Question

You want to take a simple random sample (SRS) of 50 of the 816 students who live in a dormitory on campus.

You label the students 001 to 816 in alphabetical order.
In the table of random digits,
you rad the entries
95592 94007 69769 33547 72450 16632 81194 14873
The first three students in your sample have labels
a) 955, 929, 400
b) 400, 769, 769
c) 929, 400, 769
d) 400, 769,335
e) 559, 294, 007

Answer 1

To select a simple random sample of 50 students from 816, label each student with a three-digit number and use the table of random digits to choose unique numbers within range. Option c) 400, 769, 335 from the given choices is correct because it adheres to the rules and range set for the selection process.

Step-by-step explanation:

The question is regarding how to select a simple random sample of 50 students from 816 who live in the dormitory on campus, using a table of random digits.

From the options provided, the correct approach would be to label each student with a unique three-digit number, ranging from 001 to 816.

Then using the table of random digits, read three numbers at a time, skipping any that are out of range (817 and above) or repeated. Since the student numbers are from 001 to 816, option c) would be the correct one as '929' is out of range, leaving '400' and '769' as the first two selections, and '335' is the next valid number below 816.

An optimal way to conduct the process of simple random sampling is to utilize a random number generator to select numbers within the range of students. In this manner, we can avoid any biases that might inadvertently occur when manually selecting the students.

Simple random sampling, random number generator, and table of random digits are all key methods that can be employed for the sampling process.

Answer 2

The first three students in the sample are labeled with the numbers 929, 400, and 769, so the correct option is c) 929, 400, 769.

Step-by-step explanation:

To select a simple random sample (SRS), you use the table of random digits. In this case, you read the entries 95592, 94007, 69769, 33547, 72450, 16632, 81194, 14873. The labels for the first three students are derived by taking the first three digits of each entry. Therefore, the labels are 929, 400, and 769, which correspond to option c) 929, 400, 769.

In detail, the first three students are obtained from the entries:

Entry 1: 95592 → Label: 929

Entry 2: 94007 → Label: 400

Entry 3: 69769 → Label: 769

This process ensures that the selection is random, unbiased, and representative of the entire student population living in the dormitory. The correct labels are determined directly from the first three digits of the entries in the table of random digits.

In conclusion, when conducting a simple random sample, it's essential to follow a systematic and unbiased approach. Reading the entries from the table of random digits and using the first three digits for each selected student ensures a fair and random sampling process, leading to an accurate representation of the larger population.