STAT 205 Homework 1 (Due: 5:00 Pm, Tuesday, January 17, 2017)

STAT 205 Homework 1 (Due: 5:00 pm, Tuesday, January 17, 2017) Instructor: Shiwen Shen Total Points: 100 Submission instruction: Answer all the questions individually in the word file. If necessary, paste the code, output and plot from R. Put your name on the top line and submit the completed word file on the blackboard.sc.edu Assignments section before the deadline. (EMAIL SUBMISSION WILL NOT BE ACCEPTED)

1. Install R in your personal computer and finish the following questions: (Note: you have to show code, output and plot from R to get full credit.) a) Generate 500 random normal data. (10) b) Draw a histogram of the generated data. (10) c) Compute the sample mean, median, variance, and standard deviation of the generated data. (10)

2. Textbook page 15, Exercise 1.2.5. (10)

5. Refer to the collection of 100 ellipses shown in the figure in textbook page 26, which can be thought of as representing a natural population of the mythical organism C. ellipticus. The ellipses have been given identification numbers 00, 01, …, 99 for convenience in sampling. Certain individuals of C. ellipticus are mutants and have two tail bristles. a) Use your own judgement to choose a sample of size 10 from the population that you think is representative of the entire population. Note the number of mutants in the sample. (5) b) Use R to randomly choose a sample of size 10 from the population. Note the number of mutants in the sample. Using R code: sample(0:99,10). (5) c) Repeat a) and b) for another 7 times. Now, you should have 8 different numbers of mutants from each of the two methods. Calculate the average number of mutants in each method, and report your results in the following table: (10) Method 1 2 3 4 5 6 7 8 Average Judgement Random d) Actually there are 38 out of 100 mutants in the figure. Which method, judgement or random, performs better in sampling? (10)