less than 0.05 = significant, more than 0.05 = not significant

Q1) 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

Hypothesis Test:

\(H_0:p_1=p_2\) \(H_a: p_1 > p2\)

P value:

\(p_1\)= females taking the bio exam \(p_2\)= females taking the calc exam

State your decision:

The p value for this question is 2.2e-16, which means it is less than 0.05, which means it is significant. In context, this means there are more women in biology than calculus.

Significance Level

prop.test(c(84200, 144790), c(102598, 211693), alternative = "greater")
## 
##  2-sample test for equality of proportions with continuity correction
## 
## data:  c(84200, 144790) out of c(102598, 211693)
## X-squared = 6531.4, df = 1, p-value < 2.2e-16
## alternative hypothesis: greater
## 95 percent confidence interval:
##  0.1341319 1.0000000
## sample estimates:
##    prop 1    prop 2 
## 0.8206788 0.6839622

Q2) 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.

Hypothesis Test: \(H_0:µ1=µ2\) \(H_a:µ1=µ2\)

P value: \(µ1\)= avg infants crying when held by mother \(µ2\)= avg infants crying when given shot

mothers <- 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)
conventional<-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)

Significant Level

t.test(mothers,conventional,alternative ="less")
## 
##  Welch Two Sample t-test
## 
## data:  mothers and conventional
## t = -0.029953, df = 57.707, p-value = 0.4881
## alternative hypothesis: true difference in means is less than 0
## 95 percent confidence interval:
##      -Inf 9.135003
## sample estimates:
## mean of x mean of y 
##  35.13333  35.30000

State your decision: The p value for this question is 0.4881, which means it is more than 0.05, which means it is not significant. In context, this means we don’t have enough evidence to judge whether that infants cried less on average when they are held by their mothers than if held using conventional methods.