Statistics Test 1 Solutions & Points Scoring Guide - Prof. A. R. Sinn, Exams of Statistics

Download Statistics Test 1 Solutions & Points Scoring Guide - Prof. A. R. Sinn and more Exams Statistics in PDF only on Docsity! Intro to Stats, Test 1 R. Sinn, Spring 2007 Student Solutions & Points Scoring Guide Test is out of 90 Points Total Directions Answer each question in full. In some cases in statistics, more than one answer may be counted correct. Please justify your statements if in doubt. You may use a graphing calculator on any problem. Please mark “CALC” in the margin next to any steps performed on the calculator. Questions 1 and 2 relate to Histogram 1 shown at right. 1. [5 Points] Check all the statements that apply:  The distribution is approximately normal.  The distribution is skewed left.  The distribution is skewed right.  The mean and median are approximately equal. 2. [5 Points] Check all the statements that apply:  The mean is likely to be less than the median.  The mean is likely to be greater than the median.  The data set is not likely to contain outliers.  Outliers likely exist, and the majority are on the left.  Outliers likely exist, and the majority are on the right. Questions 3 and 4 relate to Histogram 2 shown at right. 3. [5 Points] Check all the statements that apply:  The distribution is approximately normal.  The distribution is skewed left.  The distribution is skewed right.  The mean and median are approximately equal. 4. [5 Points] Check all the statements that apply:  The mean is likely to be less than the median.  The mean is likely to be greater than the median.  The data set is not likely to contain outliers.  Outliers likely exist, and the majority are on the left.  Outliers likely exist, and the majority are on the right. [Grading for Q’s 1 - 4: 5 Pts -1 Pt for each correct option not marked, and -1 Pt for each incorrect option marked.] 5. [10 Points] Essay: During the Fall semester 2006, a team of NGCSU students found a correlation between age (x-variable, measured in years) and interest in rock climbing (y-variable, measured on a scale from 1 – 10, with 10 indicating high interest and 1 indicating no interest). Write 2 – 5 complete sentences explaining everything you know and can infer based upon the output shown to the right. Be sure to focus your analysis upon real-world implications. The researchers found a strong, negative real-world (moderate negative book) correlation between age and interest in rock climbing [2 Pts]. They found that 22% of the variance in interest in rock climbing was accounted for by age [2 Pts], with older people less interested than younger [1 Pt]. The slope from the prediction equation indicates that for each one year older a person is, his or her interest in rock climbing will decrease by .37 units [2 Pts]. Following directions [3 Pts]: awarded for writing in complete sentences and for connecting statistical output to the real world research scenario. Regression Statistics Line of Best Fit y = a x + b r -0.4827 a -0.372 R 2 0.2230 b 7.483 Histogram 1 0 1 2 3 4 5 6 7 8 9 10 90 to 9 9 10 0 t o 10 9 11 0 t o 11 9 12 0 t o 12 9 13 0 t o 13 9 14 0 t o 14 9 15 0 t o 15 9 16 0 t o 16 9 17 0 t o 17 9 18 0 t o 18 9 Histogram 2 0 1 2 3 4 5 6 7 8 9 10 50 to 5 4 55 to 5 9 60 to 6 5 65 to 6 9 70 to 7 4 75 to 7 9 80 to 8 4 85 to 8 9 90 to 9 4 95 to 9 9 6. [5 Points] A statistician computes a regression comparing a father’s height (in inches) to his daughter’s height (in inches). She finds that R2 = .39. Interpret this finding. This means that 39% of the variance in a daughter’s height is accounted for by father’s height. 7. [5 Points] Given Scatter Plot 1 shown at right, check all the statements that apply:  Linear Regression is appropriate.  Linear Regression is not appropriate.  The (linear) correlation is positive.  The (linear) correlation is negative.  The (linear) correlation is strong.  The (linear) correlation is weak.  No linear correlation exists. [Grading for Q 7 & 8: 5 Pts -1 Pt for each correct option not marked, and -1 Pt for each incorrect option marked.] 8. [5 Points] Given Scatter Plot 2 shown at right, check all the statements that apply:  Linear Regression is appropriate.  Linear Regression is not appropriate.  The (linear) correlation is positive.  The (linear) correlation is negative.  The (linear) correlation is strong.  The (linear) correlation is weak.  No linear correlation exists. 9. [10 Points] A tallish female college student was studying dating patterns. She wonders if tall women tend to date taller men than do short women. She measures the height of several women in her dorm; then she measures the next man each woman dates. Here are the data (heights in inches), and linear regression is appropriate: Women (x) 66 64 66 65 70 65 Men (y) 72 68 70 68 71 65 See calculator screen shots at end of test for correct calculator steps. a. Find the correlation coefficient and analyze it. r = 0.565 which indicates a strong, positive relationship (real-world) [3 Pts] b. If a woman is 5’5” tall, estimate the height of her boyfriend. Plug in 65” for x in line of best fit: y = 0.68 x + 24 → Boyfriend will be approximately 68.2” tall [2 Pts] c. Analyze R2 in the context of this problem. R2 = 0.32 meaning that 32% of the variance in boyfriend height is accounted for by the girl’s height [2 Pts] d. Analyze the slope of the prediction equation. How meaningful is this relationship (the one between the variables, not the dating relationships)? Hint: refer to your answer in part (c). 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