Sampling distribution
For this Discussion Board, you will apply the concept of sampling distribution. A critical part of inferential statistics involves determining how far sample statistics are likely to vary from each other and from the population parameter. The sampling distribution of a statistic is the distribution of the statistic for all possible samples from the same population of a given size. The sampling distribution depends on the underlying distribution of the population, the statistic being considered, the sampling procedure employed, and the sample size used.
Instructions
Consider the population of the Reese’s Pieces candies manufactured by Hershey. Suppose that you want to learn about the distribution of colors of these candies, but you can only afford to take a sample of 25 candies.
Physical Sample: Reese’s Pieces come in three colors: orange, brown, and yellow. Buy a small bag of Reese’s Pieces, take a random sample of 25 of the candies, and record the number and proportion of orange candies in your sample.
Consider the following questions:
Is the proportion of orange candies among the 25 you selected a parameter or a statistic?
Is the proportion of orange candies manufactured by Hershey’s process a parameter or a statistic?
What is your best estimate (based on your sample) of the true population proportion?
Do you suspect that every person in the class obtained the same proportion of orange candies in their sample?
If everyone in the class estimates the population proportion of orange candies with the proportion of orange candies in their sample, will everyone have the same estimate?
Virtual Sample: Take many random samples of Reese’s Pieces. Use the Java applet (Links to an external site.) to simulate this process and answer the following questions, so you can discuss the results you get:
Step 1: Set Probability of Orange to .45, the Number of Candies to 25, the Number of Samples to 1, and click on “Proportion of Orange.” Then, click “Draw Samples.” Watch the applet draw one sample of 25 virtual Reese’s Pieces. Below, it plots the proportion of orange pieces in its virtual sample.
Step 2: Change the Number of Samples to 500 and uncheck the Animate box, then click “Draw Samples.” What do you notice about the graph? Click on “Summary Stats” to display the mean and standard deviation of your sample proportions. Record the mean and standard deviation of your sample proportions, and any observations you have about the graph.
Step 3: Draw 500 samples of 75 candies each. What do you notice about the graph? How did the graph change when your sample size increased? Record the mean and standard deviation of these sample proportions, and any observations you have about the graphs and how they’re alike or different.