stats holder stuff db

library(UsingR)
#P(Z > Za) = a
#P(Z > Z0.01) = 0.01
#Z0.01 = ?

qnorm(1-0.01,0,1)
#This is 1 mius the area to the right of the Z score
#Notation: P(Z > 2.33) = 0.01

#Sampling distrobution
#-A firm believes the internal rate of return for all its proposed investments
#--has a mean of 50% and standard deviation of 3%
#--A random sample of 35 investments is obtained

#Random Variable: The internal rate of return on invesments
#Quantitative Contenuous
#Population: All Proposed Investments
#Sample: 35 Investments
#Parameter: Mean + Data Population
#--In words: The True mean internal rate of return for all investments
#Startistic: (Symbol is X with a bar over it) Mean + Data Sample
#--In Words: The Mean internal rate of return for 35 investments

#What is the Sampling Distrobution of (X Bar)?
#Requirement: Sample Size is greater than 30, or if the text says it's normal
#The Sampling Distrobution is (X bar) is about normal with
#--Mu(Xbar) = 50%, and a Stabdard Deviation of (Standard Deviation / Square Root of Sample Size)

#(Import data sets as "From Excel")

#Test the hypothesis that the weights of UCA Students who do want to try the japonese cheese cakes
#--Is greater than those who don't.
#Parameters: Mu1 = Weight of students who want to try, Mu2 = Weight of students who don't want to try
#Both these Mus are Parameters

attach(upsurvey1)
#Seperate the erights by j_cheese
names(upsurvey1)
weight_yes <- weight[j_cheese == "Yes"]
weight_no <- weight[(j_cheese == "No") | (j_cheese == "Maybe")]

#H0: Mu1 == Mu2
#H1: Mu1 > Mu2

t.test(weight_yes, weight_no, var.equal = F, alternative = "greater")
#P Value = 0.485
#We fail to reject the Null Hypothesis (H0) because P Value is greater than the Alpha Value (0.485 > 0.01)
#Weight yes has over 30 Samples so it meets requirements
#Weight no has less than 30 so it needs a Shapiro test
shapiro.test(weight_no)
#Shapiro P = 0.04756
#0.04756 < 0.05, so this does not meet requirements

#Center = mean [mean()]
#Spread = Standard Deviation [sd()]
#Shape = Boxplot [boxplot(weight, horizontal = T)]