Prediction-using-R/Stattistical tests code at main · RoseWMumbi/Prediction-using-R · GitHub

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#AUTHOR NAME: Rose Mumbi

#loading dataset
HappinessFile <- read_excel("C:/Users/Rose/Documents/Prediction/HappinessFile.xlsx")
#One-tailed Test Predicting a LOWER sample score for happiness

#Step 1: The hypotheses
#H0: μs = μP (Happiness sample mean is equal to the population mean)
#H1: μs < μP (Happiness sample mean is lower than the population mean)

#Step : Criteria for decision
#reject the null hypothesis if the z statistic is smaller than the critical value at α =0.05.
#α =.05
#the critical z-score is -1.65.

#Step 3: Collect data; compute sample statistics
#define vector to calculate standard deviation
data1 <- c(HappinessFile$Happiness)
#calculate standard deviation
HappinessStd <- sd(data1)
#calculate mean
HappinessMean <- mean(data1)
#calculate size
HappinessSize <- length(data1)
sqrtSize <- sqrt(HappinessSize)
SEM <- HappinessStd/sqrtSize
#SEM = 0.1077
#sample statistic
SampleStatisticHapp <- (HappinessMean-5.43)/(SEM)
#Z test statistic = -0.3448

#Step 4 Decision
#The z statistic -0.3448 is larger than the critical value which is -1.65 as a result we do
#not reject the null hypothesis. In this case the sample mean is not significantly from the population mean.

# a type 1 error may occur if I reject a null hypothesis in an instance where it is true.
# The risk of a type 1 error in this hypothesis test is 5%.
#If I had done a non directional (2-tailed) hypothesis testing with an alpha level α =.05 the critical value would be +/-1.960
# I would have still not rejected the null hypothesis since the z statistic is not extreme and lies within the range +/-1.960.


#One-tailed Test Predicting a LOWER sample score for FreeLifeChoice

#Step 1: The hypotheses
#H0: μs = μP (FreeLifeChoice  sample mean is equal to the population mean)
#H1: μs > μP (FreeLifeChoice  sample mean is larger than the population mean)

#Step 2: criteria for decision
#reject the null hypothesis if the z statistic is larger than the critical value at α =0.05.
#α =.05
#the critical z-score is 1.65.

#Step 3: Collect data; compute sample statistics
#define vector to calculate standard deviation
data2 <- c(HappinessFile$FreeLifeChoice)
#calculate standard deviation
FreeLifeChoiceStd <- sd(data2)
#calculate mean
FreeLifeChoiceMean <- mean(data2)
#calculate size
FreeLifeChoiceSize <- length(data2)
sqrtSize2 <- sqrt(FreeLifeChoiceSize)
SEM2 <- FreeLifeChoiceStd/sqrtSize2
#SEM2 = 0.0129
#sample statistic
SampleStatisticFreeLife <- (FreeLifeChoiceMean-0.724)/(SEM2)
#Z test statistic = 0.5130

#Step 4 Decision
#The z statistic 0.5130 is smaller than the critical value which is 1.65 as a result we do
#not reject the null hypothesis. In this case the sample mean is not significantly different from the population mean.

# a type 1 error may occur if I reject a null hypothesis in an instance where it is true.
# The risk of a type 1 error in this hypothesis test is 5%.
#If I had done a non directional (2-tailed) hypothesis testing with an alpha level α =.05 the critical value would be +/-1.960
# I would have still not rejected the null hypothesis since the z statistic is not extreme and lies within the range +/-1.960.

#Two-tailed Test Predicting a DIFFERENT sample score for Generosity.
#Step 1: The hypotheses
#H0: μs = μP (Generosity  sample mean is equal to the population mean)
#H1: μs ≠ μP (Generosity  sample mean is different from the population mean)

#Step 2: criteria for decision
#reject the null hypothesis if the z statistic is extreme in that it is larger than the upper critical value or smaller than the lower critical value at α =0.05.
#α =.05
#the critical z-score is +/-1.960.

#Step 3: Collect data; compute sample statistics
#define vector to calculate standard deviation
data3 <- c(HappinessFile$Generosity)
#calculate standard deviation
GenerosityStd <- sd(data3)
#calculate mean
GenerosityMean <- mean(data3)
#calculate size
GenerositySize <- length(data3)
sqrtSize3 <- sqrt(GenerositySize)
SEM3 <- GenerosityStd/sqrtSize3
#SEM3 = 0.0145
#sample statistic
SampleStatisticGenerosity <- (GenerosityMean-0.001)/(SEM3)
#Z test statistic = 0.8213

#Step 4 Decision
#The z statistic 0.8213 is smaller than the upper critical value which is 1.960 as a result we do
#not reject the null hypothesis. In this case the sample mean is not significantly different from the population mean.

# a type 1 error may occur if I reject a null hypothesis in an instance where it is true.
# The risk of a type 1 error in this hypothesis test is 5%.
#If I had done a directional (lower-tailed) hypothesis test with an alpha level α =.05 the critical value would be +/-1.960
# I would have still not rejected the null hypothesis since the z statistic is not smaller than the critical value which would have been -1.65.