Question

(Most questions refer to this passge) 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". Using the R-code tb=matrix(c(i,ii,iii, iv), nrow=2), fill in the blanks: QUESTION 1: What is the value of 'i? QUESTION 2: What is the value of "H"? QUESTION 3: What is the value of "ii"? QUESTION 4: What is the value of "iv"? QUESTION 5: If the researcher is trying to prove that the vaccination lowers the chances of getting infected with TB, what would be the null hypothesis? QUESTION 6: If the researcher is trying to prove that the vaccination lowers the chances of getting infected with TB, what would be the alternative hypothesis? QUESTION 7: If p1 and p2 are both close to 1, what type of comparison should be used? QUESTION 8: Which of the following is the correct way to perform the difference in proportions test in R? QUESTION 9: The following is the R- Output: data: (for questions 9-12) f(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? QUESTION 10: M What decision do you make with a significance level of 0.05? QUESTION 11: What conclusion do you make? QUESTION 12: M Interpret the confidence interval

Answer 1

	Vaccinated	Not Vaccinated
TB	16	68
No TB	173	254

1. i = 16

2. ii = 68

3. iii = 173

4. iv = 254

5. Ho : The vaccination is not significant in reducing the chances of TB or

6. H1: The vaccination is significant in reducing the chances of TB or

7. We can use difference or ratio to compare them.

8. chi-square test is most appropriate to see the association between TB and vaccine.

9. X-squared = 13.88 is the test statistic

10. p-value = 0.0001949 < 0.05 (we reject Ho) or

11. can conclude that The vaccination is significant in reducing the chances of TB or

12. We are 95% confident that the population difference in proportion of people with TB vaccinated and not avccinated ranges from -0.067 to -0.186

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