Many high school students take the AP tests in different subject areas. In 2017, of the 144,790 students who took the biology exam 84,200 of them were female. In that same year, of the 211,693 students who took the calculus AB exam 102,598 of them were female. Is there enough evidence to show that the proportion of female students taking the biology exam is higher than the proportion of female students taking the calculus AB exam? Test at the 5% level.
prop.test(c(84200, 102598), c(144790, 211693), alternative = "greater")##
## 2-sample test for equality of proportions with continuity correction
##
## data: c(84200, 102598) out of c(144790, 211693)
## X-squared = 3234.9, df = 1, p-value < 2.2e-16
## alternative hypothesis: greater
## 95 percent confidence interval:
## 0.09408942 1.00000000
## sample estimates:
## prop 1 prop 2
## 0.5815319 0.4846547Hypothesis Tests:
p1: Proportion of female students taking the AP Biology exam p2: Proportion of female students taking the AP Calculus AB exam
Ho: p1 = p2 Ha: p1 > p2
α = 0.05
p-value: 2.2e-16
Decision: Reject the null. With the p-value being extremely small, we can conclude that the proportion of female students taking the AP Biology exam is higher than the proportion of female students taking the AP Calculus AB exam.
A vitamin K shot is given to infants soon after birth. The study is to see if how they handle the infants could reduce the pain the infants feel. One of the measurements taken was how long, in seconds, the infant cried after being given the shot. A random sample was taken from the group that was given the shot using conventional methods, and a random sample was taken from the group that was given the shot where the mother held the infant prior to and during the shot. Is there enough evidence to show that infants cried less on average when they are held by their mothers than if held using conventional methods? Test at the 5% level.
conventional_shots <- c(63,0,2,46,33,33,29,23,11,12,48,15,33,14,51,37,24,70,63,0,73,39,54,52,39,34,30,55,58,18)new_shots <- c(0,32,20,23,14,19,60,59,64,64,72,50,44,14,10,58,19,41,17,5,36,73,19,46,9,43,73,27,25,18)t.test(new_shots, conventional_shots, conf.level = 0.99, alternative = "greater")##
## Welch Two Sample t-test
##
## data: new_shots and conventional_shots
## t = -0.029953, df = 57.707, p-value = 0.5119
## alternative hypothesis: true difference in means is greater than 0
## 99 percent confidence interval:
## -13.48032 Inf
## sample estimates:
## mean of x mean of y
## 35.13333 35.30000Hypothesis Tests:
μ1: Mean crying time for when infants are held by their mothers μ2: Mean crying time for when infants are treated by conventional methods
Ho: μ1 = μ2 Ha: μ1 < μ2
α = 0.05
p-value: 0.5119
Decision: Fail to reject the null. Since the p-value is slightly larger than 0.05, there is not enough evidence to conclude that infants cried less on average when they were held by their mothers than when they were treated using conventional methods.