Sampling Methods and Random Digit Tables

Day 2: Sampling

Do Now (May 5th, 2025)

  • Problem: Selecting 3 people randomly from a class of 10 to represent the class at a math competition.

Homework Review

  • Last Night's HW:
    • 1a) Experiment: Treatment is being imposed (mints in soda).
      • Treatment: Mints dropped in the soda.
      • Response Variable: Height of the soda.
    • 1b) Observational Study: No treatment is imposed.
      • Population of Interest: Fifth-grade students.
    • 2) Conclusion: It is not reasonable to draw a cause-and-effect relationship because it is not an experiment. Only experiments can demonstrate causation.
    • 3a) Issue: Rats don't normally use drugs.
    • 3b) Method: Randomly assign 10 rats to each group (0 mg, 1 mg, 2 mg). Measure the time taken to complete the maze.
    • 4) Identifying studies:
      • A) II - Treatment is being imposed.
      • B) III - Depends on the population of interest.
      • C) A treatment is not being imposed.

Random Digit Tables

  • Definition: Lists of digits 0-9.
  • Property 1: Each digit has the same likelihood of appearing in each spot.
  • Property 2: Each entry is independent of the next.
  • How to Use: Assign each member of the population a unique number and select numbers from the random digit table until the desired amount of distinct subjects is obtained.

Example: Mrs. Isaac & Syosset HS Sophomores

  • Scenario: Mrs. Isaac wants to gauge the proportion of Syosset HS sophomores (612 total) who think the pool should be replaced with a student arcade.
    • a) Assign numbers to the students.
    • b) Use the random digit table to select the first 5 students.

Representative Samples

  • If a sample is taken to generalize to a population, the sample must be representative (similar to the population, but smaller).

Example: Senior Class President Election

  • Scenario: Campaign manager wants to know what proportion of students would vote for their friend running for senior class president (314 students total).
    • a) Polling everyone in the friend’s math class is not representative.
    • b) Assign every student a number from 1 to 314, then use a random number generator to select 10 students to poll. This is a better approach.
    • c) Asking every student going through the lunch line is not ideal as it may not be fully representative.

Example: Ramon & Football Games

  • Ramon wants to know if students at Syosset High School would be more likely to go to home football games on Friday nights.
  • Problem with Method: Standing outside the boys' locker room at the end of the school day is biased because it's not representative of the entire school population.

Example: Nomar & Netflix Accounts

  • Nomar wants to know the proportion of adults ages 18-25 that have a Netflix account. He decides to go to the phone book and randomly select 50 landlines to call.
  • Problem: This won’t accurately represent the population because many people in that age group may only have cell phones. Therefore, using landlines will exclude a significant portion of the target population.