HW7

##Question 1:

#Hypothesis

Null \[ H_0: p_{Bio} = p_{Calc} \] Alternative \[ H_1: p_{Bio} > p_{Calc} \] #Significance Level \[ \alpha = 0.05 \]

prop.test(
  x = c(84200, 102598),
  n = 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 0.4846547

#Decision At the 5%, there is sufficient evidence to say that there is a hiigher proportion of female students taking the AP Biology exam than the AP Calculus exam.

##Question 2:

#Hypothesis

Null \[ H_0: \mu_{New} = \mu_{Conventional} \]

Alternative \[ H_1: \mu{New} < \mu_{Conventional} \] #Significance Level \[ \alpha = 0.05 \]

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)

new_methods <- 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_methods, 
  conventional, 
  alternative = "less"
  )

## 
##  Welch Two Sample t-test
## 
## data:  new_methods 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

#Decision At the 5% signficance level, there is not enough evidence to conclude that babies given shots using the new methods cried less than when using conventional methods.