Applied Statistical Methods 1000
Solutions to Midterm 1
-
- (ii) Brand B because its stemplot is centered around higher speeds
- (iii) both about the same, because stemplots show comparable spreads
- (ii) fairly symmetric
- 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
- Q3+1.5(IQR)=66+1.5(66-52)=87
-
- 32+1.8(20)=68
- 1.8(5)=9
-
- (iii) side-by-side boxplots (1 quan.var. credits compared for 2
categorical groups on/off campus)
- (iii) compare Five Number Summaries, not means and s.d.s, because
of skewness/outliers
-
- (i) piechart (1 categorical variable)
- (i) counts or percents
-
- (iv) scatterplot (2 quan.vars., computer time and age)
- (iv) correlation
-
- 0
- 1
- 1
- .9901
- .8413-.0228=.8185
- -1.08 (Several students answered -1.8, which is of course wrong. Be
careful to read the normal table correctly.
- -.44
-
- 46+3(10)=76
- P(X>30)=P(Z>-1.6)=P(Z<+1.6)=.9452
- 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
-
- overall taxes is the response y, plotted vertically
- (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
- .59 because it is positive and moderate, but you could also take the
square root of .345
- (ii) the regression line is affected by the assignment of explanatory
and response variables but r is not
- (ii) the regression equation tells us to (approximately) take state&local
tax and add 21
- 21.3 + .992(9.9)=31.12
- (iii) almost exactly correct
- (ii) decrease because it would reduce the tightness of the clustering
around a line (we did this in lecture)
- (ii)random scatter is what to look for in a residual plot
- (i) lower (we learned that correlations based on averages tend to
overstate the strength of the relationship compared to that for individuals)
-
- (i) Design I because a treatment (feeding certain amounts) is imposed
- (ii) Design II because observational studies are more susceptible to
lurking variables
- (i) randomization is one of the basic principles of experimental design
- (ii) whether a dog is given reduced feedings or not
- (ii) side-by-side boxplots because 1 quantitative variable (lifespan)
is compared for 2 categorical groups (regular or reduced feedings)
- (iv) large samples reduce variability
- (ii) a statistic x-bar
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