Data Science for Doctors – Part 4 : Inferential Statistics (1/5) Solutions

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#                  #
#    Exercise 1    #
#                  #
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iter <- 10000
means <- rep(NA, iter)

for (i in 1:iter){
  sam_50 <- sample(data$mass, 50)
  means[i] <- mean(sam_50)
}

hist(means)

hist(data$mass)

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#                  #
#    Exercise 2    #
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mean(data$mass)

sd(data$mass)/sqrt(50)

#OR 
mean(means)

sd(means)

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#                  #
#    Exercise 3    #
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####################

library(moments)
skewness(means)

#  slight positive skewness, which means that it is slightly light tailed
kurtosis(means)

# The kurtosis is close to the expected value 3.

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#                  #
#    Exercise 4    #
#                  #
####################

z = (30.5-mean(data$mass))/(sd(data$mass)/sqrt(50))
z

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#                  #
#    Exercise 5    #
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####################

pnorm(z)

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#                  #
#    Exercise 6    #
#                  #
####################

z = (31-mean(data$mass))/(sd(data$mass)/sqrt(150))

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#                  #
#    Exercise 7    #
#                  #
####################

pnorm(z)

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#                  #
#    Exercise 8    #
#                  #
####################

z*sd(data$mass)/sqrt(150)

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#                  #
#    Exercise 9    #
#                  #
####################

z = 1.96
low <- 31 - z*sd(data$mass)/sqrt(250)
high <- 31 + z*sd(data$mass)/sqrt(250)
low;high

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#                  #
#    Exercise 10   #
#                  #
####################

z = 2.33
low <- 31 - z*sd(data$mass)/sqrt(250)
high <- 31 + z*sd(data$mass)/sqrt(250)
low;high

z = 2.58
low <- 31 - z*sd(data$mass)/sqrt(250)
high <- 31 + z*sd(data$mass)/sqrt(250)
low;high