Math Problem Statement

Question content area top Part 1 A community college employs 88 ​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 88. Complete parts​ (a) and​ (b) below. LOADING... Click the icon to view the random number table. Question content area bottom Part 1 ​(a) Using the provided random number​ table, the president closes his eyes and drops his ink pen on the table. It points to the digit in row​ 3, column 6. 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. The numbers for the faculty members are    79 comma 42 comma 77 comma 11 comma 41 comma 53 comma 14 comma 30 comma 39. ​(Use a comma to separate answers as​ needed.) Part 2 ​(b) The president uses technology to produce the following random numbers. 50  45  84  46  74  45  55  65  16  4 Determine the numbers for 9 faculty members who will be included in the sample. The numbers for the faculty members are    enter your response here. ​(Use a comma to separate answers as​ needed.)

Solution

To solve this problem step by step, let’s address each part:

Part 1: Random Number Table

The president starts at row 3, column 6 of the random number table and proceeds downward. We'll extract two-digit numbers from the table as the faculty members are numbered from 1 to 88. Numbers greater than 88 are skipped, and duplicates are avoided.

The provided sequence of selected faculty members is:
79, 42, 77, 11, 41, 53, 14, 30, 39.

Part 2: Random Numbers from Technology

Here are the random numbers generated by technology: 50, 45, 84, 46, 74, 45, 55, 65, 16, 4.

Since the problem asks for a sample of 9 faculty members, duplicates must be removed. Let’s adjust:

  1. List of unique numbers: From the sequence, we eliminate duplicate 45, resulting in:
    50, 45, 84, 46, 74, 55, 65, 16, 4.

  2. The final sequence for the sample of 9 faculty members is:
    50, 45, 84, 46, 74, 55, 65, 16, 4.

Final Answer:

  • Part (a): 79, 42, 77, 11, 41, 53, 14, 30, 39.
  • Part (b): 50, 45, 84, 46, 74, 55, 65, 16, 4.

Would you like more details about random sampling, or do you have any questions?

5 Questions to Expand Understanding:

  1. How are random numbers typically generated using a table versus technology?
  2. What are the advantages of using simple random sampling for surveys?
  3. Why is it necessary to remove duplicate numbers when creating a sample?
  4. How does the sample size (n = 9) affect the validity of results for a population of 88?
  5. What are other methods of sampling apart from simple random sampling?

Tip: When using a random number table, always ensure you skip over invalid entries (e.g., numbers out of range) and duplicates to maintain the integrity of the sample.

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Math Problem Analysis

Mathematical Concepts

Simple Random Sampling
Random Number Selection
Elimination of Duplicates

Formulas

-

Theorems

Random Sampling Principle

Suitable Grade Level

Grades 10-12

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