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Study Guide for EXAM Your exam will have two sections. Part I will be equivalent to a class test over ANOVA, Chi- Square, and Correlation/Regression, with the test being similar to a typical class test with problems and multiple choice questions. Part II of the exam will be comprehensive covering material from the entire course. Study guides for Parts I and II are provided below. Part 1—ANOVA, Chi-Square, and Correlation/Regression 1. Re-read “One-way Analysis of Variance; Chi-Square—Sections 11.1 & 11.2; and Regression—Ch 4 and Section 11.3. Review notes on the web for ANOVA, Regression, and Chi-Square. 2. Review labs 12, 13, 14 & 15 that cover the material in ANOVA, 4.1-4.3, 11.1-11.3. 3. Study the Chapter Reviews for ANOVA, Ch 4, Ch 11 (Sections 11.1-11.3). Read Historical Notes throughout ANOVA, Ch 4, and Ch 11 (Section 11.1-11.3). 4. Study the Tables and Formula sheet in the back of your text (this will be provided with your exam). 5. Go to www.prenhall.com/sullivanstats and click on the textbox in the upper left corner where you see “jump to …”. This brings up a menu of chapters, with practice prob lems available for each chapter. ***** Final Exams : TR class 1:30-4:00 p.m. Thursday May 3. MWF class 1:30-4:00 a.m. Friday May 4. Practice Proble ms for ANOVA, Chi-Square, and Regression/Correlation ANOVA Section You s hould be able to … Review Exe rcises 1. Verify the requirements to perform a one-way ANOVA (p. 2 of ANOVA handout on course web page under “Resources”). 2. Conduct a one-way ANOVA hypothesis test. Be able to 6 (a)-(d)* perform the calculations (by hand) to find MSB, MSW, and F. 3. Construct 95% confidence intervals for each population 6(e)* mean 4. Conduct a least-significant difference test to determine Use the data in whether the mean math scores are equal in Canada and problem 6. the U.S. (see Notes_ANOVA on the course web page). *Problem 6 is found in “One-way Analysis of Variance” on the course web page under “Resources.” Chi-Square, Sections 11.1-11.2 Review Exe rcises Section You s hould be able to … (pp. 526-30) a/ 11.1 1. Perform a chi-square goodness of fit test (p. 476). 1 11.2 1. Perform a chi-square test for independence (p. 488). 5 2. Perform a chi-square test for homogeneity of proportions 9 (p. 494). a/ Additional Review Exercises are found in your text on p. 526. Chapter 4 Review Exe rcises Section You s hould be able to … (pp. 182-84) a/ 4.1 1. Draw a scatter diagram (p. 149); interpret the scatter 1-4 diagram (p. 151); and compute and interpret the linear correlation coefficient. (p.154). 2. Understand the properties of the linear correlation coefficient (p. 151). 4.2 1. Find the least-squares regression line (p. 165). 5(a) 2. Interpret the slope and y-intercept of the least-squares 5(c) regression line (p. 167) 3. Predict the value of the response (dependent) variable, 5(d) based upon the least-squares regression line (p. 167) 4. Determine errors (residuals), based upon the least-squares 5(e)-(f) regression line (p. 168). 4.3 1. Be able to draw Figure 14 (p. 177) and explain the three sources of deviation. 2. Compute and interpret the coefficient of determination (p. 11 176). a/ Additional Review Exercises are found in your text on p. 182. Regression, Section 11.3 Review Exe rcises Section You s hould be able to … (pp. 526-30) a/ 11.3 1. Understand the difference between the Population Model and the Statistical Model (see Notes_Regr1 on the web). 2. Compute the standard error of the estimate (p. 507) 11(b) (Note that you found b0 and b1 in Exercise 5(a) from Section 4.2.) 3. Test the claim that a linear relation exists between two 11(e) variables (p. 510 and Notes_Regr1, pp. 20-21) 4. Compute a confidence interval about the slope of the least- 11(f) squares regression model (p. 514). a/ Additional Review Exercises are found in your text on p. 526. Part II—Compre hensive Material from Entire Course 1. What is descriptive statistics? Give an example. 2. What is inferential statistics? In your answer be sure to define population, random sample, parameter, statistic, and inference. Give an example of inferential statistics. 3. What is a census? Compare using a census to using inferential statistics to find information about a population. 4. The mean and standard deviation are, respectively, measures of central tendency and dispersion. Calculate the mean and standard deviation for the following variable X. X 4 8 10 16 Make sure you know how to calculate the variance with both the definition and short-cut formulas (see Notes_Ch3). 5. Review how to interpret the mean and standard deviation. As an example, consider three investments with their respective means and standard deviations (with returns in %/year). #1 #2 #3 Mean 4 6 11 SD 0 10 25 Compare these investments based on the mean and SD. Which investment has the smallest risk (i.e., smallest uncertainty in return)? Largest risk? Would you prefer #1 or #2?—Why? Would you prefer #2 or #3?—Why? 6. When a fair coin is tossed, the probability of a head is 0.50. What does probability mean in terms of this example? Compare Classical and Empirical probability. Is the coin toss an example of Classical or Empirical probability? 7. A venture capitalist wants to evaluate the potential of a new business to convert biomass into energy. The profitability of the new business is unknown, but to determine whether to move forward with organization of the business, the venture capitalist has developed a discrete probability distribution for the return (X) of the business (in millions of dollars). X | -3 +4 10 P(X=x) | 0.40 0.35 0.25 Calculate the venture capitalist’s estimate of the mean (E(X)) and standard deviation for the new business. Interpret E(X), i.e., what does E(X) tell the venture capitalist about this investment? Interpret standard deviation of X, i.e., what does the standard deviation tell the venture capitalist about the investment? 8. What is a probability distribution function for a continuous random variable? Name the four probability distributions we studied this semester and describe the characteristics of each (draw a diagram of each distribution with the characteristics listed beside the diagram). 9. The variable X has a normal distribution with μ=200 and σ=20. a) Find P(175<X<210). Use a diagram with labels to illustrate your answer. b) Find the two values of X (X1 & X2 ) that include the middle 50% of X’s. Use a diagram with labels to illustrate your answer. c) Find the value of X such that 25% of the X’s are above this value (i.e., find X0 such that P(X>X0 )=0.25). Use a diagram with labels to illustrate your answer. 10. What is the distribution of the sample mean? Draw the distribution of x showing its mean and standard deviation. Draw the distribution of x for a normal population with mean μ = 80 and standard deviation σ = 12 and for sample size n = 4. Label your graph. How does the distribution of the sample mean change when the sample size is increased from n=4 to n=36? Draw this distribution (for n=36) on the diagram above. Does increasing n improve the accuracy of x as an estimate of μ? Why or why not? Explain. 11. The variable X has a normal distribution with μ=420 and σ=80. a) For a random sample of 16 observations, find P(415< X <425). Use a diagram with labels to illustrate your answer. b) For samples of size n=64, find the two values of X ( X 1 & X 2 ) that include the middle 50% of X ' s . Use a diagram with labels to illustrate your answer. c) For a sample of size n=100, find the value of X such that 35% of the X ' s are below this value (i.e., find X 0 such that P( X < X 0 )=0.35). Use a diagram with labels to illustrate your answer. 12. What is the Central Limit Theorem? 13. Review how to perform the 4-steps of a hypothesis test. Consider the example problem below. A popular traditional variety of dryland cotton in west Texas yields an average of μ = 425 pounds/acre. A local cotton breeder has developed a new variety which he believes will provide a higher yield. To test the new variety, the cotton breeder grows 6 plots of the new variety under typical west Texas dryland conditions. The yields for the plots are shown below (in pounds/acre): X=New Variety 431 460 430 425 435 450 Is the New Variety preferred over the Traditional Variety? Use the Classical Approach to test the appropriate null hypothesis at the 5% significance level. Show all 4 steps of test of a hypothesis. Interpret your conclusion in terms of the question at hand. 14. Review how to calculate a P-value based on a test statistic and how to use the P-value to test a hypothesis. Be prepared to use a diagram to show how to calculate a P-value (do not rely on your calculator to find a P-value). Use the data from Question #13 and apply the P- value approach to test the appropriate null hypothesis at the 5% significance level. Show all 4 steps of test of a hypothesis. Interpret your conclusion in terms of the question at hand. 15. Review the page of “Important Points to Remember about Hypothesis Tests” from Notes_Ch9. 16. Considering the example in Question #13, explain why statistics must be used to “prove” that a new variety of cotton has a higher yield than the established, traditional variety. 17. Review how to calculate a confidence interval and HOW TO INTERPRET A CONFIDENCE INTERVAL. Use the data from Question #13 to calculate a 95% confidence interval. Interpret your confidence interval. 18. Based on the data in the table below, answer the following questions. Table 1. Growth and carcass traits and economic returns from implanted or non-implanted steers. No Measurement Implant implant SD diff. t-value p-value Days fed: 178 days No. of steers 9 10 ADG, lb/day 3.1 2.5 0.23 2.80 <0.02 Net return, $/head 5 20 4.7 -3.19 <0.01 Feed efficiency 6.5 5.1 1.2 1.17 <0.3 Hot carcass weight, lb 683 705 45 -0.48 ns Source: http://www.ansci.cornell.edu/courses/as360/lab/feedlot/feedlot.html (taken on 11-28-06). (a) Would you recommend using implants on steer cattle? Why or why not? Justify your answer. (b) State the null and alternative hypotheses for one line of results in the table. What statistical test was used in the statistical analysis? Demonstrate how the t-value was calculated. Demonstrate how the p-value was calculated. Interpret the p- value.