Statistics in a Modern World 800
Solutions to Practice Exam 2
-
- (ii) 3 is the typical distance of those values from their mean of 20.4;
.3 would be way too low and 30 or 300 would be way too high
- (iii) skewed right/high outliers
- (i) median less than the mean (outliers pull mean up)
- (i) 1 is the width of the box, which represents the distance between
Q1 and Q3.
-
- (ii) bargraph (for two categorical variables
- (iii) scatterplot (for two measurement variables)
- (iv) multiple boxplots (for values of one measurement variable compared
for five categorical groups)
- (ii) 0,since there shouldn't really be any relationship between a
student's age and how well he or she did on the SATs in high school
(I even did this example in lecture)
-
- z=(120-100)/10=2; the proportion OVER 2 would be the same as the
proportion UNDER -2, or about .025 or .02, according to Table
- slowest (longest) 10% have z=+1.28, observed value = 100 + 1.28(10)
= 112.8
-
- predicted height = 34 + .5(70) = 69
- (iii) stay the same: r is independent of units of measurement
-
- $1.48(178/172)=$1.53
- (iii) $1.60 is $.07 higher than $1.53
-
- (i) long term downward trend: over several months, consumer confidence
decreased
- (iv) irregular cycle: one unusual event (the war) caused a major
irregularity in the graph
- A lot of people got (f) 4 and (g) 5 mixed up; I only took off 5 points instead
of 10 because the difference is subtle.
- (3)
- 6 (heights and salaries both changing over time)
- 7 (especially for small samples, results may be due to chance)
- 2
- 1
- 4 (race/ethnicity is a confounding variable)
- 5 (higher socio-economic bracket is a common cause)
- (d) and (e) are both implausible
-
- (ii) undecided: 18/28=.64 as opposed to 19/58=.33 for decided
- calculate (column total * row total)/table total: 33, 16, 25, 12
- 1.1, 2.3, 1.4, 3.0
- 1.1+2.3+1.4+3.0=7.8
- (ii) 7.8 > 3.84, so we have convincing statistical evidence of a
relationship; however, we cannot conclude causation in either direction
as (iii) or (iv) suggest. Rather, the relationship is confounded by year.
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