Applied Statistical Methods 1000
Solutions to Midterm 1

1.  
   1. (ii) Brand B because its stemplot is centered around higher speeds
   2. (iii) both about the same, because stemplots show comparable spreads
   3. (ii) fairly symmetric
   4. For 12 values, report the 1st, av of 3rd & 4th, av of 6th & 7th, av of 9th & 10th, and 12th: 45, 52, 59, 66, 78
   5. Q3+1.5(IQR)=66+1.5(66-52)=87
2.  
   1. 32+1.8(20)=68
   2. 1.8(5)=9
3.  
   1. (iii) side-by-side boxplots (1 quan.var. credits compared for 2 categorical groups on/off campus)
   2. (iii) compare Five Number Summaries, not means and s.d.s, because of skewness/outliers
4.  
   1. (i) piechart (1 categorical variable)
   2. (i) counts or percents
5.  
   1. (iv) scatterplot (2 quan.vars., computer time and age)
   2. (iv) correlation
6.  
   1. 0
   2. 1
   3. 1
   4. .9901
   5. .8413-.0228=.8185
   6. -1.08 (Several students answered -1.8, which is of course wrong. Be careful to read the normal table correctly.
   7. -.44
7.  
   1. 46+3(10)=76
   2. P(X>30)=P(Z>-1.6)=P(Z<+1.6)=.9452
   3. top 10% have .9000 below, so z=+1.28 and x=46+1.28(10)=58.8, which rounds to 59 but I also accepted 58
8.  
   1. overall taxes is the response y, plotted vertically
   2. (i) lower: the scatterplot shows that lower-than-average state&local taxes are associated with lower-than-average overall taxes, which is another way of saying that the relationship is positive
   3. .59 because it is positive and moderate, but you could also take the square root of .345
   4. (ii) the regression line is affected by the assignment of explanatory and response variables but r is not
   5. (ii) the regression equation tells us to (approximately) take state&local tax and add 21
   6. 21.3 + .992(9.9)=31.12
   7. (iii) almost exactly correct
   8. (ii) decrease because it would reduce the tightness of the clustering around a line (we did this in lecture)
   9. (ii)random scatter is what to look for in a residual plot
   10. (i) lower (we learned that correlations based on averages tend to overstate the strength of the relationship compared to that for individuals)
9.  
   1. (i) Design I because a treatment (feeding certain amounts) is imposed
   2. (ii) Design II because observational studies are more susceptible to lurking variables
   3. (i) randomization is one of the basic principles of experimental design
   4. (ii) whether a dog is given reduced feedings or not
   5. (ii) side-by-side boxplots because 1 quantitative variable (lifespan) is compared for 2 categorical groups (regular or reduced feedings)
   6. (iv) large samples reduce variability
   7. (ii) a statistic x-bar

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