Math 80+80S Module 4 Written Assignment Numerical Methods for Describing Data Name: _____________________________________ Please show all work for this assignment, because you will be graded on the...

Module 4 Written Assignment


Math 80+80S Module 4 Written Assignment Numerical Methods for Describing Data Name: _____________________________________ Please show all work for this assignment, because you will be graded on the clarity of your explanation as well as the correctness of your work. An answer with no work will receive no credit. Roman Mint Gold Content (% by weight) 0.15 0.28 0.17 0.32 0.17 0.36 0.18 0.38 0.20 0.38 0.21 0.42 0.22 0.43 0.23 0.47 0.24 0.50 0.24 1) The measurements in the table at the right are from coins minted in Rome during the first three centuries AD. Historians believe that different mints reveal themselves in different trace element profiles in the coins. Atomic Absorption Spectrometry was used to estimate the % by weight of various elements in these coins, and the % by weight of gold is presented here. (a) Calculate these numerical summaries. Mean_________________________ Median_________________________ Standard Deviation_________________________ Interquartile Range_________________________ (b) Construct a skeletal box plot for the data from the previous page. (c) Using only the data and your responses in parts (a) and (b), would you say this distribution is skewed or approximately symmetric? Justify your response using appropriate statistical terminology. 2) In 1997, a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard (Genessey v. Digital Equipment Corporation). The jury awarded about $3.5 million for pain and suffering, but the court then set aside that award as being unreasonable compensation. In making this determination, the court identified a “normative” group of 27 similar cases and specified a reasonable award as one within 2 standard deviations of the mean of the awards in the 27 cases. The 27 award amounts were the following, in thousands of dollars. What is the maximum possible amount that could be awarded under the “2-standard deviations rule?” 37 60 75 115 135 140 149 150 238 290 340 410 600 750 750 750 1050 1100 1139 1150 1200 1200 1250 1576 1700 1825 2000 3) To investigate the effects of the insecticide lead arsenate on table wines, 35 bottles of white wine from different wineries in a certain region where the insecticide was used were sample, and the amount of lead (mg/l) was determined by carbon rod atomic absorption spectrophotometry. The findings were as follows. 0.30 0.35 0.37 0.41 0.43 0.45 0.47 0.31 0.36 0.39 0.41 0.43 0.45 0.47 0.34 0.36 0.39 0.41 0.44 0.45 0.47 0.34 0.37 0.39 0.42 0.44 0.45 0.47 0.34 0.37 0.40 0.43 0.44 0.46 0.50 (a) Compute the mean and standard deviation of the amount of lead. (b) Find the percentages of the observations falling in the intervals and . Are these percentages close to those given by the Empirical Rule? Why or why not? Page 4 of 4