HW 5 Exemplars

# HW 5 Exemplars - Exemplars for the Homework Problems from...

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Exemplars for the Homework Problems from Chapter 4 Required for Homework #5 Problems 11, 18, and 50 11. Frequency cross-tabulation: Region Yes No Total NE 148 52 200 MW 162 54 216 S 296 74 370 W 252 48 300 Total 858 228 1086 Probability table (using relative frequency concept): Regio n Yes No Total NE 0.14 0.05 0.18 MW 0.15 0.05 0.20 S 0.27 0.07 0.34 W 0.23 0.04 0.28 Total 0.79 0.21 1.00 a. Total drivers = 858 + 228 = 1086 P (Seatbelt) = 858 .79 1086 = or 79% b. Seat belt use probability WAS 0.75 (for previous year). Hoped seat belt use probability will be 0.78. Seat belt use probability IS 0.75 (for current year). Yes, the overall probability is up from 0.75 to 0.79, or 4%, in one year. Thus 0.79 does exceed previous year and his 0.78 expectation. c. Probability of seat belt user from each region: Northeast 148 .74 200 = HW 5 exemplars 1 © Harvey Singer 2010

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Midwest 162 .75 216 = South 296 .80 370 = West 252 .84 300 = The West with 0.84 shows the highest probability of use. d. Probability of selection by region: Northeast 200 .184 1086 = Midwest 216 .200 1086 = South 370 .340 1086 = West 300 .286 1086 = South has the highest probability (.34) and West was second (0.286). e. Nationally, the probability of seat belt use is 858/1086 = 0.7900, as in part a. But from part b, see that regionally, some probabilities are higher (NE and MW) and some are lower (S and W) than 0.79. So, probabilities are not distributed evenly by region. Also, as an example of independence: What is the chance that 2 people selected at random are both from the northeast (NE)? Want Prob(2 from NE) = Prob(NE and NE) HW 5 exemplars 2 © Harvey Singer 2010
Assume that the two people don’t know each other (they are total strangers). Then they are independent of each other. Then Prob(2 from NE) = Prob(NE) × Prob(NE) = 0.18 × 0.18 = 0.0324 Result: There is a 3.24% chance that any two randomly selected people will both be from the northeast (NE). HW 5 exemplars 3 © Harvey Singer 2010

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18. Population is all families. Variable of interest is how often families eat at home as a family, measured as the number of family meals per week.
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