stats

Population Sampling and Stratified Sampling

• Population Proportions

  • Resident students: 28% of sample
  • Commuters: 61% of sample
  • Staff: Remaining percentage (11%)

• Sample Size Calculation

  • Total Sample Size: 21,909
  • Resident Students: 28% of 21,909 = 20 residents
  • Commuters: 61% of 21,909 = 13,304 commuters
  • Staff: 11 out of 2,401 faculty

• Stratified Sample Representation

  • Proper representation for residents, commuters, and staff achieved by obtaining a random sample within each group.
  • Simple Random Sample Process:
  • Use a different seed for each stratum (e.g., faculty: seed = 4,032).
  • Faculty sampling: Ranges from 1 to 2,401.

• Calculator Instructions:

  • Press C 4,032, then press the STOW button.
  • Access the Math > Probability, scroll to #8: RN in interval, no repeat.
  • Enter lower = 1, upper = 2,401, n = 11.
  • Example Outputs: 243, 2,308, 2,380, 1,565, etc.

• Random Sampling for Resident Students and Commuters:

  • Residents: Use numbers 1 to 6,204 to sample 28.

Systematic Sampling

• Definition: A systematic sample is obtained by selecting every k-th individual from the population.

• Step-by-Step Process:

  • Randomly select the first individual, representing a number between 1 and k.
  • For example, survey every 8th individual starting from a randomly selected start point.

• Example in a Food Store:

  • Sampling process: survey every 7th customer leaving the store.
  • If the first customer selected is the 5th, continue surveying every 7th thereafter (5th, 12th, 19th, …, 278th).
  • Maintain