HW6 - :r\<.~ Normal Q-Q Plot of JI score 10 i I Observed Value 1 0 I I j CIl!il9 ~1l.2 i 20 10 0 30 40,j p'0 0'a I I II The data appear to be

HW6 - :r<.~ Normal Q-Q Plot of JI score 10 i I Observed...

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I 4.0 3.5 3.0 - 57- 1.0 1,5 2.0 2.5 Observed Value •.. ",." :r?' .•... '.. .' .~' \<, ". . Normal Q-Q Plot of Log of JI score 2 p' Normal Q-Q Plot of JI score , . o ,j ,'a 9' i . I . , . , ! . , 0, 0°, , I .,' 1 ,. I 0- j p' I ~1l . I * i , . CIl .2] !il- I I ·10 0 10 20 30 40 Observed Value The data appear to be right-skewed. (b) A log transformation is one "wayto induce normality. It works here, as can be_'" the normal plot of the transformed data below. 4.27 (a)
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- 61- :..J. 1980 1981 1982 1983 1984 1985 9 10 11 12 7 Month Number 1000 1 2 3 4 Gender Low Income High Income Female 110 90 Male 130 170 Black White Graduated Did not Graduate Graduated Did not graduate 54 .. 89 498 298 197463 878 747 4OO0~-- ~ The proportions of women high earners is 45%, while for men it is about 57%. This would seem to indicate that men tend to earn more than women. However, this difference is driven by the fact that more men pursue engineering degrees which pay higher salaries. This is an example of Simpson's Paradox. There is a dip in sales around October. Otherwise, it stays relatively fiat. ~ alii format makes it easier to d~tect the cycles. (d) The trend is not detectable from the histogram. 3126 is an outlier in either case- (e) The separate run charts is most useful because it allows one to detect the cyclical ••••• (b) Solutions for Section 4.4 4.29 (a) False (b) False (c) True (d) False 4.30 (a) For each type of degree, the proportion of high income earners are the same for DIeD •••• women (40% for liberal arts, and 60% for engineering). 4.31 (a)
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. ~ (b) For blacks, 38% of females graduated compared to 30% of males. For whites, 63% females graduated compared to 54% of males. In both ethnic groups, women higher graduation rate by about 8-9%. (c) Gender Graduated Did not Graduate Female 552 387 Male 10751210 The graduation rate for women is 59% compared to 47% for men. This disparity graduation rates, similar to that found in (b), indicates that graduation rate is independent of gender. 4.32 (a) For each income, the proportions of drug users who played soccer is the same as proportion of drug users who did not play soccer. This indicates that involvemeul; soccer does not affect drug use. (b) Played Drug Use Soccer Yes No Yes 26 274 No 42 258 The proportion of drug users among soccer players is 9%. The proportion of drug among teenagers who did not play soccer is 14%.
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