"x"

"1" 1.87354618925767

"2" 2.68364332422208

"3" 1.66437138758995

"4" 4.09528080213779

"5" 2.82950777181536

"6" 1.67953161588198

"7" 2.98742905242849

"8" 3.23832470512922

"9" 3.07578135165349

"10" 2.19461161284364

"11" 4.01178116845085

"12" 2.88984323641143

"13" 1.8787594194582

"14" 0.2853001128225

"15" 3.62493091814311

"16" 2.45506639098477

"17" 2.48380973690105

"18" 3.4438362106853

"19" 3.32122119509809

"20" 3.09390132121751

"21" 3.41897737160822

"22" 3.28213630073107

"23" 2.57456498336519

"2

Question 2 (28 marks) The dataset dat.txt contains a sample of 1500 observations. (a) Import the dataset into R using an appropriate command. Remember to check whether the dataset has a header. Your answer should be in R. You do not need to type anything here. [2] (b) Using R, plot a dot plot and include the figure here. Discuss whether a dotplot is suitable to visualize the shape of this data set. Discuss from the aspect of symmetry vs skewness, and whether any peaks can be observed. (3 (c) Using R, plot a density histogram. You do not need to include the breaks argument in your code. We will use the default setting in R here. For this histogram plot, the r-label should be r. Omit the main title. Refer to the code in pg. 22 of Chapter l's lecture notes to see how to set the z-label and main title. Colors are not necessary. Include the histogram in your answer using the include aphics command. Then, describe the distribution of the data set. (d) Discuss whether you are able to detect any outliers from the histogram. If not, what would be a more appropriate graphical summary observe outliers? Use R to plot the graphical summary that you mentioned, and include the plot in your answer. For this question, you do not need to compute the IQR nor identify the outliers. (3) (e) For this data set, use appropriate R functions to compute the sample mean and sample stan- dard deviation. Then, compute the estimated standard error of the sample mean. You need not necessarily use an in-built R function to compute the estimated standard error. In your LATEX an- swer, type out the notations along with the corresponding values. For example, sample mean = = 1.2345. Round your answers to 4 decimal places. Your R code submission should have the code used to compute these values. (6 (f) In part (e), the values of the sample standard deviation and the estimated standard error should be different. Why do you think they are different? Your answer should include the definition of the standard deviation and standard error, not just the formulas. 2 (g) (i) Based on your observations thus far, what do you think would be a plausible distribution for this data set? Choose between the uniform distribution, normal distribution, and exponential distribution. Justify your choice. [2] (ii) Based on your choice of the distribution, use the method of moments to obtain an appro- priate estimator for the mean y. Then, find the corresponding estimate. (3) (iii) Determine whether the estimator you found is an unbiased estimator for u. (3) 3/3 Question 2 (28 marks) The dataset dat.txt contains a sample of 1500 observations. (a) Import the dataset into R using an appropriate command. Remember to check whether the dataset has a header. Your answer should be in R. You do not need to type anything here. [2] (b) Using R, plot a dot plot and include the figure here. Discuss whether a dotplot is suitable to visualize the shape of this data set. Discuss from the aspect of symmetry vs skewness, and whether any peaks can be observed. (3 (c) Using R, plot a density histogram. You do not need to include the breaks argument in your code. We will use the default setting in R here. For this histogram plot, the r-label should be r. Omit the main title. Refer to the code in pg. 22 of Chapter l's lecture notes to see how to set the z-label and main title. Colors are not necessary. Include the histogram in your answer using the include aphics command. Then, describe the distribution of the data set. (d) Discuss whether you are able to detect any outliers from the histogram. If not, what would be a more appropriate graphical summary observe outliers? Use R to plot the graphical summary that you mentioned, and include the plot in your answer. For this question, you do not need to compute the IQR nor identify the outliers. (3) (e) For this data set, use appropriate R functions to compute the sample mean and sample stan- dard deviation. Then, compute the estimated standard error of the sample mean. You need not necessarily use an in-built R function to compute the estimated standard error. In your LATEX an- swer, type out the notations along with the corresponding values. For example, sample mean = = 1.2345. Round your answers to 4 decimal places. Your R code submission should have the code used to compute these values. (6 (f) In part (e), the values of the sample standard deviation and the estimated standard error should be different. Why do you think they are different? Your answer should include the definition of the standard deviation and standard error, not just the formulas. 2 (g) (i) Based on your observations thus far, what do you think would be a plausible distribution for this data set? Choose between the uniform distribution, normal distribution, and exponential distribution. Justify your choice. [2] (ii) Based on your choice of the distribution, use the method of moments to obtain an appro- priate estimator for the mean y. Then, find the corresponding estimate. (3) (iii) Determine whether the estimator you found is an unbiased estimator for u. (3) 3/3