Statistics

(a) To obtain a simple random sample of 5 students from a population of 423 students, we must ensure that each student has an equal chance of being selected. Let's evaluate each of the given procedures: A. Number the names from 1 to 423 and use a random number table to produce 5 different three-digit numbers corresponding to the names selected. This method is a valid approach for obtaining a simple random sample because it gives each student an equal chance of being selected. B. Ask the students to come to a meeting and pick five from those who come to the meeting. This method is not valid for obtaining a simple random sample because it introduces bias. Only students who are able and willing to come to the meeting would have a chance of being selected. C. List the names in alphabetical order and take the first five names on the list. This method is not valid for obtaining a simple random sample because it does not give each student an equal chance of being selected. It systematically selects students based on their position in the alphabet, which is not random. D. List each name on a separate piece of paper; place them all in a hat, and pick five. This method is a valid approach for obtaining a simple random sample because it gives each student an equal chance of being selected, assuming the draw is conducted fairly. The valid procedures for obtaining a simple random sample are A and D. (b) To obtain the sample using the random number table provided, we will assume the table looks something like this: ``` 135 049 865 792 321 276 503 014 058 930 ... ``` Since we have 423 students, we are interested in three-digit numbers from 001 to 423. We will start with the first column of the first row and work down each column, skipping any numbers that are outside our range (424 and above) or any duplicates. Let's proceed with the selection: 1. The first number in the first column is 135, which is within our range, so we select student number 135. 2. Moving down the first column, the next number is 276, which is also within our range, so we select student number 276. 3. We continue to the second column, starting from the top. The number 049 is within our range, so we select student number 049. 4. The next number in the second column is 503, which is outside our range (greater than 423), so we skip it. 5. We move to the third column and find 865, which is also outside our range, so we skip it. 6. The next number in the third column is 014, which is within our range, so we select student number 014. 7. We continue to the fourth column and find 792, which is outside our range, so we skip it. 8. The next number in the fourth column is 058, which is within our range, so we select student number 058. We have now selected 5 students: 135, 276, 049, 014, and 058. These are the numbers corresponding to the students chosen, and we have obtained our simple random sample.

(a) Which of the following procedures could you follow to obtain a simple random sample of 5 students? Select all that apply. A. Number the names from 1 to 423 and use a random number table to produce 5 different three-digit numbers corresponding to the names selected. B. Ask the students to come to a meeting and pick five from those who come to the meeting. C. List the names in alphabetical order and take the first five names on the list. D. List each name on a separate piece of paper; place them all in a hat, and pick five. (b) Obtain this sample using the portion of the random number table provided in the problem statement. Start with the first column of the first row and work down each column. Type the numbers corresponding to the students chosen. (Use a comma to separate answers as needed.)

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