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Material Type: Exam; Professor: Zhao; Class: Elementary Statistical Methods; Subject: STAT-Statistics; University: Purdue University - Main Campus; Term: Fall 2007;
Typology: Exams
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MATCHING: For the following problems, write the letter of the most appropriate statistical analysis technique next to the story. Note: each answer choice may be used once, more than once, or not at all. A. Mean and/or standard deviation B. Simple linear regression C. Multiple linear regression D. 1-sample mean t-test E. Matched pairs t-test F. Comparison of means t-test G. 1-sample proportion Z-test H. 2-sample proportion Z-test I. Chi-squared test J. One-way ANOVA K. Two-way ANOVA L. Five number summary _____ 1. Is college major associated with the region of the country a student is from? _____ 2. A group of taste testers is asked to rate (in random order) both Coke and Pepsi on a scale of 1-10. Is Coke better tasting than Pepsi on average? _____ 3. What is the average taste test rating for Coke on a scale of 1-10? _____ 4. Do major and region of the country a student is from affect his/her GPA? _____ 5. Which of the following are important for predicting a student’s graduation GPA: the number of semesters a student spends in college, their high school GPA, and their SAT scores? _____ 6. Is the percentage of people in Tippecanoe county who are Purdue students significantly higher in 2007 than it was in 1994 if a random sample of residents was taken both years? _____ 7. Are height and weight independent? _____ 8. Are freshman taller than seniors on average? _____ 9. Are average GPAs the same for science and engineering majors? _____ 10. Are average GPAs the same for science, engineering, nursing, and communications majors? _____ 11. Is the average GPA 3.0? _____ 12. What is the middle GPA for this group of students?
MATCHING: (3 points each) For problems 2-12, write the letter of the most appropriate statistical analysis technique next to the story. Note: each answer choice may be used once, more than once, or not at all. _____ 6. Does knowing a college student’s SAT score tell us anything about his or her first year college GPA? _____ 7. Do college grade point averages differ for male athletes in major sports (e.g., football), minor sports (e.g., swimming), and intramural sports? _____ 8. A college instructor wants to know whether the average high school GPA for freshman enrolled in college algebra is below 3.0. _____ 9. Does knowing high school seniors’ IQ scores, SAT scores, and high school GPA tell us anything about their first year college GPAs? _____ 10. Do New Mexican high school seniors score higher on average than Vermont high school seniors on the national achievement exam? _____ 11. Is college major related to political party affiliation? _____ 12. Do identical twins differ from each other on average in reading achievement scores? _____ 13. Is support for a school bond issue (Yes or No) higher in University Farms than in Chauncey Village neighborhoods? _____ 14. Is there a difference in average national achievement exam scores for seniors from New Mexico, Florida, and Vermont? _____ 15. What is the average national achievement exam score for New Mexico high school seniors? _____ 16. Do college major and gender affect the mean GPA for Purdue students? a. Mean and/or standard deviation b. Five number summary c. Simple linear regression d. Multiple linear regression e. 1-sample mean t- test f. Matched pairs t- test g. 2-sample (Comparison of means) t-test h. 1-sample proportion Z-test i. 2-sample proportion Z-test j. Chi-squared test k. One-way ANOVA l. Two-way ANOVA
So how do you know which is which? To get started, decide whether your variable(s) is/ are categorical or quantitative. Mean and/or standard deviation : just looking for a summary statistic, variable is quantitative Simple linear regression : using x to predict y, are x and y independent?, x and y are correlated, as x increases what happens to y, x and y are both quantitative variables Multiple linear regression : similar to simple linear regression except there will be more than one x, all variables will be quantitative 1-sample mean t-test : comparing a single mean to a number, each unit is asked a numerical question (“how many times a week do you ride the bus?”), don’t know the population standard deviation, quantitative variable Matched pairs t-test : before and after, left and right, all units are tested twice (a unit could be a pair of subjects or pair of units) and measurements are compared to each other, average difference, quantitative variable Comparison of means t-test : 2 distinct populations with samples chosen independently, each unit is measured only once, one quantitative variable (your measurement) and one categorical variable (how you distinguish between your groups, like gender or eye color) 1-sample proportion Z-test : each unit is asked a yes/no question (“did you ride the bus today?”), proportion comes from taking the # of successes / # of trials, comparing a proportion or percentage to a number between 0 and 1 2-sample proportion Z-test : similar to 1-sample proportion Z-test except there are 2 distinct populations with samples selected independently so that the proportions can be compared to each other Chi-squared test : 2 categorical variables, testing whether there is an association between the variables One-way ANOVA : one categorical variable (how you distinguish between your groups) and one quantitative variable (your measurement), similar to comparison of means t-test except you can have more than 2 groups to compare Two-way ANOVA : two categorical variables (how you distinguish between your groups) and one quantitative variable (your measurement), similar to doing one-way ANOVA twice except you can also look for the interaction between the two categorical variables Five-number summary : Min, Q1, M, Q3, Max, summary statistics for a quantitative variable