Reference no: EM132787108
Question 1. Use all of the digits of student number as your population of interest. Produce and upload an R script or RMarkdown file to do the following parts. Note that your codes must reproduce your answers, else this question will be awarded 0 marks. Where appropriate, round your final answers to 2 decimal places. All plots produced must have properly labelled axes and be given an appropriate title which includes your student number.
(a) Numerically describe the population of digits by finding the mean, median, variance,sum and proportion of digits like the first digit in your number.
(b) Produce a frequency histogram of your population.
(c) Produce the frequency histogram of the sampling distribution of the sample meanbased on drawing samples of size 3 without replacement from your population. (Hint: The base R function choose() and the combn() function in the R package combinatcan be used to answer this part.)
(d) Compute the mean and variance of the sample means of part (c).
(e) Set the seed of your randomization to be your student number. Simulate the sampling distribution of the sample mean by using 250, 000 samples of size 3 based on drawing with replacement from your population. Produce the frequency histogram of the empirical sampling distribution of the sample mean.
(f) Compute the mean and variance of the sample means based on part (e).
(g) Compare the results of part (c) and (e) to the theoretical properties of the samplemean based on samples of size 3. Explain the similarities or differences found.
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