Basic Applied Statistics 200
Solutions to Midterm 1 at 12:00
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- stem 0 followed by 0 0 0 1 1
stem 0 followed by 2 3 3 3 3 3
stem 0 followed by 4 4 4 5 5 5 5
stem 0 followed by 6 6 7
stem 0 followed by no leaves
stem 1 followed by no leaves
stem 1 followed by no leaves
stem 1 followed by 5 5
- median is 4 (12th value)
- Q1 is 2 (6th value)
- (i) mean is higher because of high outliers
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- (ii) (vertical positions of boxplots are comparable)
- (ii) (spreads of boxplots are comparable)
- (iii) (there will be a few unusually old students)
- (iii) 20.5: because of high outliers, mean should be greater than
median 19.46
- (iii) 4: because of outliers, it must be larger than males' s.d. of
1.509, but 10 would be too large
- (i)
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- .9699
- .7291-.6591=.0700
- the mean of z is zero
- .1400 are above, or .8600 are below, 1.08
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- 42 plus or minus 3(2): between 36 and 48
- x < 300 means z < -1.74; proportion is .0409
- x >45 means z >(45-42)/2 = 1.5; same as proportion with z < -1.5,
or .0668
- bottom 10% have z= -1.28, so x=42-1.28(2) = 39.44
-
- age
- (i) positive because points slope up
- (ii) moderate/weak because cluster isn't that tight; also, from
Rsq you can find r=.70, not that close to 1 and probably inflated by the
influential observation in the upper right corner (in lecture we agreed that
we'd call it strong if r was more than .75)
- (v) +.70 (in fact, you can take the positive square root of Rsq=.515)
- (ii) same (r unaffected by change in units of measurement)
- -19168 + 1157(20) = 3972, round to 4000
- 6000 - 4000 = 2000
- (ii) 33 (its residual is farthest from 0
- 33,28.8,48.3 (marked X by MINITAB)
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- 6/28 = .21
- 24/94=.26
- 9/94 = .06
- females: 22/70 = .31 higher than males 6/24 = .25
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- Student A (50 people instead of just 10)
- Student C (used identical-looking bottles)
- 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...
-
- (ii) observational studies; neither weight nor socio-economic status
are easy treatments to impose
- (i) explanatory; suggesting obesity causes low socio-economic status
- (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.
- (i) volunteer bias. Their willingness to lose weight could easily
pre-dispose them to improvement on other fronts
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