Transcript Concept Quiz - University of Virginia

Exam 2 Preparation
Concept Quiz
Statistics in Business
1. To investigate an apparent relationship between 2
categorical variables, Al correctly implements a chi-squared
independence test. Bo doubled all the counts in Al’s
contingency table. How will Al and Bo’s calculated chi-squared
stats compare?
A.
B.
C.
D.
Al’s will be higher than Bo’s
Bo’s will be higher than Al’s
They will be equal
One cannot know without the data.
Doubling all the counts exactly doubles the calculated chi-squared
statistics…resulting in a lower p-value. Distance = (O-E)^2/E.
2. The mean of a difference of 2 random variables (X1X2) is the difference in the means (μ1-μ2). The variance
of the difference (if X1 and X2 are independent) is…
A.
B.
C.
D.
The difference in the variances (σ12 – σ22)
The sum of the variances (σ12 + σ22)
The average of the variances (σ12 + σ22)/2
Depends on whether the random variables are
normally distributed.
The difference is more variable (less predictable), the more variable (less
predictable) is X2.
3. Al gathered n=10 observations of a numerically-scaled
variable, and Bo separately gathered n=40. Remarkably (it’s
my question) they got identical sample means and sample
standard deviations. How do the widths of their 95%
confidence intervals for the mean compare? AtoE
A.
B.
C.
D.
E.
Al’s will be ½ the width of Bo’s
Al’s will be < ½ the width of Bo’s
Bo’s will be ½ the width of Al’s
Bo’s will be < ½ the width of Al’s.
It depends on the sample mean and standard
deviation.
Bo’s “standard error” (s/ 𝑛) will be ½ Al’s…..AND…Bo’s t.inv.2t(0.05,39) will be
smaller than Al’s t.inv.2t(0.05,9). This latter fact makes the width of Bo’s Confidence
inteval < ½ the width of Al’s.
4. Al did a one-tailed test. Bo was lazy (he didn’t want
to take the time to specify a 1T alternative), and did a
2T test. If they apply their tests to the same data, how
will their p-values compare?
A.
B.
C.
D.
Al’s will be always be lower than Bo’s.
Al’s will always be higher than Bo’s.
They will always be equal.
One cannot know without the data.
If Al “guesses right” with his Ha, then his p-value will be ½ of Bo’s. If Al “guesses
wrong” it is possible his p-value will be higher. (Imagine if Al thought men were
shorter, on average, than women.)
5. Al used a paired t-test because the data came from n
matched pairs. Bo loved ANOVA single factor…and
applied it to the two-column data set. Which statement
best summarizes these two approaches. A-F
A.
B.
C.
D.
E.
F.
Neither test is valid.
Al’s is valid, Bo’s is not.
Bo’s is valid, Al’s is not.
Both are valid, and Al’s is probably better.
Both are valid, and Bo’s is probably better.
Both are valid, and will give identical p-values.
Bo’s is equivalent to a two-sample t-test of means. It is valid. But when the data are
paired, the paired test is usually better (gives a lower p-value).