STA321: Week #02 Assignment

#1 Variable The variable I’m using is Tree nuts. These are edible seeds of specific trees. These nuts include almonds, cashews, walnuts, pecans, and hazelnuts.

#2 Confidence Interval

url="https://pengdsci.github.io/STA321/ww02/w02-Protein_Supply_Quantity_Data.csv"
protein = read.csv(url, header = TRUE)
t.test(protein$Treenuts, conf.level = 0.95)

## 
##  One Sample t-test
## 
## data:  protein$Treenuts
## t = 11.228, df = 169, p-value < 2.2e-16
## alternative hypothesis: true mean is not equal to 0
## 95 percent confidence interval:
##  0.2008097 0.2864856
## sample estimates:
## mean of x 
## 0.2436476

#3 Bootstrap Method

 original.sample = na.omit(protein$Treenuts)
 
 bt.sample.mean.vec = NULL
for(i in 1:1000){
  ith.bt.sample = sample(x = original.sample,
     size = length(original.sample),
      replace = TRUE
  )
       bt.sample.mean.vec[i] = mean(ith.bt.sample)
  }
quantile(bt.sample.mean.vec, c(0.025, 0.975))

##      2.5%     97.5% 
## 0.2017903 0.2914604

#4 Bootstrap Sampling Distribution of Sample Mean

hist(bt.sample.mean.vec,
     breaks = 20,
     xlab = "Sample Means of Treenuts",
     main = "Sampling Distribution of Treenut Means"
     )

#5 Comparison between Confidence Intervals The t-test 95% confidence interval for the treenut sample means was (.2008, .2865). The 95% confidence interval for the boostrap method was (.2016, .2864). These intervals are very similar to each other.