Sampling Distributions of a Sample Proportion
Reece’s Pieces applet at
Launch the Reece’s Pieces applet above. In the top panel, set the probability of orange to 0.45 (the proportion that Reece’s Pieces claims to have in their product). Set the number of candies to 25, and the number of samples to 1. Make sure ‘animate’ button is checked and select ‘proportion of orange.’ This will display the sample proportions of 25 candies from a population with 45% orange candies. Also check the ‘summary stats’ box too.
Click on ‘draw sample’ many, many times and look at the graph/dot plot each time. As you click each time, look at what is being graphed. Also take notice of the ‘most recent’ sample proportion of orange candies. Ultimately click to about 50 samples.
As you progress through this (reaching 50 samples) answer the following questions (note: if it is laggie/slow, turn off your ‘animate’ button):
- Each time you ‘randomly’ select 25 candies out of the candy machine (that contains lots and lots and lots of Reece’s Pieces), are you getting the same proportion of orange candies each time? Why or why not?
- After you have done 50 random samples (randomly selected 25 candies for each of the 50 samples), what is the range in the dot plot (i.e., what is your lowest proportion of orange candies? What is your highest proportion of orange candies?) ?
- The above graph/dot plot is a graphical representation of a sampling distribution. Put into your own words what a sampling distribution is.
- Looking at the graph/dot plot, what is the center and the standard deviation of the distribution (look at the summary stats)? What is the shape of the distribution (Uni-modal? Symmetric? Outliers?)
- Don’t clear anything; now check the box for ‘Normal approximation.’ Is your distribution approximately Normal? Why or why not?
- Press ‘reset.’ Keep ‘probability of orange’ at 0.45; and keep ‘number of samples’ at 1; but change ‘number of candies’ (or you can think of this as your sample size) to 100. Run 50 samples (just like before). What is your center? What is your standard deviation (look at the summary stats)?
- Press ‘reset.’ Keep probability of orange at 0.45; and keep ‘number of samples’ at 1; but now change ‘number of candies’ (or you can think of this as your sample size) to 1000. Run 50 samples (just like before). What is your center? What is your standard deviation (look at the summary stats)?
- Based on the above (increasing the sample size) what can you say happens to a distribution’s center and standard deviation when we increase sample size?