1. False. The reasoning here is false because it is only going off of the number of cardiovascular incidents in each category, which is slightly skewed considering the two medications have different sample sizes.
  2. False. More data testing should be done to determine the correlation between the medications and cardiovascular events, not just comparing rate of incident.
  3. False. More data testing should be done.
  4. True
  1. Control dead: 30/34= .88, Treatment dead: 45/69 = .65
  3. Null: no difference in proportion, Alternative: p2<p1
  1. 28, 75, 69, 34, 0, negative
  2. The simulated distribution suggests that the treatment program most often results in a difference of proportion between -0.05 and 0.05, which is low enough to suggest that the treatment program is effective at keeping patients alive during heart transplants and resulting recovery.
  1. This is an experimental study with a control vs treatment group sampling method
  2. Yes, because patients were not aware of the placebo vs actual variable of the medication provided.
  3. p(antibiotic) = 66/85 = .77, p(placebo) = 65/81 = .80, p(antibiotic- placebo) = .77-.80 = -0.03
  4. At a first glance, it appears that the antibiotic and the placebo had a similar effect in improving how people felt about their symptoms. This is based on the proportions from above, that indicate that there was only a 0.03 difference in the proportions of both groups who reported improved symptoms, and that is a small enough value to indicate that their effectiveness is about the same.
  5. The null hypothesis here proposes that the antibiotic will have no impact on symptom improvement, and therefore there should be no difference in the proportion of people who report improved symptoms. The alternative hypothesis, however, claims that the antibiotic will impact sinus symptoms more effectively than not using the antibiotic, and therefore there should be a significant difference between the proportions of those who improved symptoms in each group.
  6. Based on the simulated histogram, the observed value of 66 patients reporting symptom improvement is not far from the observed mean, and therefore it is logical to conclude that the null hypothesis is true.
  1. Null: person yawning will not make another person yawn, Alternative: person yawning will make another person yawn
  2. p(treatment – control) = 0.294 – 0.25 = 0.04
  3. estimated p-value: 0.0004. This would imply that the null is true.
  1. H0:p = 0.69, HA: p ≠ .69
  2. p(high schoolers) = 17/30 = 0.57
  3. In order to perform a simulation for the data, one could take 100cards, 69 saying `follow news’ and 31 saying ‘don’t follow news’, shuffling them and then drawing 30 cards, with replacement, to represent the high schoolers. Then, using the sample proportion of students who followed the news in this sample data, you would use software to plot this simulation many times (i.e.~10,000).
  4. p value estimate: 0.2. Since this is greater than 0.05, we couldreject the null hypothesis.
  5. First, I calculated the test stat and set up some values for the simulation, and then I simulated some data based on the values from the problem and puled a histogram from it
x1 <- 69
n1 <- 100
x2 <- 17
n2 <- 30

p_hat1<-x1/n1
p_hat2<-x2/n2

pooled<-(x1+x2)/(n1+n2)

test_stat<-(p_hat1-p_hat2)/sqrt(pooled*(1-pooled)*(1/n1+1/n2))

nsim=10000
people<-c(rep("adults", 100), rep("highschoolers", 30))
answer<-c(rep("yes_news", 86), rep("no_nes", 44))
d<-rep(NA, nsim)

for(i in 1:nsim){
  permuteGen<-sample(people)
  tab<-table(permuteGen, answer)
  d[i]<-diff(tab[,2]/24)
}

permuteGen
##   [1] "adults"        "adults"        "adults"        "adults"       
##   [5] "adults"        "adults"        "adults"        "adults"       
##   [9] "adults"        "adults"        "highschoolers" "adults"       
##  [13] "adults"        "highschoolers" "adults"        "adults"       
##  [17] "adults"        "adults"        "adults"        "adults"       
##  [21] "adults"        "adults"        "adults"        "adults"       
##  [25] "adults"        "adults"        "adults"        "adults"       
##  [29] "adults"        "adults"        "adults"        "highschoolers"
##  [33] "adults"        "adults"        "adults"        "adults"       
##  [37] "adults"        "adults"        "adults"        "adults"       
##  [41] "adults"        "adults"        "adults"        "adults"       
##  [45] "adults"        "highschoolers" "highschoolers" "adults"       
##  [49] "highschoolers" "adults"        "highschoolers" "highschoolers"
##  [53] "highschoolers" "highschoolers" "highschoolers" "adults"       
##  [57] "adults"        "adults"        "highschoolers" "adults"       
##  [61] "adults"        "adults"        "adults"        "adults"       
##  [65] "adults"        "highschoolers" "highschoolers" "adults"       
##  [69] "highschoolers" "adults"        "adults"        "adults"       
##  [73] "highschoolers" "adults"        "highschoolers" "adults"       
##  [77] "adults"        "adults"        "highschoolers" "adults"       
##  [81] "highschoolers" "adults"        "highschoolers" "adults"       
##  [85] "adults"        "adults"        "adults"        "adults"       
##  [89] "adults"        "adults"        "adults"        "highschoolers"
##  [93] "adults"        "adults"        "adults"        "highschoolers"
##  [97] "highschoolers" "adults"        "adults"        "adults"       
## [101] "adults"        "adults"        "adults"        "highschoolers"
## [105] "adults"        "adults"        "highschoolers" "adults"       
## [109] "adults"        "adults"        "highschoolers" "adults"       
## [113] "adults"        "highschoolers" "adults"        "adults"       
## [117] "adults"        "adults"        "adults"        "adults"       
## [121] "highschoolers" "adults"        "adults"        "adults"       
## [125] "adults"        "highschoolers" "adults"        "adults"       
## [129] "adults"        "highschoolers"
hist(d)