Download the Module Six Problem Set Template Zip File and import it into Overleaf. Complete each portion of the template. Type your solutions into the document using LaTeX. Note: Be sure to show all steps for arriving at your solution. Just giving a final number may not receive full credit. Export your work as a PDF file

A binomial random variable X is defined as the number of successes achieved in the n trials of a Bernoulli process. Describe an event in your life that fits the properties of a Bernoulli process, being sure to explain how each property is met by your event. Finally, state the number of trials and the number of successes for your event. Be specific.

R Programming Assignment1) Load a data set into R. This can be any data set that has at least two quantitative variables and one qualitative variable and can be used to complete the rest of this assignment.a) If you have an interest (chess, avocados, gender wage gap), this is a great opportunity toexplore that topic. I’ve listed potential data sources at the end of this document. Look fordata that is “.csv” file type. You must get my approval of your data set before you start working on it.b) If you do not have an interest in mind, you can use the default data set from the 2016 American Community Survey from Colorado. It is located on Canvas as“ACS_2016_CO.csv” with an accompanying codebook describing the variable values.NOTE: the default data set is nice to have, but a lot of the variables are top coded as 9999* because the information is missing. This isn’t valuable data when calculatingstatistics or creating plots and should not be used! (The command subset() in R is helpful for dealing with this.)2) Describe the data set with words. How many variables are there? How many observations? What is the unit of observation for the data set (e.g. state, month, person-year)? Is this a cross-section, or multiple observations overtime? Do we have repeated observations for the same subject? Describe a few key variables that you will use in your data set including their units (feet, miles, $).3) Summarize one of the quantitative variables for the full sample using sample statistics. Then, summarize the same quantitative variable for a subset the observations that meet a specific condition. (E.g. report the average and standard deviation of the monthly price of avocados in 20 major cities in the US from 2010 to 2015, then repeat for all 20 cities only in the month of February). Try to choose the subsample in a way that is meaningful. How do the summary statistics between the full sample and subsample compare? What do you learn from this comparison? Include R code and output here with your interpretation.4) Create a histogram of the variable that you summarize in part 3 with properly labeled axes and title. (Bonus points if you can create two histograms of the same variable, split by some other variable (e.g. gender), to show a striking difference.) Include R output here.5) Calculate a confidence interval for difference of means. Choose one variable (e.g. income) and create two subsample of the data using another variable (e.g. gender). Calculate the means for the subsamples and create a confidence interval for the difference in means. Pick something interesting to you and interpret your findings. Include your R code here and output here. Interpret your results.6) Formalize a hypothesis you wish to test with these data (e.g. is the average salary from men the same as the average salary for women?). You might not have all the knowledge to test the exact hypothesis you are interested in. Stick to doing a difference of means test or a test for if the mean of a variable is equal to a specific value.7) Conduct the hypothesis at the 𝛼 = 0.05 level of significance and interpret your results in a meaningful way. Include your R code and output here.8) Visualize at least two variables from the data set using a scatter plot with an appropriate title, axis labels, and legend. Quantitative variables work best for this type of visual. The goal is for this image to tell a story that is clear to the reader. Include R code and output here. Interpret the plot.9) Finally, think and write about who would be a good “consumer” of this information. Whowould be interested in the facts you present here? How could you improve the analysis in the future by incorporating new data or using the existing data to answer a more interesting question?