Other's On-Line Resources (Chapter 6)

 

Flipping Coins
  • Description:
    This interactive on-line resource allows you to quickly see what will happen if you flip a fair coin multiple times. As this applet will demonstrate, you are very, very likely to have sampling error in your sample of coin flips unless your sample size is gigantic.

  • What to Do:
    1. Click on the colored title of this on-line resource: "Flipping Coins."
    2. In the screen that pops up, scroll down until you can see the "Flip" and "Reset" buttons located below the 2 black bars on the left side of the screen.
    3. Using the drop-down menu between those 2 buttons, change the sample size from "n = 1" to "n = 10."
    4. Click the "Flip" button and look to see whether the fair coin being flipped produced 5 heads and 5 tails.
    5. Click the "Flip" button 9 more times so that you end up with a total sample of 100 flips of a fair coin. If the final position of the blue line in the "Cumulative Proportion" graph is ligher or lower than .50, then tell yourself that you have--over the collection of flips in your sample--a sampling error. Most like, this will be the case.

  • Sky Huck's Puzzle Question:
    Do you think you'd end up with exactly 50% heads if you flip a fair coin 10,000 times? First, answer the question asked in the previous sentence. Then, do these things: (a) Click the "Reset" button; (b) Click the check mark to the left of the word "Animate" (to give you fast results); (c) Change "n" to 10000; (d) Click the "Flip" button. Was your prediction right?
     
Sampling Distributions
  • Description:
    Through this interactive exercise, you'll see (1) how a sampling distribution is created, (2) how the standard error decreases if n is increased, and (3) how the sampling distribution will be approximately normal even if the population is nonnormal.

  • What to Do:
    1. Click on the colored title of this on-line resource: "Sampling Distributions."
    2. After clicking on "Begin," click "Animated Sample" in the next screen. Watch what happens. Then click on "Animated Sample" some more. This will show you how sampling distributions are built.
    3. Click on "5 Samples" (or "1,000 Samples" or "10,000 Samples") to look at the sampling distribution that's created quickly for lots of samples.
    4. Change the n, the population's shape, and the statistical focus (from the mean to the median) to see how these things affect sampling distributions.

  • Sky Huck's Puzzle Question:
    In which of these two cases is the standard error smaller: (a) When n = 10 and the sample's median is computed, or (b) When n = 5 and the sample's mean is computed?
     
Confidence Intervals (A)
  • Description:
    You're able to see a visual display of 100 confidence intervals, each built for a sample of a given size extracted from a population having M = 50 and SD = 10. You'll see which of the 100 CIs "overlap" the population mean . . . and which ones do not. And you'll also see a simple frequency count of how many of the 100 CIs "catch" mu.

  • What to Do:
    1. Click on the colored title of this on-line resource: "Confidence Intervals (A)."
    2. After clicking on "Begin," click "sample" in the new screen. Clicking "sample" again adds 100 new CIs to your 1st set.

  • Sky Huck's Puzzle Question:
    Set the sample size equal to 10. Then, after hitting "sample" 10 times in a row, observe the "Proportion Contained" results in the bottom 2 windows. Now, if you repeat these steps but this time set n = 20, will the "Proportion Contained" results go up, go down, or remain the same?
     
Confidence Intervals (B)
  • Description:
    Using this interactive on-line resource, you'll get to see a picture showing 50 CIs, each computed for the mean of a different random sample drawn from the same population. The picture will show how many of these CIs overlap the population mean. You can control the level of confidence and the number of CIs that are computed.

  • What to Do:
    1. Click on the colored title of this on-line resource: "Confidence Intervals (B)."
    2. On the screen that pops up, read the instructions, look at the "alpha bar," and examine the set of CIs displayed in the picture.
    3. Click the "More Intervals" button to get a new batch of 50 CIs.
    4. Move the black triangle to change alpha from .05 to .01, and then click on the "New Alpha" button to produce a brand new set of 50 CIs.
    5. Set alpha equal to either .05 or .01, click the "New Alpha" button, and then repeatedly click the "More Intervals" button until you can see the combined results for 1,000 CIs.

  • Sky Huck's Puzzle Question:
    If we could somehow change the word "alpha" in this on-line resource to "confidence," what changes (if any) would we need to make in the numbers inside the "Alpha" bar?
     

Copyright © 2012

Schuyler W. Huck
All rights reserved.

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