Exam 2 Review. Review. Cathy Poliak, Ph.D. (Department of Mathematics ReviewUniversity of Houston ) Exam 2 Review

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1 Exam 2 Review Review Cathy Poliak, Ph.D. cathy@math.uh.edu Department of Mathematics University of Houston Exam 2 Review Exam 2 Review 1 / 20

2 Outline 1 Material Covered 2 What is on the exam 3 Examples Exam 2 Review 2 / 20

3 What to Expect on the Exam The test has two parts 1. 40% of the grade is based on multiple choice questions. Five questions % of the grade is based on free response questions. Three free response questions with multiple parts. Exam 2 Review 3 / 20

4 Chapter 4 Section 1 - Density curves and the Uniform distribution Section 2 - Normal distribution: Empirical rule and using R (pnorm and qnorm) Section 3 - Standard Normal Calculations: z-scores and using the z-table value - mean z sd Section 4 - Sampling distributions of x and ˆp. Exam 2 Review 4 / 20

5 Sampling Distributions The distribution of the sample mean, x. Center: Expected value of x = µ the population mean of the original distribution. Spread: Standard error of x= σ/ n the population standard deviation divided by the square root of the sample size. 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, ˆp. Center: Expected value of ˆp = p the population proportion. p(1 p) Spread: Standard error of ˆp = n. Shape: Normal if np > 10 and n(1 p) > 10. Exam 2 Review 5 / 20

6 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 plot plot(x,resid(lm(y x))). residual = observed y predicted y Section 5: Non-linear Models, transformations. Section 6: Relations in categorical data. Using a two-way table. Finding percents. Determining marginal distributions. Determining conditional distributions. Exam 2 Review 6 / 20

7 Chapter 6: Sampling and Experiments Section 1: Types of sampling designs Section 2: Types of experiments Section 3: Simulating experiments Exam 2 Review 7 / 20

8 Possible Free Response Questions Find probabilities for a Normal distribution. Be able to sketch the distribution and shade the approprate area in the Normal curve. Find z-scores. Find the value of X corresponding to a particular probability. Draw a scatterplot, find the LSRL, interpret the slope, find the correlation coefficient, coefficient of determination (and interpret these values), find a residual value, show the residual plot and determine if the model is a good fit or not based on all observations of values found. Given a section from the random digit table be able to simulate an experiment, see problem #7 from section 6.3. Exam 2 Review 8 / 20

9 What You Need an What is Provided Provided Basic calculator; it will be a link you see in the exam. R; it will be a link you see in the exam. z-table; it will be a link you see in the exam. Can bring Calculator; if it is memory based CASA will remove the memory. Pencil; you will need something to write with for the free response questions. Your Cougar Card. Exam 2 Review 9 / 20

10 Uniform Distribution 1. Consider a uniform density curve defined from x = 0 to x = 8. What percent of observations fall below 5? a) 0.20 b) 0.75 c) 0.63 d) 0.50 e) Consider a uniform density curve defined from x = 0 to x = 9. What percent of observations fall between 1 and 6? a) 0.17 b) 0.68 c) 0.56 d) 0.67 e) 0.11 Exam 2 Review 10 / 20

11 Normal Distribution 1. If X is normally distributed with a mean of 10 and a standard deviation of 2, find P(10 X 13.4). a) b) c) d) e) Find a value of c so that P(Z c) = a) 1.08 b) 0.42 c) d) 0.08 e) 0.92 Exam 2 Review 11 / 20

12 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) = Find c such that P(Z > c) = Exam 2 Review 12 / 20

13 Sampling Distributions Suppose a random sample of 70 measurements is selected from a population with a mean of 35 and a variance of 300. Select the pair that is the mean and standard error of x. a) [35, 2.571] b) [35, 2.371] c) [35, 2.071] d) [70, 2.571] e) [35, 2.271] Exam 2 Review 13 / 20

14 LSLR Answer the questions below with the following data set: x y 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. Exam 2 Review 14 / 20

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16 Two-Way Table The following two-way table describes the preferences in movies and fast food restaurants for a random sample of 100 people. McDonalds Taco Bell Wendy s Iron Man Dispicable Me Harry Potter What percent of people in the sample like the movie Dispicable Me? 2. What percent of the Dispicable Me lovers also like McDonald s? Exam 2 Review 16 / 20

17 Sampling 1. A radio talk show wanted to know whether Houstonians think Texas should continue to use the death penalty. The station asked for listeners to call in and give their opinion. a) Convenience Sample b) Stratified Random Sample c) Voluntary Response d) Simple Random Sample 2. To judge the appeal to American adults of a proposed television sitcom, a sample of 10 people from each of three different age groups was selected and those chosen were asked to rate a pilot show. a) Convenience Sample b) Stratified Random Sample c) Voluntary Response d) Simple Random Sample Exam 2 Review 17 / 20

18 More Sampling Examples Subscribers to the magazine Sound Alive were assigned numbers. Thirty numbers were selected at random. The subscribers with the chosen numbers were asked to rate a new compact disk player for a "What Subscribers Think" column. (Assume all chosen did respond) a) Convenience Sample b) Stratified Random Sample c) Voluntary Response d) Simple Random Sample Exam 2 Review 18 / 20

19 Simulating Experiments Assume that the percentage of women in the labor force of a large metropolitan area is 40%. A company hires ten workers, two of whom are women. We want to see if this is likely. 1. Assign the digits, 0 through 9, to represent the men and women in this situation. Describe how you will run the simulation using those digits and the random digit table. 2. Start on line 136 of the random digit table and carry out the simulation with 3 runs. 3. What is the expected number of women that should be hired, based on your simulation? Exam 2 Review 19 / 20

20 Other Questions? Exam 2 Review 20 / 20