Central Limit Theorem

Central Limit Theorem: Finding the smallest sample size. Each group of students will be assigned a set of two probability distributions and, for each of these distributions, you will determine the smallest sample size for which the conditions of the CLT are satisfied. Instructions: For each distribution, you must:
a. Include the command set.seed(value) as the first line in each R script, where value should be replaced by your group number.
b. Simulate 100 samples (𝑚 = 100).
c. Vary the sample size (𝑛 =?) until you find the smallest sample size for which the conditions of the CLT are satisfied.
d. Confirm your choice of 𝑛 by replicating your analysis at least ten times.
e. Justify your selection with the use of probability plots, hypothesis tests, and descriptive statistics.
Deliverables: For each distribution, you must provide:
a. A commented R script (.R or .rmd) file.
b. A minimum of three sets of results:
i. Results for 10 replicates on a sample size smaller than the suggested 𝑛 for which the conditions of the CLT are not yet satisfied. You may include only three of the probability plots and hypothesis tests.
ii. Results for 10 replicates on the suggested 𝑛 for which the conditions of the CLT are satisfied. You may include only three of the probability plots and hypothesis tests.
iii. Results for 10 replicates on a sample size larger than the suggested 𝑛 for which the conditions of the CLT are satisfied. You may include only three of the probability plots and hypothesis tests.
c. A technical report (.pdf) with all outputs and a thorough interpretation of the probability plots, hypothesis tests, and descriptive statistics included in the report.
Hint: For each set of results, it is strongly recommended that you combine the information for the descriptive statistics and the hypothesis tests in a single table, where each row represents the data, you input into your probability plot. You may use the following table format
Hint: Be wary of the output of the specific R function used to calculate kurtosis. You may simulate standard normal data and calculate its kurtosis to better understand whether the output is kurtosis or kurtosis – 3.