5) Perform simple random sampling by using the given portion of a random number

Question

5) Perform simple random sampling by using the given portion of a random number table. (5 points) a. The roster size of a statistical course is capped out if 40 students are enrolled. Assume that there are no dents on the waiting list, and 37 students are enrolled. A list of 9 students that wants to add to the course i shown from below where their names are arranged in alphabetical order. Crashing Students Alice 4 David Gilbert 2 Benjamin EdgarHelen Ivan 3 Christina 6 Fiona 9 In order to be fair to those students, the instructor randomly selects 3 students. Use the given portion of a random number table shown from below to obtain a sample size of 3 from the given list of students by starting from the far left. Then identify the names of those students. (2 points) 84842 84352 b. 500 people wish to participate in a raffle ticket drawing for a prize. Suppose these people are labeled from through 500 and only 5 can be randomly selected. Use the given portion of a random number table shown from below by starting from the far left of the top row and moving down to the next row. Then identify the randomly selected numbers. (3 points) 7767739942 3938 02944 63324 24568 17450 29131 52079

Explanation / Answer

a. We shall take one digited numbers from the portion of the random number table by starting from the far left. To ensure equal probability for each individual, we shall take the numbers from 1 to 9 and they are 8,4,8 (repeated), 4(repeated), 2. For without replacement peocedure, we ignore repetition. Hence they are 8,4,2 and the corresponding students are Helen, David, Benjamin.

b.

At first we number the people serially in a suitable order from 1 to 500. Next we are to assign random numbers to the people so that each may get the same peobability of being selected. since 500 is 3-digit number, we consider random numbers from 001 to 500 (since the greatest three digited multiple of 500=500) and shall ignore other three digited numbers. Since we consider sampling without reolacements, a person once slected cannot be selected again.  We shall take 3- digited numbers from the portion of the random number table by starting from the far left and they are:

776 (ignore), 773 (ignore), 994(ignore), 239, 384, 029, 446, 332.

The serial numbers of the people selected are 239, 384, 029, 446, 332.

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