Null Hypothesis (H0): The proportion of female students taking the biology exam is equal to the proportion of female students taking the calculus AB exam. H0: P1 = 0 H1: P1> P2
Alternative Hypothesis (H1): The proportion of female students taking the biology exam is greater than the proportion of female students taking the calculus AB exam. significans level(N1)=0.05
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 0.4846547 The p-value which is very close to 0 much smaller than the significance level of 0.05. so we reject the null hypothesis.so there is sufficient evidence to conclude that the proportion of female students taking the biology exam is significantly greater than the proportion of female students taking the calculus AB exam .
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)
mother_holding <- 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(conventional, mother_holding, alternative = "less")
Welch Two Sample t-test
data: conventional and mother_holding
t = 0.029953, df = 57.707, p-value = 0.5119
alternative hypothesis: true difference in means is less than 0
95 percent confidence interval:
-Inf 9.468337
sample estimates:
mean of x mean of y
35.30000 35.13333 Null Hypothesis (H0):there is no difference in the amount of time crying between the two groups. Alternative Hypothesis (H1): Infants held by their mothers cry is less. Significance Level (N1): 0.05 p-value: 0.5119 H0:??1 =0 H1:??1 >??2
Fail to reject the null hypothesis. There is insufficient evidence at the 5% significance level to conclude that holding infants by their mothers reduces the duration of crying compared to conventional holding methods.