ch 6 exercise

##chapter 6 exercise
    ## part a)
> sample=rpois(1000,1)
> samples=as.data.frame(matrix(rbinom(1000*40,1,0.5),ncol = 40))
 ## part b)
    #mean_n=rowMeans(samples[,1:n]) ##row means for a sample size of n
> mean_5=rowMeans(samples[,1:5])
> mean_15=rowMeans(samples[,1:15])
> mean_40=rowMeans(samples[,1:40])
 ## c) 6 lines; means and sd of each sample size ^
    #mean(mean_n) and sd(mean_n) <- where "mean_n" is a generic vector of 1000 means from b ^
> mean(mean_5)
> sd(mean_5)

> mean(mean_15)
> sd(mean_15)*15

> mean(mean_40)
> sd(mean_40)*40
 ## d) 4 lines; shapiro test a single column of 'samples' & each set of means ^^
    #shapiro.test(samples[,1])
> shapiro.test(samples[,1])
> shapiro.test(samples[,5])
> shapiro.test(samples[,15])
> shapiro.test(samples[,40])
 ## e) gen 'by groups' boxplot; groups are the single col of 'samples' & each set o means ^^^
> boxplot(cbind(samples[,1],samples[,5],samples[,15],samples[,40]))
> boxplot(cbind(samples[,1]))
##############################################
#  questions                                 #
# 1. <filled out chart on paper>
# 2. population is skewed high, negative
#   n=5 is skewed high, negative
#   n=15 is skewed low, positive
#   n=40 is skewed high, positive
# 3. As the sample size increases I expect the mean of the sample means to become closer to the population mean.
#   The results from question 1 support this by having the sample mean increase as the sample size increased from 5 to 15 to 40