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

1.What is the test statistic, what decision do you make with a significance level of 0.05, interpret the confidence interval and what conclusion do you make?

Answer 1

Given :

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:

Pro1 Pro 2

0.08465608 0.21118012

From the above output :

a) Test statistic : = 13.88

b) Dicision :

Since P-value is less than significance level 0.05, we Reject the null hypothesis.

Reject the null hypothesis.

c) We are 95% confident that the proportion is between -0.18620923 and -0.06683885.

d) Conclusion : There is sufficient evidence to conclude that The Bacille Calmette Guerin (BCG) vaccine is said to provide decades of protection against tuberculosis (TB).