Statistics in a Modern World 800
Solutions to Exam 2

1.  
   1. (i) 5 is the typical distance of those values from their mean of 86; all the other numbers are way too high
   2. (ii) fairly symmetric
   3. (iii) about equal to the median
2.  
   1. (iv) multiple boxplots (for values of one measurement variable compared for two categorical groups)
   2. (i) stemplot (for one measurement variables
   3. (iii) scatterplot (for two measurement variables)
   4. (ii) piechart (for one measurement variable)
3. (i) negative; price almost always tends to be lower for older cars (I even did this example in lecture)
4.  
   1. z=(9-7.6)/1.1=1.27; the proportion OVER 1.27 would be the same as the proportion UNDER -1.27, or about .10, according to Table A
   2. lightest 5% have z=-1.64, observed value = 7.6 + (-1.64)(1.1) = 5.8 lbs.
5.  
   1. r is about halfway between 0 and 1, so we'd call the relationship moderate
   2. predicted weight = -106 + 3.7(70) = 153
   3. (i) 60 is outside the range of x-values used to produce the regression line
   4. (iii) stay the same: r is unaffected by assignment of roles for explanatory and response variables
6.  
   1. $2490(172/82.4)=$5,198
   2. (iii) These universities became relatively more expensive (almost double what they would have been in terms of cost of living)
7.  
   1. (i) long term trend
   2. (ii) seasonal components: each year it changes from summer to winter
8. A lot of people got (b) 5 and (g) 4 mixed up; I only took off 5 points instead of 10 because the difference is subtle.
   1. (7)
   2. 5 (the common cause is slower metabolism)
   3. 1
   4. 3
   5. 2
   6. 6
   7. 4 (income is a confounding variable)
9.  
   1. (i) males: 18/34 as opposed to 17/50 for the females
   2. calculate (column total * row total)/table total: 20,29,14,21
   3. .8, .6, 1.1, .8
   4. .8+ .6+ 1.1+ .8=3.3
   5. 3.3 < 3.84, so we do not have convincing statistical evidence of a relationship

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