Editing Statistics and Statistical Programming (Spring 2019)/Problem Set: Week 5
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: '''PC4.''' Let's look beyond the mean. Compare the distribution from your sample of <code>x</code> to the true population of <code>x</code>. Draw histograms and compute other descriptive and summary statistics. What do you notice? Be prepared to discuss and explain any differences. | : '''PC4.''' Let's look beyond the mean. Compare the distribution from your sample of <code>x</code> to the true population of <code>x</code>. Draw histograms and compute other descriptive and summary statistics. What do you notice? Be prepared to discuss and explain any differences. | ||
: '''PC5.''' Calculate the conditional mean of <code>x</code> for each of the groups in the population and the standard deviation of this distribution of conditional means. Compare this standard deviation to the standard error of the mean you calculated in PC2 above. Explain the relationship between these values. | : '''PC5.''' Calculate the conditional mean of <code>x</code> for each of the groups in the population and the standard deviation of this distribution of conditional means. Compare this standard deviation to the standard error of the mean you calculated in PC2 above. Explain the relationship between these values. | ||
: '''PC6.''' I want you to run a simple simulation that demonstrates a fundamental insight of statistics. Please see the R lecture materials from | : '''PC6.''' I want you to run a simple simulation that demonstrates a fundamental insight of statistics. Please see the R lecture materials from last week for ideas about how to do this (but note that there are some differences between that example and this programming challenge). | ||
:* (a) Create a vector of 10,000 randomly generated numbers that are uniformly distributed between 0 and 9. | :* (a) Create a vector of 10,000 randomly generated numbers that are uniformly distributed between 0 and 9. | ||
:* (b) Calculate the mean of that vector. Draw a histogram of the distribution. | :* (b) Calculate the mean of that vector. Draw a histogram of the distribution. |