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PSTAT 120B
Instructions: the exam is open book and open note and has no strict time limit. You can use any
course materials, and you are allowed to cite results in the book, lecture notes, and past homeworks
and quizzes without repeating proofs or derivations. Your work should be your own – please do not
consult or work with anyone else.
1
Background
The CDC’s National Center for Health Statistics website publishes state-level data on heart disease
mortality by year. The CDC comments, “Although adjusted for differences in age-distribution
and population size, rankings by state do not take into account other state specific population
characteristics that may affect the level of mortality. When the number of deaths is small, rankings
by state may be unreliable due to instability in death rates.” For this exam, you’ll investigate the
change in heart disease mortality rates over a ten-year period using tools you’ve learned in the class
based on a sample of 20 randomly selected states.
Below, Figure 1 shows the distributions of mortality rates for 20 randomly selected U.S. states
in 2005 and 2015, as well as a stacked bar chart of the rates for individual states. In the bar chart,
the height of the blue bar shows the rate in 2015, and the height of the red bar shows the rate in
2005.
Figure 1: Top, histograms of age-adjusted heart disease mortality rates (deaths per 100,000) for
each of 20 randomly selected states in 2005 and in 2015; bottom, stacked bar chart of rates for each
state by year.
2
Exam 2 PSTAT 120B, Fall 2021
Next, Figure 2 shows a histogram and bar chart of the differences by state in mortality rates
between the two years for the selected states.
Figure 2: Left, bar chart of change in age-adjusted heart disease mortality rates (deaths per 100,000)
by state between 2005 and 2015; right, histogram of differences by state between the two years.
The differences are calculated as (2015 rate − 2005 rate).
Finally, the summary statistics for the age-adjusted mortality rates in each year separately
(Figure 1) and for the change in rates (Figure 2) are shown below in Table 1.
Mean Standard deviation
2005 204.00 31.70
2015 162.27 22.29