180 Fundamentals of Statistics
e. Reaction times are important for de-
termining whether a runner has false-
started. If the runner’s reaction time
is less than 0.1 second, a false start
is declared. Where would a reaction
time of 0.1 second fall on your
boxplot: as a typical value, a moderate
outlier, or an extreme outlier? Does
this defi nition of a false start seem
reasonable given your data?
f. Is there an association between re-
action time and the order of fi nish?
Calculate descriptive statistics for the
reaction times broken down by order
of fi nish. Pay particular attention to
the mean and the median.
g. Create a boxplot of the reaction times
broken down by order of fi nish. Is
there anything in your descriptive
statistics or boxplots to suggest that
reaction time plays a part in how the
runner fi nishes the race?
h. Save your changes to the workbook
and then write a report summarizing
your observations and calculations.- The Labor Force workbook shows the
change in the percentage of women
in the labor force from 19 cities in the
United States from 1968 to 1972. You
can use these data to gauge the growing
presence of women in the labor force
during this time period.
a. Open the Labor Force workbook from
the Chapter04 folder and save it as
Labor Force Statistics.
b. Calculate the difference between the
1968 and 1972 values, storing the cal-
culations in a new column. Calculate
descriptive statistics for the values in
the Difference column.
c. Calculate the mean of the Difference
value.
d. Create a boxplot of the Difference
value. Are there any outliers present
in the data? Identify which city the
value comes from. What do the data
tell you about the change of the pres-
ence of women in the labor force from
1968 to 1972?
e. Describe the shape of the distribution
of the Difference values. Are the data
positively or negatively skewed or
symmetric? Can you use the mean to
summarize the results from this study?
f. Save your workbook and write a re-
port summarizing your analysis.- In 1970, draft numbers were determined
by lottery. All 366 possible birth dates
were placed in a rotating drum and se-
lected one by one. The fi rst birth date
drawn received a draft number of 1, and
men born on that date were drafted fi rst;
the second birth date received a draft
number of 2; and so forth. Data from the
draft number lottery can be found in the
Draft workbook.
a. Open the Draft workbook from the
Chapter04 folder and save it as Draft
Statistics.
b. Create a box plot of the draft numbers
broken down by month. Also create a
table of counts, means, medians, and
standard deviations. Is there any evi-
dence of a trend in the draft numbers
selected compared to the month?
c. Repeat part b, this time breaking the
numbers down by quarters. Is there
any evidence of a trend between draft
numbers and the year’s quarter?
d. Repeat part b, breaking the draft num-
bers by fi rst half of the year versus
second half. Is the typical draft num-
ber selected for the fi rst half of the
year close in value to the draft num-
ber for birthdays from the second half
of the year?
e. Discuss your results. The draft num-
bers should have no relationship to the
time of the year. Does this appear to be
the case? What effect does breaking the
numbers down into different units of
time have on your conclusion?