Question

A small community college employs 58​ full-time faculty members. To gain the​ faculty's opinions about upcoming contract​ negotiations, the president of the faculty union wishes to obtain a simple random sample that will consist of 5 faculty members. She numbers the faculty 1 to 58.

Using Table I from Appendix​ A, the president of the faculty union closes her eyes and drops her ink pen on the table. It points to the digits in row ​, column 7. Using this position as the starting point and proceeding​ downward, determine the numbers for the 5 faculty members included in the sample.
a) 7, 15, 23, 31, 39
b) 7, 8, 9, 10, 11
c) 7, 14, 21, 28, 35
d) 7, 22, 37, 52, 67

Answer 1

The correct sequence of the 5 faculty members in the sample would depend on the actual sequence of numbers in the table used. We must consider only numbers between 1 and 58 while avoiding repeats and ignoring numbers above 58. Without the table, we cannot determine the actual sequence.

Step-by-step explanation:

To determine the numbers for the 5 faculty members included in the sample using simple random sampling, we start with the digit in row 10, column 7 as indicated in the question. Since the community college employs 58 full-time faculty members, we must only consider random numbers between 1 and 58. As we do not have Table I from Appendix A, we cannot provide the exact members selected, but the approach would be to list numbers formed by two subsequent digits and select the faculty members with corresponding numbers, ignoring any numbers above 58 or repeated numbers until five distinct faculty members are identified.

If we look at the options given and apply this approach:

Option a) would be a correct sequence if the table produced these two-digit numbers sequentially without any numbers above 58 in betwBased on these considerations, the correct answer depends on the actual sequence of numbers in the table used by the president of the faculty union, which is not provided in the question.