1. Lesson 9 - R
Chapter 9 Review

2. Objectives Summarize the chapter Define the vocabulary used
Complete all objectives
Successfully answer any of the review exercises

3. Vocabulary
None new

4. 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 χ²-interval
Compute Z-interval
n≥30
n≥30
yes no no
yes
yes & σ
1) apx normal population
2) no outliers
yes & s no
Compute Z-interval
Nonparametics
Compute t-interval

5. 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, ∞)

6. 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

7. 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

8. Chapter 9 – Section 2
What issue do we have in calculating σ / √ n when 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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

16. Homework
1: (α/2=0.005, df=18-1=17) read from table: : (α/2=0.025, df=22-1=21) read from table: , : a) n>30 large sample (σ known) b) (α/2=0.03) Z=1.88 [315.15, ] c) (α/2=0.01) Z=2.326 [312.81, ] d) (α/2=0.025) Z=1.96 n > : 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, ] 15: a) x-bar = 3.244, s = 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