In Question 12, you’ll use a tool to generate 1,000 sample mean word lengths. The tool is designed to produce samples that are representative of the population of the speech excerpt sampling frame with its mean word length of 4.68.
question 12
12) One set of randomly-generated sample mean word lengths from a single class may not be large enough to visualize the results. Let’s have a computer generate 1,000 sample mean word lengths for us.
Go to the DCMP Sampling Distribution of the Sample Mean (Discrete Population) tool at https://dcmathpathways.shinyapps.io/SampDist_discrete/.
Step 1) Under Select Population Distribution, select Word Length Sotomayor.
Step 2) Then select 10 for the Sample size (n) (you may need to scroll down to display more options) and select 1,00” for the number of samples to simulate drawing from the population. Click Draw Sample(s).
The plot labeled “Sampling Distribution of the Sample Mean” displays the 1,000 randomly-generated sample mean word lengths. How would you describe a typical sample mean?
Question 13
13) Explain why the sampling method of using a random number generator to generate a sample is better than choosing 10 words “by eye.”
Guidance
[Wrap-up: What did you find when you produced 1,000 samples intended to be representative of the population mean? Chances are, your Sampling Distribution of Sample Means showed a high concentration of means near 4.68. That’s because the tool is designed to produce representative samples in a simulation of taking samples using an unbiased method. When we collect a sample from a population, it is important that we do everything in our power to ensure the method we use will have a tendency to produce representative samples.]
