Basic Applied Statistics 200
Solutions to Midterm 1 at 11:00

1.  
   1. (iii) 5 number summary values (and boxplots) are higher for males (except for one female high outlier)
   2. (iii) the box is taller for males, and IQR is 6, as opposed to 2 for females
   3. (iii) the 3 high outliers are obvious
   4. (iii) for right skewness/high outliers, mean > median
   5. Five Number Summary is better in the case of skewness and/or outliers
2. 1. stems should be 0 (leaves 122334), 0 (leaf 5), 1 (leaves 000), 1 (leaf 5), 2 (leaves 00)
   2. no: the shape is skewed right
   3. 5 (the 7th value of 13)
   4. (ii) 6 [the numbers look to be about 6 away from their mean, typically]
3.  
   1. 1-.6700=.3300, or by symmetry look up z=-.44
   2. .0228-.0013=.0215
   3. -1.64 or -1.65
4. 1. 500 plus or minus 2(115): between 270 and 730
   2. x < 300 means z < -1.74; proportion is .0409
   3. the mean, 500
   4. cut-off for top 15% same as for bottom 85%: z= +1.04, so x=500+1.04(115) =619.6
5.  
   1. heights
   2. (i) positive (iii) linear (v) strong
   3. positive square root of .830 (Rsquared) is .91
   4. .91 (r unaffected by change in units of measurement)
   5. -21.7 + (0.455)70 = 10
   6. 9.5 - 10 = -.5
   7. (iii) [the output indicates both R and X for this observation]
   8. (i) without that student, the points exhibit looser clustering
   9. (i) a random residual plot indicates a straight line alone is a good summary
6. 1. males: 12/20 = .6 vs 21/42 = .5
   2. 21/29 = .72
   3. 21/62 = .34
7. 1. (i) an observational study; imposing a treatment of meals would be unrealistic
   2. (i)
   3. (iii)
8. 1. Pitt students constitute the population
   2. 3 times 2 = 6
9. 1. (ii) treatment is chewing, so control should be not chewing
   2. (i) randomness avoids bias
   3. (i) adequate replication is another principle of good design

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