270 Fundamentals of Statistics
- The Junior College workbook contains
salary information for faculty at a col-
lege. The female faculty members claim
that they are underpaid relative to their
male counterparts. Investigate their
claim.
a. Open the Junior College workbook
from the Chapter06 folder and save it
as Junior College Salary Analysis.
b. Write down your null and alternative
hypotheses. What is the signifi cance
level for this test?
c. Perform a two-sample t test on the sal-
ary data broken down by gender. Does
it make any difference whether you
perform a pooled or an unpooled test?
Do the data suggest that there is a
salary difference between male and
female faculty members? Create his-
tograms of the distribution of salary
data for male and female instructors.
d. Redo the two-sample t test, this time
breaking down the analysis of sal-
ary versus gender by the Rank_Hired
variable. Are there signifi cant gender
differences in terms of salary for the
various employee ranks? (Note: Some
combinations of gender and rank hired
will have sample sizes of 0. This will
result in Excel displaying a #VALUE!
result in the workbook. You can ignore
these employee ranks because there
are no values to investigate.)
e. Save your workbook and summarize
your conclusions. Is there evidence
that the college has underpaid its
female faculty? If so, does this differ-
ence exist for all teaching ranks? Why
does this study not prove sexual dis-
crimination? What factors have been
ignored? - The Big Ten workbook has graduation
information on Big Ten schools. (See
Chapter 3 for a discussion of this data
set.) Explore whether there is a
difference in the graduation rates be-
tween white male athletes and white
female athletes.
a. Open the Big Ten workbook from the
Chapter06 folder and save it as Big
Ten Graduation Analysis.
b. State your null and alternative
hypotheses.
c. Perform a paired t test of the white
male and white female athlete gradu-
ation rates. Is there statistically sig-
nifi cant evidence of a difference in
the graduation rates? What is a 95%
confi dence interval for the differ-
ence? What is the 90% confi dence
interval?
d. Redo the analysis using the Wilcoxon
Signed Rank test and the Sign test.
e. Why is this an example of paired
data?
f. Save your workbook and write a re-
port summarizing your conclusions.
Can you apply your results to univer-
sities in general? Defend your answer.- The Mortgage workbook contains infor-
mation on refusal rates from 20 lending
institutions broken down by race and
income status from the late 1980s. It was
claimed in reports to Congress that lend-
ing institutions had signifi cantly higher
refusal rates for minorities. Examine the
statistical basis for that claim.
a. Open the Mortgage workbook from
the Chapter06 folder and save it as
Mortgage Refusal Analysis.
b. State your null and alternative
hypotheses.
c. Apply a paired t test to the refusal
rates for minority and white appli-
cants. What is the 95% confi dence
interval for the difference in refusal
rates? What is the p value for the test?
d. Create a histogram and normal prob-
ability plot of the difference in refusal
rate. Do the data appear normal?