STA321: Week #02 Assignment

1 Purpose

This report will analyze the difference in standard sampling and bootstrap sampling. The sample distribution and confidence intervals will be used to justify the use of bootstrap sampling in future analysis.

2 Data Set Description

This data set includes the percentage of protein intake from different types of food in countries around the world. The last couple of columns also includes counts of obesity and COVID-19 cases as percentages of the total population for comparison purposes.

Data can be found at kaggle.com. This data set is also uploaded to the course Github repository. w02-Protein_Supply_Quantity_Data.csv.

url="https://pengdsci.github.io/STA321/ww02/w02-Protein_Supply_Quantity_Data.csv"
protein = read.csv(url, header = TRUE)
var.name = names(protein)
kable(data.frame(var.name))

var.name
Country
AlcoholicBeverages
AnimalProducts
Animalfats
CerealsExcludingBeer
Eggs
FishSeafood
FruitsExcludingWine
Meat
MilkExcludingButter
Offals
Oilcrops
Pulses
Spices
StarchyRoots
Stimulants
Treenuts
VegetalProducts
VegetableOils
Vegetables
Miscellaneous
Obesity
Confirmed
Deaths
Recovered
Active
Population

3 Variable of Study

The studied variable was “Animal Products”. The responses of this variable correspond to the percentage of protein intake different countries’ populations consume from animal products. This response can vary from a number of factors, including livestock availability, economy, prevalence of dietary restrictions, and much more.

4 Sample Mean and Distribution

The following is the distribution of the standard sample. The sample mean was 21.3.

set.seed(123)
animalproducts <- sample(protein$AnimalProducts,
               100,
               replace = FALSE
)

hist(animalproducts,
     breaks = 8,
     xlab = "Protein Intake % Via Animal Products",
     main = "Approximated Distribution of Animal Product Consumption"
)

CI <- quantile(animalproducts, c(0.025, 0.975))
mean(animalproducts)

## [1] 21.33699

5 Bootstrap Method

The following is the distribution of the bootstrap sample. The sample mean was 21.4

set.seed(123)
animalproducts.bootstrap <- sample(protein$AnimalProducts,
                         100,
                         replace = TRUE
                         )
hist(animalproducts.bootstrap,
     breaks = 8,
     xlab = "Protein Intake % Via Animal Products",
     main = "Bootstrap Approx. Dist. of Animal Product Consumption")

bootstrap.CI <- quantile(animalproducts.bootstrap, c(0.025, 0.095))
mean(animalproducts.bootstrap)

## [1] 21.41313

6 Comparison

The following table compares the confidence intervals of the standard sample and the bootstrap sample. Note the smaller range of the bootstrapped sample. Bootstrapped samples have normal distributions, meaning parametric analysis can be continued on this sample. We also can narrow our estimation of the sample mean with an equal level of confidence as the standard sample. This is ensured because the same sample size was used. Overall, the bootstrap sample is useful to performing further analysis.

kable(data.frame(CI,bootstrap.CI))

	CI	bootstrap.CI
2.5%	8.063812	8.952372
97.5%	32.598145	11.190900