ch 9 prob 9 & 10

##ch 9 prob 9
ch9_prob3_data <- read.csv("C:/Users/benny/Downloads/ch9_prob3_data.csv")
data=ch9_prob3_data

install.packages("BSDA") #this took obscenely long to install and i think it's bc i didnt put BDSA in quotations
library(BSDA)
SIGN.test(data$post,data$pre,alternative="greater")
## OUTPUT:
# Dependent-samples Sign-Test
# data:  data$post and data$pre
# S = 20, p-value = 0.002039
# alternative hypothesis: true median difference is greater than 0
# 95 percent confidence interval:
#   2 Inf
# sample estimates:
# median of x-y
#           3
#Achieved and Interpolated Confidence Intervals:
#                 Conf.Level L.E.pt U.E.pt
# Lower Achieved CI     0.8998      2    Inf
# Interpolated CI       0.9500      2    Inf
# Upper Achieved CI     0.9506      2    Inf
#####  questions ####
# a. the paired t-test alt hypo focuses on the true mean and it be not equal to 0, while the sign test's A.H. is the true median #difference being greater than 0
# b. the probability (p=0.002039) of the difference of the mean being greater than 0
# c. the data suggest that it is likely that the ginkgo supplement improved memory
# d. determining which test to use depends on what assumptions are true for the data, which would make a certain test stronger
# e. the non-parametric sign test is weaker than the parametric paired t-test because the Normality assumption has been violated

### problem 10 ###
ch9_prob5_data <- read.csv("C:/Users/benny/Downloads/ch9_prob5_data.csv")
data5=ch9_prob5_data
wilcox.test(data5$treatment,data$pre,conf.int = TRUE,exact = FALSE)
## OUTPUT ##
#  Wilcoxon rank sum test with continuity correction
# data:  data5$treatment and data$pre
# W = 531.5, p-value = 0.2305
# alternative hypothesis: true location shift is not equal to 0
# 95 percent confidence interval:
# -1.999932  8.000014
# sample estimates:
# difference in location
#           3.000008
### questions ###
# a. the p-value (0.2305) lands in the grey zone of p-val. significance, so it suggests that the ginkgo supplements may somewhat #improve memory test scores
# b. 8.000014 - 3.000008 = 5.000006(+-)3
# c. the data suggest that ginkgo supplements may improve memory test scores by 5(+-)3 points, but more research is needed
# d. the M-W U-test functions off the Normality assumption being violated, while the 2-sample test assumes Normality