!1! Statistics 10/Midterm one Professor Esfandiari Summer 12 Last Name ________________ First Name____________________ Student ID ______________________________ Name of TA ______________________ Section ___________________ Questions Possible points Actual points One to six _____ 24________ _________________ Seven ______7________ _________________ Eight ______10_______ _________________ Nine ______10______ _________________ Ten _______24______ _________________ Total _______75________ _____________ • You can have a cheat sheet 8.5 by 11 written on both sides. • No access to phone, email, computer. • Need to have your ID to take the test. • You need a calculator that takes a square root.!2!Good Luck! Question one: You have three plots in which: A: Q3 – Q2 = Q2 – Q1 (mean = median /case 2) B: Q3 – Q2 > Q2 – Q1 (Hard exam exam/case 1) C: Q3 – Q2 < Q2 – Q1 (Easy exam/case 3) You are given three scenarios: 1) The final exam was easy and 80% of the scores are above the mean. When the exam is easy the majority of the people are clustered around high scores and the outliers are low. So, Q3 – Q2 < Q2 – Q1 2) The mean and median one the final exam were almost equal to each other. This is a symmetrical case in which Q3 – Q2 = Q2 – Q1 3) The final exam was difficult and 80% of the scores are below the mean When the exam is difficult the majority of the scores are clustered around Q1 and Q2 and the outliers are large. Thus, Q3-Q2 > Q2 – Q1 a) Plots A, B, and C correspond to scenarios 2, 3, and 1 respectively. b) Plots A, B, and C correspond to scenarios 3, 1, and 2 respectively. c) This question cannot be answered with the given data. We need to see the actual histograms. d) Plots A, B, and C correspond to scenarios 2, 1, and 3 respectively.!3! Question two. Given the following histogram and boxplot, what do you recommend as measures of center and spread and what is true about the outlier at 21? I will recommend a) Median and IQR. Outlier is approximately> 16.5 + 1.5*2.5 b) Median and SD. Outlier is approximately > 16.5 - 1.5*2.5 c) Mean and SD. Outlier is approximately > 16.5 – 1.5*2.5 d) Mean and IQR. Outlier is approximately > 16.5 + 1.5*2.5 510152025303540TimeSeconds_L (thousands)10 12 14 16 18 20 22 24marathons.txtHistogram!4! Question three: You are given the following data on a random sample of 400 undergraduates. • Letters of recommendation (excellent, good, satisfactory) • Level of volunteer work in the community (High, Average, Low) • Attitude toward making a difference for the community (scale of 0-100) • Level of optimism (scale of 0-100) What would be the best way to display the following? You cannot transform any of the variables. You need to use them the way they are. a. Letters of recommendation and level of optimism b. Level of volunteer work and letters of recommendation TimeSeconds_L (thousands)10 12 14 16 18 20 22marathons.txtBox Plot!5!c. Attitude toward making a difference for the community and level of optimism a) side-by-side boxplot for A, Segmented bar chart for B, , and scatterplot for C. b) Side-by-side boxplot for A, scatterplot for B , and segmented bar chart for C. c) Scatterplot for A, segmented bar chart for B, and side-by-side boxplot for C. d) Scatterplot A, back to back stem and leaf plot for B, Contingency table for C. Question four. What do we mean by the “least square line” in regression? a) We mean that if we subtract the actual scores from the predicted scores and add, the sum will be a minimum. b) We mean that the sum of the residuals around the regression line is minimum. c) We mean that the sum of the square of the residuals around the regression line is minimum.!6!d) We mean that if we subtract the actual scores from the predicted scores, square, and add, the sum will be a minimum. Question five. The following regression equation was reported for the prediction of men’s height weight as a function of age. Weight is measured in pounds and age is measured in years. Predicted weight = 132.9 + 2.4 age What is the best interpretation of the intercept? a. If we set age equal to zero, the expected weight for men will be 132.9 b. It makes no sense to try to interpret the intercept in this situation.!7!c. Given the formula for intercept, we need the mean of age and weight to interpret the intercept. d. For each year that age increases, the average increase in weight is 2.4 pounds. Question six. There is a data set with 100 observations. 80 of the observations are above the mean. There are ten very large outliers at the left end of the distribution so that the distribution is negatively skewed. If you compute ∑(Xi - X), what do you expect to find? a) We need the real data to estimate this quantity. b) Due to the large outliers the above sum will be large and positive.!8!c) The above sum is expected to be zero. d) Since the mean is less than the median, the above sum will be negative Question seven. A doctor strongly believes that antidepressants work better than “talk therapy” for patients who are severely depressed. He designs the following study to answer this question. He is treating 90 patients for depression. He divides them into two groups of severely depressed (N = 40) and moderately depressed (N = 50). He assigns the severely depressed to the antidepressant and the moderately depressed to “talk therapy”. He then compares the drop in their depression level after six months. Given the above, is this study observational or experimental? Observational________ Experimental______ Explain why. NOT MORE THAN THREE LINES.!9!This study is observational. Just having a group that takes the medication and one group that takes the placebo does not make a study experimental. There is no random assignment. To make the study Experimental, he should have randomly assigned half of the severely depressed to Anti-depressant and the other half to talk therapy and do the same with the Moderately depressed. The level of depression would be a blocking variable. Question eight. A study was conducted to examine the relationship between type of absenteeism and high school GPA of seniors (top 25% and bottom 25%). The following data was collected. • GPA in the op 25% = 1 • GPA in the bottom 25% = 0 • Excused absence = 1 • Unexcused absence =