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quiz3_key - NAME Stat 205 Quiz 3 The following table...

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Unformatted text preview: NAME: Stat 205 Quiz 3 The following table cross-classiﬁes 6549 subjects living in Massachusetts according to health risk (stressed or not stressed) and income (low, medium, or high): Stress level Stressed Not Stressed Total Income Low Medium High 526 274 216 1954 1680 1899 2480 1954 2115 Total 1016 5533 6549 This is turned into a table of probabilities by dividing each cell by the total sample size 6549: Stress level Stressed Not Stressed Total Income Low Medium High 0.08 0.04 0.03 0.30 0.26 0.29 0.38 0.30 0.32 Total 0.15 0.85 1.00 Let S be the event that a randomly selected individual is stressed and let L be the event that a randomly selected individual has low income. Use the table to answer the following questions. 1. (2 points) What is the probability that someone in this study is stressed, P (S )? Answer: 1016 = 0.15 (ﬁrst table) or 0.15 (second table). 6549 2. (2 points) What is the probability that someone with a low income in this study is stressed, P (S |L)? Answer: 526 0.08 = 0.21 (ﬁrst table) or = 0.21 (second table). 2480 0.38 3. (2 points) What is the probability that someone in this study is stressed or has low income, P (S ∪ L)? Answer: 526 + 274 + 216 + 1954 = 0.45 (ﬁrst table) or 0.08 + 0.04 + 0.04 + 0.30 (second table). 6549 You can also use the formula P (S or L) = = = = P (stressed or low income) P (stressed) + P (low income) − P (stressed and low income) 0.15 + 0.38 − 0.08 0.45. 4. (2 points) Use (1) and (3) to determine whether being stressed and having low income are independent. Answer: P (stressed|low income) = P (stressed) so they are dependent, i.e. not independent. 5. (2 Extra credit points) Is having low income independent of having high income? Why or why not? Answer: They are disjoint events, so they are dependent. If you have low income, you cannot have high income (P (low income|high income) = 0), one event tells you everything about the other. Formally, P (low income|high income) = P (low income) implies dependence. ...
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This note was uploaded on 12/14/2011 for the course STAT 205 taught by Professor Hendrix during the Fall '09 term at South Carolina.

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quiz3_key - NAME Stat 205 Quiz 3 The following table...

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