8: Sampling Distributions

Due Week 10 · Friday, October 30

Instructions

Complete the following problems and upload your answers as a PDF file to Blackboard. Upload your .do file as well.

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Questions

1. In 2022, approximately 17% of all land on the globe had been preserved and protected.¹ Not all countries protect an equal number of lands, however. The dataset protectedlands2022.dta gives the distribution of all protected lands across all countries in the world in the year 2022.
   1. A researcher samples 10 countries. What is the probability that these sampled countries protect more than 30% of their lands? (Hint: calculate the population mean and standard deviation from Stata, and use these to manually calculate a z-score.)
      
   2. If the researcher sampled 50 countries, rather than 10, what would the probability be that these sampled countries protect more than 20% of their lands?
2. The sample command in Stata draws random samples from data in memory, with the number after sample referring to the size of the sample to draw. (So, for instance, the command sample 10 would draw a 10% sample of the dataset.)
   1. Draw a histogram of the distribution of protected lands.
      
   2. Draw a 20% sample of countries from the dataset. What is the mean and standard deviation of this sample? Draw a histogram of the distribution. How close does this distribution look to the population distribution?
      
   3. Draw a 20% sample of countries 30 more times, and record the mean each time. Draw a histogram of these sample means.² What is the shape of this distribution? What is its standard deviation?

Footnotes

1. Source: https://ourworldindata.org/grapher/terrestrial-protected-areas

2. Note: this will require you to manually record what those sample means are, and then create a new dataset within Stata.