1 Introduction

The data set being used for this report shows the percentage of proein intake from different types of food all over the world. The variables are all different types of foods, an obesity and a COVID-19 percentage based off of cases in the total population. The variable I decided to use for my project was eggs.

2 Confidence Interval of the Mean

In order to find the confidence interval of the mean without bootstrapping, we need to use techniques from more basic statistic classes. We need the sample size (n), standard deviation(s), mean (x), and margin of error (e). We can plug these into the equation to find the confidence interval of the mean. \[ Lower=x-e(x/n) \] \[ Upper=x+e(x/n) \] Using this, we find the condfidence interval of the mean to be

LCL.95 UCL.95
1.043119 1.279816

3 Bootstrap Confidence Interval of the Mean

The following histogram is showing the bootstrap confidence interval of the means with n=170 to be

LCL.95 UCL.95
1.047809 1.278161

4 Analysis

In conclusion, the confidence interval of the mean is (1.043119, 1.279816) and after using the bootstrap method, the confidence interval of the mean is (1.047809, 1.278161). Since the confidence interval without bootstrapping is wider and it got narrower once we bootstrapped, the bootstrapping method is better to find estimations and make predictions on the percentage of protien intake regarding the eggs variable in the data set.