Chapter 6 Statistical Inference 273
the difference between the 1980 and
1984 voting patterns.
a. Open the Voting workbook from the
Chapter06 folder and save it as Voting
Analysis.
b. Do a paired t test for the voting per-
centage, broken down by region. Sum-
marize your fi ndings for all regions as
well.
c. For which regions was there a signifi -
cant change in the voting percentage?
For which regions was there no sig-
nifi cant change? What was the over-
all change in the voting percentage
across all regions?
d. Save your changes to the workbook
and write a report summarizing your
fi ndings, including your descriptive
statistics, p values, and confi dence
intervals.
- The Calculus workbook shows the fi rst
semester calculus scores for male and
female students. Analyze the data set to
determine whether there is a signifi cant
difference between the two groups.
a. Open the Calculus workbook from
the Chapter06 folder and save it as
Calculus Scores Analysis.
b. State your null and alternative
hypotheses.
c. Perform a two-sample t test on the calc
values using a pooled estimate of the
variance. What is the 95% confi dence
interval of the difference between the
two groups? Do you reject or accept
the null hypothesis? At what p value?
d. Chart the distribution of the calc
values for the two groups. Do the
distributions appear normal? What
property of exam scores makes it un-
likely that these exam scores follow
the normal distribution? (Hint: Test
scores are usually constrained to fall
between 0 and 100.) What property of
the t distribution might allow you to
use the t test anyway?
e. Repeat your analysis using the Mann-
Whitney non-parametric test.
f. Save your changes to the workbook
and write a report summarizing your
fi ndings and stating your conclusions.
- The Reaction workbook contains infor-
mation on reaction times and race times,
recorded by sprinters running in the fi rst
three rounds of the 100-meter dash at the
1996 Summer Olympics. You’re asked to
determine whether there is evidence that
the sprinter’s reaction time (the time it
takes for the sprinter to leave the starting
block at the sound of the gun) changes as
he advances in the competition.
a. Open the Reaction workbook from
the Chapter06 folder and save it as
Reaction Time Analysis.
b. Use the paired t test and analyze the
differences between the following
variables: React 1 vs. React 2, React 1
vs. React 3, and React 2 vs. React 3.
Calculate the 95% confi dence inter-
val for each difference pair, and test
for statistical signifi cance at the 5%
level. Are there any pairs of rounds in
which there is a signifi cant difference
in the average reaction time?
c. Create three new columns in the
Reaction Times worksheet displaying
the three paired differences, and then
create three normal probability plots
of those differences. Does the distri-
bution of the paired differences fol-
low a normal distribution?
d. Redo the analysis, this time using the
Wilcoxon Sign Rank test. Do your
conclusions change when you use
this test?
e. Save your changes to the workbook
and write a report summarizing your
results and give your conclusions.
