Question

Country Myanmar Ethiopia Japan India Burkina Faso Kenya China Ghana Nicaragua Guatemala Ecuador Austria Brazil Peru Colombia Denmark Switzerland Netherlands Sweden Belgium Portugal Germany Finland Algeria Italy Iceland Venezuela, RB Luxembourg Norway Greece France Israel Argentina Spain Ireland Tunisia Mexico Malta Turkey United Kingdom Australia Canada New Zealand Lebanon United Arab Emirates United States

Obesity % 2.9 3.3 3.5 4.7 5.2 5.9 7.3 10.9 15.5 16.4 18 20.1 20.1 20.4 20.7 21 21 21.9 22 22.1 22.1 22.7 22.8 23.6 23.7 23.9 24.3 24.8 24.8 25.1 25.7 25.8 26.5 26.5 27 27.1 27.6 28.7 29.4 29.8 29.9 30.1 30.6 30.8 34.5 35

In 2016, the World Health Organization estimated that the average obesity rate worldwide was 13%[1]. (This includes all countries of the world, not just the countries in the sample.)

[1] Source: World Health Organization.

1. Using the sorted data, determine the probability that a randomly selected country from the sample has an obesity rate greater than the worldwide rate. Show your work and round your answer to the nearest thousandth.

2. Examining the dataset, can you suggest a reason for the high proportion of countries in the dataset having an obesity rate above the worldwide average? State your reason(s) below:

3. Suppose that fifteen of the countries from the dataset were going to be randomly selected for a study to see if the obesity rates were greater than the worldwide obesity rate. Determine if this group could be treated as a binomial distribution. State each requirement.

Answer 1

Let p = proportion of obese people worldwide      
p = 0.13  13% is worldwide obesity rate as per WHO    
       
1) To find P( that a randomly selected country from the sample has an obesity rate greater than the worldwide rate)      
= number of countries with obesity rate greater than 13% / total number of countries sampled      
From the data we have,      
Number of countries with obesity rate greater than 13% = 38      
Total number of countries sampled = 46      
P( that a randomly selected country from the sample has an obesity rate greater than the worldwide rate)      
= 38/46      
= 0.8261      
P( that a randomly selected country from the sample has an obesity rate greater than the worldwide rate)  = 0.8261

2) Obesity is associated with economic development of a country. It is also associated with      
increasing urbanisation, modernisation and use of automation gadgets.      
Thus as more and more countries get economically and technologically advanced, the obsesity      
rate of the country would increase.      
Hence, high proportion of countries in the dataset have an obesity       
rate above the worldwide average      
       
3) For a binomial distribution, following are the requirements and the satisfaction of these       
requirements by the group      
a) The number of observations n is fixed      
  Here the number of observations is 15 which is fixed     
       
b) Each observation is independent.       
  The countrywise obesity data is independent of each other. Also the sample     
  of 15 countries was selected randomly.     
       
c) Each observation represents one of two outcomes (Success of Failure)      
  Here success is that a country selected has obesity rate greater than 13%     
  otherwise it is a failure     
  there are no other possibilities     
       
d) The probability of "success" p is the same for each outcome      
  We have seen that the probability of randomly selecting a country     
  with obesity rate greater than 13% is 0.8261     
  p = 0.8261     
  Thus, p = 0.8261 is same for any random selection of a country     
       
Since, all above requirements are satisfied,       
we can say that the group of 15 countries can be treated as a binomial distribution.