Mathematical Statistics Exam 1 Solutions: Descriptive Statistics and Confidence Intervals, Exams of Mathematical Statistics

Download Mathematical Statistics Exam 1 Solutions: Descriptive Statistics and Confidence Intervals and more Exams Mathematical Statistics in PDF only on Docsity! The University of Texas at San Antonio Department of Management Science and Statistics STA 3523, Mathematical Statistics Instructor: Victor De Oliveira February 4, 2009 Name: EXAM 1: SOLUTION Read carefully all the questions and do not spend too much time in any single question. Show all your work to receive credit. 1. A biologist studying the possible effects of pollution on the health of frogs of a certain kind collected ten frogs near a lake and measured their weights (in grams). The collected data were: 15.2 14.1 13.7 15.2 15.0 14.5 13.8 16.5 13.2 14.0 Compute: (a) Sample mean 14.52 (b) Sample median 14.3 (c) Sample standard deviation 0.97 (d) Interquartile range 1.4 (4 points) 2. Consider the histograms in Figure 1. (a) For each these histograms decide whether the sample mean ȳ is larger, smaller or about the same when compared to the sample median ỹ (A) ȳ < ỹ (B) ȳ ≈ ỹ (C) ȳ > ỹ (D) ȳ > ỹ (2 points) (b) For histogram (A), give a reasonable guess for the sample median 1.25 (1 point) (c) For histogram (C), give a reasonable guess for the number of observations between 0.8 and 1.0 22 (1 point) 0.8 1.0 1.2 1.4 0 2 4 6 8 10 12 14 (A) variable Y1 0 1 2 3 4 0 2 4 6 8 10 12 (B) variable Y2 0.6 0.8 1.0 1.2 0 5 10 15 20 (C) variable Y3 0.90 0.95 1.00 1.05 1.10 0 2 4 6 8 10 12 14 (D) variable Y4 Figure 1: