Lecture Notes: Sampling Distribution Using Statcrunch

Overview

• Introduction to using Statcrunch for simulating sampling distributions.
• Use of applet in Statcrunch for sampling distribution analysis.

Preparing the Simulation

• Population Mean: Set to 3500.
• Population Standard Deviation: Assumed to be 100.
• Sample Size (n): Adjusted to 9.

Steps in the Simulation

1. Population Distribution: Visual graph representing the distribution.
2. Sample Distribution: Graph showing individual samples of 9.
3. Sample Means Distribution: Graph of the means from each sample.

Simulation Process

• One-Time Sampling:
  • Clicking "one time" samples 9 data points randomly from the population.
  • Calculates the mean of these 9 items.
  • Plots the mean on the sample means graph.
• Repeated Sampling:
  • Continued sampling results in multiple sample means plotted.
  • Demonstrated by sampling 5 sets of 9, building the distribution of sample means.

Large Sample Simulation

• 1000 Samples:
  • Runs 1000 samples of size 9 quickly without animation.
  • Plots the means on the graph; shows mean of means as approximately 3498.
  • Standard deviation of sample means is 33.82, differing from population's standard deviation.
• Increasing Sample Size:
  • Expanded to 10,000 samples.
  • Mean remains close to 3500.
  • Standard deviation consistent with initial smaller sample size.

Observations

• The process illustrates how sample means approximate the population mean.
• Shows the difference in standard deviation of sample means versus population standard deviation.
• Ability to repeat the process for large numbers of samples to observe trends and central limit theorem in action.

Conclusion

• The simulation effectively demonstrates the concept of sampling distribution and how sample size and number of samples affect the estimates of population parameters.