Question

The Bacille Calmette Guerin (BCG) vaccine is said to provide decades of protection against tuberculosis (TB). To test this theory, a researcher takes a random sample of 189 individuals who have been vaccinated with BCG and 322 individuals who have not been vaccinated with BCG. Out of those who were vaccinated, 16 became infected with TB. Out of those who were not vaccinated, 68 were infected with TB.  The researcher is testing  p₁ = “the proportion of TB infected individuals who were vaccinated” vs.  p₂ = “the proportion of TB infected individuals who were not vaccinated”.   The following is the R-Output:

data: t(tb)

X-squared = 13.88, df = 1, p-value = 0.0001949

alternative hypothesis: two.sided

95 percent confidence interval:

-0.18620923 -0.06683885

sample estimates:

prop 1 prop 2

0.08465608 0.21118012

What is the test statistic?

Answer 1

From the given output:

Test statistic

$= \chi^2$

= 13.88