#### 20.*Here is a correct table of conditional proportions. Explain what we are conditioning the**proportions on in this table and interpret the statistics about the sample of volunteers.*```{r}prop.table(vaccine, 1)```***#### 21.*Here is the code to obtain a 95% confidence interval for this study.*```{r}prop.test(x = c(90, 140), n = c(100, 200))```*Interpret the confidence interval for the difference in proportions in this study.*

Medical researchers compared the efficacy of two vaccines with 300 volunteers. One thir d of the volunteers (100 people) were randomly assigned to Vaccine "A" and two thirds (200 peop le) were assigned to Vaccine "B". Four weeks after receiving the vaccine, an antibody test was giv en to every participants. Participants were assigned to "not sufficient" and "sufficient" categori es depending on whether there were enough antibodies present to successfully fight the vir us. A graph of the results is provided below. vaccine = matrix(c(90, 140, 10, 60), ncol = 2, byrow = FALSE) colnames(vaccine) = c("Sufficient", "Not Sufficient") rownames(vaccine) = c("Vaccine A", "Vaccine B") vaccine = as.table(vaccine) vaccine. props = prop.table(vaccine, 2) barplot(vaccine.props, ylab = "Frequency" main = "Sufficient Antibodies of Vaccines", col = rainbow(6)) legend("topright", legend = c("Vaccine A", "Vaccine B"), xpd = TRUE, inset = c(.1,.1), cex = .8, fill = rainbow(6)) #### 19. *This graph has two major problems. What are those problems?* #### 20. *Here is a correct table of conditional proportions. Explain what we are conditioning the* *proportions on in this table and interpret the statistics about the sample of volunteers.* prop.table(vaccine, 1)