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Lesson 9 - R. Chapter 9 Review. Objectives. Summarize the chapter Define the vocabulary used Complete all objectives Successfully answer any of the review exercises. Vocabulary. None new. Determine the Appropriate Confidence Interval to Construct. Which parameter are we estimating.

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lesson 9 r

Lesson 9 - R

Chapter 9 Review

objectives
Objectives
  • Summarize the chapter
  • Define the vocabulary used
  • Complete all objectives
  • Successfully answer any of the review exercises
vocabulary
Vocabulary
  • None new
determine the appropriate confidence interval to construct
Determine the Appropriate Confidence Interval to Construct

Which parameter are we estimating

Standard Deviation, σ, or variance σ²

Mean, μ

Proportion p

Assumptions Met?

1) normal population

2) no outliers

1) n ≤ 0.05N

2) np(1-p) ≥ 10

yes

yes

σ known?

yes

no

Compute Z-interval

Compute χ²-interval

n≥30

n≥30

yes

no

yes

no

yes & σ

yes & s

1) apx normal population

2) no outliers

no

Nonparametics

Compute Z-interval

Compute t-interval

chapter 9 section 1
Chapter 9 – Section 1

If the sample mean is 9, which of these could reasonably be a confidence interval for the population mean?

  • 92
  • (3, 6)
  • (7, 11)
  • (0, ∞)
chapter 9 section 11
Chapter 9 – Section 1

If the population standard deviation σ = 5 and the sample size n = 25, then the margin of error for a 95% normal confidence interval is

  • 1
  • 2
  • 5
  • 25
chapter 9 section 2
Chapter 9 – Section 2

A researcher collected 15 data points that seem to be reasonably bell shaped. Which distribution should the researcher use to calculate confidence intervals?

  • A t-distribution with 14 degrees of freedom
  • A t-distribution with 15 degrees of freedom
  • A general normal distribution
  • A nonparametric method
chapter 9 section 21
Chapter 9 – Section 2

What issue do we have in calculatingσ / √nwhen the population standard deviation is not known?

  • There are no issues
  • We do not know which value to use for n
  • We do not know how to calculate the sample mean
  • We do not know which value to use for σ
chapter 9 section 3
Chapter 9 – Section 3

A study is trying to determine what percentage of students drive SUVs. The population parameter to be estimated is

  • The sample mean
  • The population proportion
  • The standard error of the sample mean
  • The sample size required
chapter 9 section 31
Chapter 9 – Section 3

A study of 100 students to determine a population proportion resulted in a margin of error of 6%. If a margin of error of 2% was desired, then the study should have included

  • 200 students
  • 400 students
  • 600 students
  • 900 students
chapter 9 section 4
Chapter 9 – Section 4

Which probability distribution is used to compute a confidence interval for the variance?

  • The normal distribution
  • The t-distribution
  • The α distribution
  • The chi-square distribution
chapter 9 section 41
Chapter 9 – Section 4

If the 90% confidence interval for the variance is (16, 36), then the 90% confidence interval for the standard deviation is

  • (4, 6)
  • (8, 18)
  • (160, 360)
  • Cannot be determined from the information given
chapter 9 section 5
Chapter 9 – Section 5

Which of the following methods are used to estimate the population mean?

  • The margin of error using the normal distribution
  • The margin of error using the t-distribution
  • Nonparametric methods
  • All of the above
chapter 9 section 51
Chapter 9 – Section 5

A professor wishes to compute a confidence interval for the average percentage grade in the class. Which population parameter is being studied?

  • The population mean
  • The population proportion
  • The population variance
  • The population standard deviation
summary and homework
Summary and Homework
  • Summary
    • We can use a sample {mean, proportion, variance, standard deviation} to estimate the population {mean, proportion, variance, standard deviation}
    • In each case, we can use the appropriate model to construct a confidence interval around our estimate
    • The confidence interval expresses the confidence we have that our calculated interval contains the true parameter
  • Homework:pg 497 – 501; 1, 3, 8, 9, 15, 23, 24
homework
Homework

1: (α/2=0.005, df=18-1=17) read from table: 2.898

3: (α/2=0.025, df=22-1=21) read from table: 10.283, 35.479

8: a) n>30 large sample (σ known)b) (α/2=0.03) Z=1.88 [315.15, 334.85]c) (α/2=0.01) Z=2.326 [312.81, 337.19]d) (α/2=0.025) Z=1.96 n > 147.67

9: a) large sample size allows for x-bar to be normally distributed from a non-normal (skewed data distribution: mean vs median) b) (α/2=0.05) t=1.646 MOE=0.298 [12.702, 13.298]

15: a) x-bar = 3.244, s = 0.487 b) yes c) (α/2=0.025) [2.935, 3.553] d) (α/2=0.005) [2.807, 3.681] e) (α/2=0.005) [0.312, 1.001]

23: same because t-dist is symmetric

24: t-dist, because the tails are larger