According to a March, 2005 article in the New England Journal of Medicine, “On F

Question

According to a March, 2005 article in the New England Journal of Medicine, “On February 20, 1905,
ruling in Jacobson v. Massachusetts, the U.S. Supreme Court upheld the right of the city of Cambridge,
Massachusetts, to mandate vaccination against smallpox.” The article explains that “by 1902, vaccination
was well established in Massachusetts. Nevertheless, smallpox remained a persistent visitor: [...] in 1901,
there were 773 cases and 97 deaths, and in 1902, 2314 cases and 284 deaths.”
The observed counts are recorded in a two-way table.

a) If there were no significant difference in the death rate between 1901 and 1902, how many of
the 773 cases in Massachusetts in 1901 would we expect to result in death?

b) How does the expected count in (a) compare to the observed count that died in 1901?
Explain your answer fully.

    Died Survived Total 1901 97 676 773 1902 284 2030 2314 Total 381 2706 3087

Explanation / Answer

a) Death rate in 1902 = 284/2314 = 0.123

So, in 1901

deaths expected = d/773 = 0.123

d = 95.08

b) Observed count = 97

So, this tells us that there is not much difference between expected and observed count.

Both are almost same and it can be said that death rate in 1901 and 1902 are almost same.

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