Write a few sentences to describe the variable you are going to use in your analysis.

This data set includes the percentage of protein intake from different types of food in countries around the world. The variable that has been chosen from this data set for analysis is MilkExcludingButter. This variable was described as, “Percentage of protein intake from milk - excluding butter.” Further, this variable seems to be a continuous variable. Below, is the Structure of the data as well as some summary statistics for the chosen variable.

## 'data.frame':    170 obs. of  27 variables:
##  $ Country             : chr  "Afghanistan" "Albania" "Algeria" "Angola" ...
##  $ AlcoholicBeverages  : num  0 0.184 0.0323 0.6285 0.1535 ...
##  $ AnimalProducts      : num  9.75 27.75 13.84 15.23 33.19 ...
##  $ Animalfats          : num  0.0277 0.0711 0.0054 0.0277 0.1289 ...
##  $ CerealsExcludingBeer: num  36 14.2 26.6 20.4 10.5 ...
##  $ Eggs                : num  0.407 1.807 1.292 0.176 0.485 ...
##  $ FishSeafood         : num  0.0647 0.6274 0.635 5.4436 8.2146 ...
##  $ FruitsExcludingWine : num  0.582 1.276 1.162 1.275 1.259 ...
##  $ Meat                : num  3.13 7.66 3.51 7.62 16.07 ...
##  $ MilkExcludingButter : num  5.53 16.48 8.06 1.15 7.43 ...
##  $ Offals              : num  0.592 1.108 0.328 0.813 0.853 ...
##  $ Oilcrops            : num  0.203 0.372 0.183 2.153 0.767 ...
##  $ Pulses              : num  1.248 1.456 2.551 4.085 0.884 ...
##  $ Spices              : num  0.166 0 0.178 0 0.344 ...
##  $ StarchyRoots        : num  0.194 0.887 1.464 5.194 0.467 ...
##  $ Stimulants          : num  0.555 0.264 0.463 0.102 0.411 ...
##  $ Treenuts            : num  0.1387 0.2677 0.2745 0.0092 0.0737 ...
##  $ VegetalProducts     : num  40.2 22.3 36.2 34.8 16.8 ...
##  $ VegetableOils       : num  0 0.0084 0.0269 0.0092 0.043 0 0.0205 0.0463 0.0647 0.0217 ...
##  $ Vegetables          : num  1.137 3.246 3.127 0.813 1.602 ...
##  $ Miscellaneous       : num  0.0462 0.0544 0.1399 0.0924 0.2947 ...
##  $ Obesity             : num  4.5 22.3 26.6 6.8 19.1 28.5 20.9 30.4 21.9 19.9 ...
##  $ Confirmed           : num  0.1383 2.348 0.2331 0.0574 0.1878 ...
##  $ Deaths              : num  0.00597 0.04457 0.00637 0.00132 0.00612 ...
##  $ Recovered           : num  0.1167 1.3962 0.1582 0.0496 0.1592 ...
##  $ Active              : num  0.0156 0.90715 0.06846 0.00655 0.02245 ...
##  $ Population          : num  38928000 2838000 44357000 32522000 98000 ...
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.2644  2.4193  5.6024  5.9212  8.5017 16.4750

Construct a confidence interval of the mean.

Below is R output of a 95% confidience interval for the mean of the variable.

##     2.5%    97.5%     mean 
## 5.326584 6.515734 5.921159

Use the Bootstrap method to construct the bootstrap confidence interval for the mean of the selected variable.

Below is R output of a 95% confidence interval for the mean of the bootstrapped samples means.

##     2.5%    97.5%     mean 
## 5.303132 6.493777 5.907539

Plot the bootstrap sampling distribution of the sample mean.

Below is R output of a histogram for the means of the bootstrapped samples.

Compare the two confidence intervals and interpret your findings and interpret the intervals.

The Sample mean’s confidence interval may represent an estimate of where the population mean might be, while The Bootstrapped Sample mean’s confidence interval may represent our confidence in the sample mean’s accuracy.

Interpretation:

The Sample mean’s confidence interval may indicate that, There is a 95% chance that the confidence interval of [5.3265845, 6.5157344] may contain the true population mean for the amount of protein in MilkExcludingButter in countries around the world.

The Bootstrapped Sample mean’s confidence interval may indicate that, There is a 95% chance that the confidence interval of [5.3031319, 6.493777] may contain the true sample mean for the amount of protein in MilkExcludingButter in countries around the world.