Chapter 6 Statistical Inference 269
d. Create a boxplot of the Beds variable
for the different locations. Do the plot
and the descriptive statistics give you
any help in determining whether to
use a pooled or a nonpooled test?
Explain your answer.
e. Apply the Mann-Whitney test to the
data. What are your hypotheses? What
is your conclusion? Include informa-
tion on the p value and confi dence
interval in your discussion.
f. Save your changes to the workbook
and then write a report summarizing
your results. Do your conclusions
differ on the basis of which test you
apply? Which statistical test would
you report and why?
- Return to the nursing home data from
this chapter. This time you’ve been
asked to explore whether rural homes
are used at a lower rate than nonrural
homes after adjusting for the differing
size of the homes.
a. Open the Nursing Home workbook
from the Chapter06 folder and save it
as Nursing Home Usage Rates.
b. Create a new variable named
Days_Beds equal to the ratio of the
total number of patient days to the
number of beds in the home. Format
the data to display three decimal
places.
c. Compare the average value of the
Days_Beds variable for rural and
nonrural homes. What are your
hypotheses? What test or tests
will you use to evaluate your null
hypothesis?
d. Create a boxplot of the Days_Beds
variable for the two locations.
e. Save your changes to the workbook
and then write a report summarizing
your results, including any descrip-
tive statistics, p values, and confi -
dence intervals you created during
your analysis. Is there evidence to
suggest that rural homes are being
utilized at a lower rate?
- Draft numbers from the Vietnam War
have been recorded for you. (See the
Chapter 4 exercises for a discussion of
the draft lottery.) It’s been claimed that
people whose birthday fell in the second
half of the year had lower draft numbers
and therefore were more likely to be
drafted. Explore this claim.
a. Open the Draft workbook from the
Chapter06 folder and save it as Draft
Number Analysis.
b. Write down the null and alternative
hypotheses for your study.
c. Create a two-sample t test to analyze
your hypotheses. Do you use a pooled
or an unpooled test? Which type of
test does the distribution of the data
support?
d. Create a histogram of the distribution
of draft numbers broken down by
whether the number was assigned in
the fi rst half of the year or the second.
What probability distribution does the
data resemble? What property of the
t statistic allows you still to apply
the t test to your data?
e. Calculate a 95% confi dence interval
for the average draft number for
people born in the fi rst half of the
year and then for people born in the
second half of the year. (Hint: You can
do this using StatPlus’s 1-sample t test
command, specifying the Half variable
as the BY variable.)
f. Save your workbook and write a re-
port summarizing your results. What
is the mean difference in draft num-
ber between people born in the fi rst
half of the year and those born in the
second half? Is this a signifi cant dif-
ference? What are the practical ramifi -
cations of your conclusions?
