Basic Applied Statistics 200
Solutions to Midterm 1

1.  
   1. (iii) 1 quantitative and 1 categorical variable: use side-by-side boxplots
   2. (iii) because of skewness use Five Number Summary
2.  
   1. (iv) 2 quantitative variables: scatterplot
   2. (iv) report correlation
3.  
   1. mean plus or minus 3 sds: 2.7 to 3.3
   2. median=mean=60
   3. z=(2.8-3.0)/.1=-2
4.  
   1. (i) piano lessons (centered around higher numbers)
   2. (iii) both about the same
   3. (ii) no piano lessons
   4. 6.0 is middle of upper 17 values
5.  
   1. 150/360=.4175
   2. 90/240=.375
   3. (iv) neither: they overlap, and are dependent because females are less likely to eat breakfast than students in general
   4. mutually exclusive (and dependent, because knowing someone eats breakfast tells us the probability of not eating breakfast is zero)
   5. 100, 50, 140, 70
   6. 1+2+.7+1.4=5.1
   7. (i) less than .05 since chi-square is greater than 3.84
   8. (ii) because there is a significant difference between men and women, with women skipping breakfast more, but the cause is not established
6.  
   1. age
   2. 1.45 (the slope)
   3. (v) .5 (positive square root of .245)
   4. -25.8+1.45(20)=3.2 thousand dollars
   5. 2-3.2=-1.2 thousand dollars
   6. (iv) mark the point (20, 2) on the scatterplot to see that conforms to the main cluster of points, and could be neither an outlier nor an influential observation
7.  
   1. (i) A because no treatment is imposed
   2. (iii) the type of child who would take piano lessons is a confounding variable which could impact the response (math ability)
   3. (iii) improvement in math ability
8.  
   1. (iii) young men is the best description of the population, since all of the study's participants were aged 18 to 25, so we wouldn't try to generalize to men in other age groups. [A few students answered (iv) sleep-deprived men, but the sleep deprivation seemed to be included in the design in order to diminish daytime wakefulness to the extent that differences between early- and late-to-bed could be detected. I doubt that the researchers only wanted to draw conclusions about sleep-deprived men. However, I only took off 2 out of 5 points for that answer.]
   2. (i) time of going to sleep
   3. (ii) categorical (2 groups: early or late)
   4. (iv) daytime wakefulness
   5. (ii) lack of realism: the setting is very unnatural

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