Unit 6: Sample Size Determination

  1. Normal Distribution
  • Characteristics: mean = median = mode, symmetry about the center, 50% of values less than and greater than the mean.
  • Understanding Standard Deviation: It is crucial because it allows us to say that any value is:
  • Likely within 1 SD (68 out of 100 should be).
  • Very likely within 2 SDs (95 out of 100 should be).
  • Almost certainly within 3 SDs (99.7 out of 100 should be).
  • Example: Student heights between 1.1m and 1.7m; Mean = 1.4m; SD = 0.15m.
  1. Z-Score Example
  • Friend's height: 1.85m is 3 SDs from the mean of 1.4m, giving a Z-score of 3.0.
  • What is a Z-Score: The number of standard deviations a data point is from the mean. Calculated as (Value - Mean) / SD.
  • Standardizing Process:
  • Value → Subtract Mean → Divide by SD → Z-Score.
  1. Sampling Distribution of Mean
  • According to the Central Limit Theorem, arithmetic means of large random samples will form a normal distribution curve, matching the population mean.
  • Standard Error Formula
  • Format: Sample mean, Frequency, Deviation from assumed mean (d), d/0.5, fd, d², fd².
  • This format helps in the calculation of mean and standard deviation.
  1. Important Terms
  • Parameter: A fixed characteristic or measure of the target population.
  • Statistic: A characteristic or measure of the sample.
  • Finite Population Correction (fpc): Corrects overestimation for sample sizes ≥ 5% of the population.
  1. Sample Size Determination
  • Considerations: Allowed error, desired confidence level, estimated population SD.
  • Formula
  1. Determining Sample Size with Known Standard Deviation
  • Examples of determining the necessary sample size for estimating average amounts per invoice in populations of sales invoices with specified SDs and allowable errors.
  1. Stratified Sample Size
  • Comparing proportionate vs. disproportionate stratified sample sizes for market research in luxury retail.
  • Stratified Sampling Process:
  • Identify Strata → Determine SD and Size per Stratum → Calculate Sample Size.
  • Formula
  1. Sample Mean Frequency Format
  • Format: Sample mean, Frequency, Deviation from assumed mean (d), d/0.5, fd, d², fd².
  • This format helps in the calculation of mean and standard deviation.