Basic Applied Statistics 200
Solutions to Midterm 1 at 10:00

1.  
   1. stem 0 followed by 0 0 1 2 2 2 2 2 3 4 4
      stem 0 followed by 7 7 8
      stem 1 followed by 0
      stem 1 followed by no leaves
      stem 2 followed by no leaves
      stem 2 followed by 5
      stem 3 followed by 3
   2. median is 3 (9th value)
   3. Q1 is 2 (between 4th and 5th values)
   4. (i) mean is higher because of high outliers
2.  
   1. (ii) (vertical positions of boxplots are comparable)
   2. (ii) (spreads of boxplots are comparable)
   3. (iii) (there will be a few unusually old students)
   4. (iii) 20.5: because of high outliers, mean should be greater than median 19.75
   5. (iii) 3: because of outliers, it must be larger than males' s.d. of 1.301, but 10 would be too large
   6. (i)
3.  
   1. .9699
   2. .7291-.6591=.0700
   3. the mean of z is zero
   4. .1400 are above, or .8600 are below, 1.08
4.  
   1. 42 plus or minus 3(2): between 36 and 48
   2. x < 300 means z < -1.74; proportion is .0409
   3. x >45 means z >(45-42)/2 = 1.5; same as proportion with z < -1.5, or .0668
   4. bottom 10% have z= -1.28, so x=42-1.28(2) = 39.44
5.  
   1. age
   2. (i) positive because points slope up
   3. (ii) moderate/weak because cluster isn't that tight; also, from Rsq you can find r=.55, not too close to 1
   4. (v) +.55 (in fact, you can take the positive square root of Rsq=.309)
   5. (ii) same (r unaffected by change in units of measurement)
   6. -19413 + 1171(20) = 4007, round to 4000
   7. 6000 - 4000 = 2000
   8. (i) 23 (its residual is farthest from 0
   9. 39.4 (marked X by MINITAB)
6.  
   1. 4/13 = .31
   2. 17/72 = .24
   3. 4/72 = .06
   4. males: 4/17 = .24 higher than females 9/55 = .16
7.  
   1. Student A (50 people instead of just 10)
   2. Student C (used identical-looking bottles)
   3. Student B (randomization is the way to go; Student C might permit bias. For example, on a hot day, the first 5 might get a colder drink, which they think tastes better...
8.  
   1. (ii) observational studies; neither weight nor socio-economic status are easy treatments to impose
   2. (i) explanatory; suggesting obesity causes low socio-economic status
   3. (iii) lurking variable: region has an affect on the relationship between obesity and low socio-economic status, but was not mentioned in the original statement of results.
   4. (i) volunteer bias. Their willingness to lose weight could easily pre-dispose them to improvement on other fronts

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