Data 606 Lab 3

1. Make a histogram of men’s heights and a histogram of women’s heights. How would you compare the various aspects of the two distributions?

Both distributions look fairly normal with slight skew.

par(mfrow=c(1,2))
hist(mdims$hgt, main="Men's Height")
hist(fdims$hgt,main="Women's Height")

2. Based on the this plot, does it appear that the data follow a nearly normal distribution?

Yes, the data appears to follow a nearly normal distribution

3. Make a normal probability plot of sim_norm. Do all of the points fall on the line? How does this plot compare to the probability plot for the real data?

This plot looks similar to the plot for the real data, having points that closely follow the line, but with points deviating from the line towards the tails.

set.seed(2112)
sim_norm <- rnorm(n = length(fdims$hgt), mean = fhgtmean, sd = fhgtsd)
qqnorm(sim_norm)
qqline(sim_norm)

4. Does the normal probability plot for fdims$hgt look similar to the plots created for the simulated data? That is, do plots provide evidence that the female heights are nearly normal?

Yes, the plots look similar to the plots created by the simulated data

5. Using the same technique, determine whether or not female weights appear to come from a normal distribution.

It appears weight is skewed right, diverging from the normal distribution

set.seed(22)
qqnormsim(fdims$wgt)

6. Write out two probability questions that you would like to answer; one regarding female heights and one regarding female weights. Calculate the those probabilities using both the theoretical normal distribution as well as the empirical distribution (four probabilities in all). Which variable, height or weight, had a closer agreement between the two methods?

What is the probability that a random female is shorter than 150cm?
What is the probability that a random female is heavier than 68kg?

pnorm(150, fhgtmean, fhgtsd)

## [1] 0.01152955

fwgtmean <- mean(fdims$wgt)
fwgtsd   <- sd(fdims$wgt)
1 - pnorm(68, fwgtmean, fwgtsd)

## [1] 0.2207879

#fkn <- fdims$kne.di
qqnorm(fdims$kne.di)
qqline(fdims$kne.di)

hist(fdims$kne.di)