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Unformatted text preview: STAT 350 Assignment 1 Solutions (60pts) 11. (a) (4) The following stem-and-leaf display was constructed using MINITAB : (Its OK if the students dont include the first column in the following figure, i.e. dont cut off any point if column of 12 23 (10) 14 7 5 is not included but all the others are correct) Stem-and-leaf of C1 N = 47 Leaf Unit = 100 12 0 123334555599 23 1 00122234688 (10) 2 1112344477 14 3 0113338 7 4 37 5 5 23778 For features of the display, give full credit if they make correct descriptions for number of peaks (should be unimodal here) and the direction of skewness. A typical data value is somewhere in the low 2000's. The display almost unimodal (the stem at 5 would be considered a mode, the stem at 0 another) and has a positive skew. 14. (3) For the first question, its OK if they havent mentioned the pattern of the values, give full credit as long as they describe the peak (unimodal) and direction of skewness correctly. A very large percentage of the data values are greater than 0, which indicates that most, but not all, runners do slow down at the end of the race. The histogram is also positively skewed, which means that some runners slow down a lot compared to the others. And its unimodal. (1 pt) A typical value for this data would be in the neighborhood of 200 seconds. (1 pt) The proportion of the runners who ran the last 5 km faster than they did the first 5 km is very small, about 1% or so. (1 pt) 18. (a) (1) The classes overlap. For example, the classes 20-30 and 30-40 both contain the number 30, which happens to coincide with one of the data values, so it would not be clear which class to put this observation in. (b) (2) The histogram appears below: 1 0 0 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 0 3 0 2 0 1 0 C o n c e n tr a tio n ( p p m ) R e la tive fr e q u e n c y (c) (2) The proportion of the concentration values that are less than 50 is 17/50 = .34, or 34%. The proportion of concentrations that are at least 60 is 27/50 = .54, or 54%. 19. (a) (1) The density curve forms a rectangle over the interval [4, 6]. For this reason, uniform densities are also called rectangular densities by some authors. Areas under uniform densities are easy to find (i.e., no calculus is needed) since they are just areas of rectangles. For example, the total area under this density curve is ) 4 6 ( 2 1 = 1....
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This note was uploaded on 09/21/2011 for the course STAT 350 taught by Professor Staff during the Spring '08 term at Purdue University-West Lafayette.
- Spring '08