09 Concept Quiz
Statistics in Business
Part 1
QUESTION 1
•
In an effort to be more global, Bo multiplied each
student’s height by 2.54 and divided by 100 to
convert to meters. Al used the original heights
expressed in inches. Which statement is least
true?
A.
B.
C.
D.
Bo’s sample mean height will be 0.0254 times Al’s.
Bo’s sample standard deviation will be 0.0254 times Al’s.
Bo’s sample range will be 0.0254 times Al’s.
Trick question…A,B,C are all true.
Multiplying by a constant multiplies the sample mean, standard
deviation, range, mode, and median by that same constant. The
sample variance is multiplied by the constant squared.
QUESTION 2.
•
There were n=100 values of the continuous variable X in
the database. Al calculated the sample mean of the first
40 values. Bo calculated the sample mean of the last 60
values. Cy calculated the sample mean of all 100 values.
Which of the following statements is most true?
A. Based on sample sizes, Al’s sample mean will be smallest. Bo’s
will be in between. Cy’s will be largest.
B. Cy’s average will be in between Al’s and Bo’s.
C. It is impossible to know ahead of time how the averages will
come out.
The sample mean of all 100 will be a weighted average of the sample means of
the smaller groups—and therefore must be in between the averages of the two
smaller groups. Try it and see.
QUESTION 3
•
A class of 100 had 40 athletes (variable A is 1 for
athlete, 0 otherwise) and 60 males (variable M is 1
for male, 0 otherwise). How will the sample
standard deviations of these two variables
compare?
A.
B.
C.
D.
The sample standard deviation for A will be higher.
The sample standard deviation for M will be higher.
The sample standard deviations will be equal.
It is not possible to know how the sample standard
deviations will come out.
The sample standard deviation (and variance) measures expected distance from
the sample mean. They will be equal in this case because the data are mirror
images of each other.
QUESTION 4
•
O
87
Right
Wrong 62
149
Total
E
74.5
74.5
149
Having slept through the classes on Binomial
and Normal, Di used a chi-squared GOF test on
the Wunderdog Data. Recall that the p-value
calculated using 1-normdist(87,74.5,6.1,true)
was 0.0203.
A.
B.
C.
D.
Di’s p-value will be > 0.0203
Di’s p-value will be = 0.0203
Di’s p-value will be < 0.0203
It is impossible to know without running numbers.
There are two equivalent ways to test H0: pright=pwrong=1/2. The GOF test is “2sided” and gives a calculated p-value of 0.0406. Try it and see for yourself.
QUESTION 5
•
Thinking that more data are always better, Bo
copied the entire database and appended it to the
original database. Al calculated descriptive
statistics using the original, and Bo used the
expanded database. Which is not true?
A. Bo’s counts will be twice Al’s.
B. Bo’s sample means will equal Al’s sample means.
C. Bo’s sample standard deviations will be very close to
Al’s.
D. Trick question, all the above are true.
The sample standard deviation is the square root of the average squared distances
from the sample mean. Doubling the number of those distances will not change the
average squared distance. Bo’s sample standard deviation won’t be much different
from Al’s. More data doesn’t imply more variability in those data.
QUESTION 6
•
In the problem of points, we figured out that the
person ahead 2 to 1 in a best of five series should
get .75 of the prize. Suppose a team is ahead 3
games to 2 in a best of seven series. If the series
is canceled, the team ahead should get…
A.
B.
C.
D.
More than 0.75
The same 0.75 of the prize
Less than 0.75
A parade in New York City.
In both cases, the leader needs to win at least one of three remaining games.
QUESTION 7
•
The GOF test for the normality of lorex fill
amounts gave a calculated chi-squared
statistic of 7.577 and p-value of 0.371. Bo
doubled both the O and E counts and
recalculated the chi-squared statistic and
p-value. Which is true?
A.
B.
C.
D.
O
E
Distances
6
10
17
33
36
14
16
12
6.13
10.38
19.12
27.04
29.37
24.51
15.71
11.73
0.003
0.014
0.235
1.313
1.494
4.506
0.005
0.006
Calc chisq
pvalue
Bo’s chi-sq will be higher and pvalue lower
Bo’s chi-sq will be lower and pvalue higher
Bo’s chi-sq and pvalue will be the same.
Impossible to tell ahead of time.
Doubling the sample size doubles each distance. Any O/E gap is
less likely due to chance the bigger the sample size.
7.577
0.371