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Exam 2 ReviewReview

Cathy Poliak, Ph.D.cathy@math.uh.edu

Department of MathematicsUniversity of Houston

Exam 2 Review

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Outline

1 Material Covered

2 What is on the exam

3 Examples

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What to Expect on the Exam

The test has two parts1. 40% of the grade is based on multiple choice questions. Five

questions.

2. 60% of the grade is based on free response questions. Three freeresponse questions with multiple parts.

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Chapter 4

Section 1 - Density curves and the Uniform distribution

Section 2 - Normal distribution: Empirical rule and using R (pnormand qnorm)

Section 3 - Standard Normal Calculations: z-scores and using thez-table

z − value - meansd

Section 4 - Sampling distributions of x̄ and p̂.

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Sampling Distributions

The distribution of the sample mean, x̄ .I Center: Expected value of x̄ = µ the population mean of the original

distribution.I Spread: Standard error of x̄= σ/

√n the population standard

deviation divided by the square root of the sample size.I Shape: Normal if the original distribution is Normal or the sample

size is larger than 30, Central Limit Theorem.

The distribution of the sample proportion, p̂.I Center: Expected value of p̂ = p the population proportion.I Spread: Standard error of p̂ =

√p(1−p)

n .I Shape: Normal if np > 10 and n(1− p) > 10.

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Chapter 5: Bivariate Data

Section 1: Scatterplots

Section 2: Correlation in R cor(x,y)

Section 3: Least Squares Regression Line (LSRL) in R lm(y∼x)

Section 4: Residuals in R resid(lm(y∼x)). To plot a residual plotplot(x,resid(lm(y∼x))).

residual = observed y − predicted y

Section 5: Non-linear Models, transformations.

Section 6: Relations in categorical data.I Using a two-way table. Finding percents.I Determining marginal distributions.I Determining conditional distributions.

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Chapter 6: Sampling and Experiments

Section 1: Types of sampling designs

Section 2: Types of experiments

Section 3: Simulating experiments

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Possible Free Response Questions

Find probabilities for a Normal distribution. Be able to sketch thedistribution and shade the approprate area in the Normal curve.Find z-scores. Find the value of X corresponding to a particularprobability.

Draw a scatterplot, find the LSRL, interpret the slope, find thecorrelation coefficient, coefficient of determination (and interpretthese values), find a residual value, show the residual plot anddetermine if the model is a good fit or not based on allobservations of values found.

Given a section from the random digit table be able to simulate anexperiment, see problem #7 from section 6.3.

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What You Need an What is Provided

ProvidedI Basic calculator; it will be a link you see in the exam.I R; it will be a link you see in the exam.I z-table; it will be a link you see in the exam.

Can bringI Calculator; if it is memory based CASA will remove the memory.I Pencil; you will need something to write with for the free response

questions.I Your Cougar Card.

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Uniform Distribution

1. Consider a uniform density curve defined from x = 0 to x = 8.What percent of observations fall below 5?a) 0.20b) 0.75c) 0.63d) 0.50e) 0.13

2. Consider a uniform density curve defined from x = 0 to x = 9.What percent of observations fall between 1 and 6?a) 0.17b) 0.68c) 0.56d) 0.67e) 0.11

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Normal Distribution

1. If X is normally distributed with a mean of 10 and a standarddeviation of 2, find P(10 ≤ X ≤ 13.4).a) 0.755b) 0.855c) 0.455d) 0.655e) 0.555

2. Find a value of c so that P(Z ≤ c) = 0.47.a) 1.08b) 0.42c) -0.08d) 0.08e) 0.92

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Standard Normal Distribution

Find the following and sketch the curve.1. Find P(Z<1.2)2. Find P(Z > -1.39)3. Find c such that P(Z < c) = 0.8454. Find c such that P(Z > c) = 0.845

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Sampling Distributions

Suppose a random sample of 70 measurements is selected from apopulation with a mean of 35 and a variance of 300. Select the pairthat is the mean and standard error of x̄ .a) [35,2.571]

b) [35,2.371]

c) [35,2.071]

d) [70,2.571]

e) [35,2.271]

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LSLR

Answer the questions below with the following data set:

x 2 8 8 13 16 19y 22 29 28 40 33 41

1. Create a scaterplot from the data.2. What is the correlation coefficient?3. Determine the coefficient of determinatin.4. Develop a LSLR for the given data.5. Give the residual value for x = 13.

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Two-Way Table

The following two-way table describes the preferences in movies andfast food restaurants for a random sample of 100 people.

McDonalds Taco Bell Wendy’sIron Man 20 12 8Dispicable Me 12 7 9Harry Potter 6 14 12

1. What percent of people in the sample like the movie DispicableMe?

2. What percent of the Dispicable Me lovers also like McDonald’s?

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Sampling

1. A radio talk show wanted to know whether Houstonians thinkTexas should continue to use the death penalty. The station askedfor listeners to call in and give their opinion.a) Convenience Sampleb) Stratified Random Samplec) Voluntary Responsed) Simple Random Sample

2. To judge the appeal to American adults of a proposed televisionsitcom, a sample of 10 people from each of three different agegroups was selected and those chosen were asked to rate a pilotshow.a) Convenience Sampleb) Stratified Random Samplec) Voluntary Responsed) Simple Random Sample

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More Sampling Examples

Subscribers to the magazine Sound Alive were assigned numbers.Thirty numbers were selected at random. The subscribers with thechosen numbers were asked to rate a new compact disk player for a"What Subscribers Think" column. (Assume all chosen did respond)a) Convenience Sampleb) Stratified Random Samplec) Voluntary Responsed) Simple Random Sample

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Simulating Experiments

Assume that the percentage of women in the labor force of a largemetropolitan area is 40%. A company hires ten workers, two of whomare women. We want to see if this is likely.

1. Assign the digits, 0 through 9, to represent the men and women inthis situation. Describe how you will run the simulation using thosedigits and the random digit table.

2. Start on line 136 of the random digit table and carry out thesimulation with 3 runs.

3. What is the expected number of women that should be hired,based on your simulation?

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A line like the following will be given on the test instead of using therandom digit table.

Line112 07965 89754 96881 98455 94642 72528 12427 65076

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Other Questions?

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