Lesson 9 - R Chapter 9 Review. Objectives Summarize the chapter Define the vocabulary used Complete...
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![Page 1: Lesson 9 - R Chapter 9 Review. Objectives Summarize the chapter Define the vocabulary used Complete all objectives Successfully answer any of the review.](https://reader035.fdocuments.net/reader035/viewer/2022080923/56649f4d5503460f94c6e1ee/html5/thumbnails/1.jpg)
Lesson 9 - R
Chapter 9 Review
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Objectives• Summarize the chapter
• Define the vocabulary used
• Complete all objectives
• Successfully answer any of the review exercises
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Vocabulary• None new
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Determine the Appropriate Confidence Interval to Construct
Which parameter are we
estimating
Proportion pMean, μStandard Deviation, σ,
or variance σ²
1) n ≤ 0.05N2) np(1-p) ≥ 10
1) normal population2) no outliers
Assumptions Met?
1) apx normal population2) no outliers
Compute Z-interval Compute t-interval
Compute χ²-interval Compute Z-interval
Nonparametics
σ known?
n≥30 n≥30yes yes
yes no
no
no no
yes & σ yes & s
yes yes
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Chapter 9 – Section 1
If the sample mean is 9, which of these could reasonably be a confidence interval for the population mean?
1) 92
2) (3, 6)
3) (7, 11)
4) (0, ∞)
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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) 1
2) 2
3) 5
4) 25
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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?
1) A t-distribution with 14 degrees of freedom
2) A t-distribution with 15 degrees of freedom
3) A general normal distribution
4) A nonparametric method
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Chapter 9 – Section 2
What issue do we have in calculatingσ / √ n when the population standard deviation is not known?
1) There are no issues
2) We do not know which value to use for n
3) We do not know how to calculate the sample mean
4) We do not know which value to use for σ
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Chapter 9 – Section 3
A study is trying to determine what percentage of students drive SUVs. The population parameter to be estimated is
1) The sample mean
2) The population proportion
3) The standard error of the sample mean
4) The sample size required
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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
1) 200 students
2) 400 students
3) 600 students
4) 900 students
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Chapter 9 – Section 4
Which probability distribution is used to compute a confidence interval for the variance?
1) The normal distribution
2) The t-distribution
3) The α distribution
4) The chi-square distribution
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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
1) (4, 6)
2) (8, 18)
3) (160, 360)
4) Cannot be determined from the information given
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Chapter 9 – Section 5
Which of the following methods are used to estimate the population mean?
1) The margin of error using the normal distribution
2) The margin of error using the t-distribution
3) Nonparametric methods
4) All of the above
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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?
1) The population mean
2) The population proportion
3) The population variance
4) The population standard deviation
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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
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Homework1: (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