STAT 100 - Midterm II STAT 100 - Midterm II Sample Exam (short) 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 ∑ x= z= r= n x i=1 i n ∑ (x − x ) n sx = ( n + 1) observation − mean standard deviation i=1 2 2 i n −1 and percentile = mean + z × ( standard deviation ) n ⎛ x − x ⎞ ⎛ yi − y ⎞ 1 ⋅ ∑⎜ i n − 1 i=1 ⎝ sx ⎟⎠ ⎜⎝ sy ⎟⎠ index number = value CPI at time B × 100 dollars at time B = dollars at time A × base value CPI at time A 1 STAT 100 - Midterm II QUESTION 1 (4 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: 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 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: 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? 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. 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. 3 STAT 100 - Midterm II A. (1 pt) Which of the following is the mean of the data? (Choose one) 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) 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? D. (1 pt ) In what interval is the 90th percentile of the data? E. (2 pts) Is the normal density a good model for these data? Explain. Question 4 A. (2 pts) Describe the relationship between X and Y. B. (1 pt) On the plot above, draw in your best guess for where the regression line would go. 4 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 Calculate a 5-number summary for these data. 102 61 48 42 34 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. 5