Statistics in a Modern World 800
Solutions to Exam 2

1.  
   1. (ii) 3 is the typical distance of those values from their mean of 20.4; .3 would be way too low and 30 or 300 would be way too high
   2. (iii) skewed right/high outliers
   3. (i) median less than the mean (outliers pull mean up)
   4. (i) 1 is the width of the box, which represents the distance between Q1 and Q3.
2.  
   1. (ii) bargraph (for two categorical variables
   2. (iii) scatterplot (for two measurement variables)
   3. (iv) multiple boxplots (for values of one measurement variable compared for five categorical groups)
3. (ii) 0,since there shouldn't really be any relationship between a student's age and how well he or she did on the SATs in high school (I even did this example in lecture)
4.  
   1. z=(120-100)/10=2; the proportion OVER 2 would be the same as the proportion UNDER -2, or about .025 or .02, according to Table
   2. slowest (longest) 10% have z=+1.28, observed value = 100 + 1.28(10) = 112.8
5.  
   1. predicted height = 34 + .5(70) = 69
   2. (iii) stay the same: r is independent of units of measurement
6.  
   1. $1.48(178/172)=$1.53
   2. (iii) $1.60 is $.07 higher than $1.53
7.  
   1. (i) long term downward trend: over several months, consumer confidence decreased
   2. (iv) irregular cycle: one unusual event (the war) caused a major irregularity in the graph
8. A lot of people got (f) 4 and (g) 5 mixed up; I only took off 5 points instead of 10 because the difference is subtle.
   1. (3)
   2. 6 (heights and salaries both changing over time)
   3. 7 (especially for small samples, results may be due to chance)
   4. 2
   5. 1
   6. 4 (race/ethnicity is a confounding variable)
   7. 5 (higher socio-economic bracket is a common cause)
9. (d) and (e) are both implausible
10.  
    1. (ii) undecided: 18/28=.64 as opposed to 19/58=.33 for decided
    2. calculate (column total * row total)/table total: 33, 16, 25, 12
    3. 1.1, 2.3, 1.4, 3.0
    4. 1.1+2.3+1.4+3.0=7.8
    5. (ii) 7.8 > 3.84, so we have convincing statistical evidence of a relationship; however, we cannot conclude causation in either direction as (iii) or (iv) suggest. Rather, the relationship is confounded by year.

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