Estimate + Margin of Error)
Point Estimate for a given Confidence Interval (CI):
Margin of Error (ME or E) for a given Confidence Interval (CI):
t-Statistic for Matched-Pairs Data:

Chapter 11: Required Formulas – Will be Given on Tests

One Condition Required to Construct a CI for p:
Another Condition Required to Construct a CI for p: n ≤ 0.05N OR 20n ≤ N