A small community college employs 87 full-time faculty...

A small community college employs 87 full-time faculty members. To gain the faculty's opinions about an upcoming building project, the college president wishes to obtain a simple random sample that will consist of 9 faculty members. He numbers the faculty from 1 to 87. (a) Using Table I from Appendix $A$, the president closes his eyes and drops his ink pen on the table. It points to the digit in row $5,$ column $22 .$ Using this position as the starting point and proceeding downward, determine the numbers for the 9 faculty members who will be included in the sample. (b) If the president uses the randInt( feature of a graphing calculator with a seed value of $47,$ determine the numbers for the 9 faculty members who will be included in the sample.

A small community college employs 87 full-time faculty members. To gain the faculty's opinions about an upcoming building project, the college president wishes to obtain a simple random sample that will consist of 9 faculty members. He numbers the faculty from 1 to 87.
(a) Using Table I from Appendix $A$, the president closes his eyes and drops his ink pen on the table. It points to the digit in row $5,$ column $22 .$ Using this position as the starting point and proceeding downward, determine the numbers for the 9 faculty members who will be included in the sample.
(b) If the president uses the randInt( feature of a graphing calculator with a seed value of $47,$ determine the numbers for the 9 faculty members who will be included in the sample.

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Key Concepts

Simple Random Sampling

A sampling technique where every individual in the population has an equal probability of being selected. This method ensures that the sample is representative and unbiased since the selection process is completely random.

Random Number Tables

These are pre-arranged tables of random numbers used to simulate randomness in the selection process. In statistics, such tables can be used to pick sample units from a larger population by indexing through the table starting at a random position.

Computer-Aided Random Number Generation

Modern tools, such as graphing calculators, can generate random numbers using built-in functions. The randInt feature is an example that produces random integers within a specified range, offering a quick and efficient alternative to manual random selection.

Seed Value in Random Number Generation

A seed value is an initial value provided to a pseudorandom number generator to produce a reproducible sequence of numbers. This is important for replicability in studies where the exact sequence of random numbers needs to be recreated for verification or consistent simulation results.

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