STAT 100 - Midterm II STAT 100 - Midterm II Sample Exam (short) SOLUTIONS Spring 2013 Instructions 1. 2. 3. 4. 5. 6. Do not panic. It rarely helps. Read all questions carefully. Write your answers clearly in the spaces provided. Where computations are required, you should show work. Cross out any material you do not wish to have considered. Correct answers with insufficient justification or accompanied by additional incorrect statements will not receive full credit. 7. Write all answers on the exam itself. 8. The exam has 33 total marks Name: ____________________________________________ Student Number: ____________________________________________ Signature: ____________________________________________ Useful formula: The counting rule for a median is z= r= observation − mean standard deviation and ( n + 1) 2 percentile = mean + z × ( standard deviation ) n ⎛ x − x ⎞ ⎛ yi − y ⎞ 1 ⋅ ∑⎜ i n − 1 i=1 ⎝ sx ⎟⎠ ⎜⎝ sy ⎟⎠ index number = value × 100 base value dollars at time B = dollars at time A × CPI at time B CPI at time A 1 STAT 100 - Midterm II QUESTION 1 (5 points) A random sample of patients who attended a clinic was selected. The age of the patient (years) and the number of days since the last visit were collected and are displayed in the figure below. The least-squares regression line for predicting number of days since the last visit from the age of the patient is y = 600.081 – 8.694x. Days Since Last Visit 500 375 250 125 0 0 18 35 Age of Patient 53 70 A. The slope of this line is: (Ans: C) A) 600.081. B) 8.694. C) –8.694. D) 600.081 – 8.694 = 591.387. B. The slope of this line tells us the (Ans: C) correlation between age of patient and days since last visit. b) change in days since last visit for each year older a patient is, on average. c) change in the age of the patient for each extra day since the last visit. d) average days since last visit for all of the patients. a) C. Using this line, you predict that the number of days since last visit to the clinic for a 50-yearold patient will be about: Ans: C A) 63 days. B) 78 days. C) 165 days. D) 200 days. E) 252 days. D. A least-squares regression line is not just any line drawn through the points of a scatterplot. What is special about a least-squares regression line? (Ans: E) a) b) c) d) e) It passes through all the points. It minimizes the squared values of the data. It has slope equal to the correlation between the two variables. It describes how a response variable y changes as an explanatory variable x takes different values. It minimizes the sum of the squared vertical distances of the data points from the line. 2 STAT 100 - Midterm II Question 2 Consider a large number of countries around the world. There is a positive correlation between the number of Nintendo games per person x and the average life expectancy y. Does this mean that we could increase the life expectancy in Rwanda by shipping Nintendo games to that country? Explain. Solutions No. The positive correlation just shows that richer countries have both more Nintendo games per person and higher life expectancies. 3 STAT 100 - Midterm II Question 3 Answer the questions below about the graph above, which shows a histogram with a normal density that has the same mean and standard deviation as the data. A. (1 pt) Which of the following is the mean of the data? (Choose one) (Ans: B) a) 12.1% b. 0.019 c. 0.005 d. 16.2% B. (1 pt) Which of the following is the standard deviation of the data (Choose one) (Ans: C) a) 0.055 b. 18.4% c. 0.0125 d. 10.0% C. (1 pt) In what interval is the first quartile of the data? .0075 to .0125 - ½ mark if they just say .010. D. (1 pt ) In what interval is the 90th percentile of the data? .0325-.0375 - ½ mark if they just say .035 E. (2 pts) Is the normal density a good model for these data? Explain. 4 STAT 100 - Midterm II No. Data show a right-skew pattern (long tight tail, short left tail). Normal density is symmetric. (Normal model expects more data at and below 0, and less data below the mean, and in the far right tail.) Any words that clearly express this concept are fine. Give partial credit for partially correct ideas. For example, saying only that the normal density does not fit the data without any specifics is worth 1.5. Question 4 A. (2 pts) Describe the relationship between X and Y. 1. Direction: Positive (increasing) 2. Shape: Fairly straight line (may note a slight wiggle if they want 3. Strength: Not very tight to line/not very strong 4. Deviations: Possible outliers between x=5-6 ½-mark each for comments on direction, shape, strength, and deviations. Be accepting of alternative interpretations that are believable B. (1 pt) On the plot above, draw in your best guess for where the regression line would go. Answers will vary. Look at plot: does it seem to go through the middle of the data? If so, give full marks. If clearly biased but still sort of middle, give ½. 5 STAT 100 - Midterm II Question 5 A. (5 pts) A sample was taken of the salaries of 10 employees of a large company. The following are the salaries (in thousands of dollars) for this year. 41 67 28 52 42 102 61 48 42 34 Calculate a 5-number summary for these data. Place your 5 numbers in the blanks below in order from smallest to largest. Question 6 The graphic at right was circulated around Facebook shortly before the 2012 US Presidential Election. For reference, US presidents are elected every four years and take office in the January after their election. Comment on how accurately the graphic represents the factual statement that 4,400 jobs have been lost in coal-related industries since Obama took office. Solutions The “y” axis on the graphic does not extend to zero, so the decrease in jobs looks much more severe that it really is (it looks like almost ¾ were lost, but really should depict about a 6000/88000 = 7% decline over the time period shown) 6 STAT 100 - Midterm II The time period does not extend all the way to the beginning of Obama’s taking office. (In fact, since the plot shows a decline of 6000 from start to finish, that means that there were about 1600 jobs gained from Jan 2009-Sept 2011! 1 mark for each item. 1 bonus mark for discovering the underlined statement. 7