PValue Applet

# Is the coin fair?

Instructions

Instructions

Overview

Use a p-value to make a decision about whether a coin is fair (i.e. the probability of tossing a head is 50%).

This tool consists of two 'views': the investigate view and the test view. Use the button at the bottom to move between views.
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Investigate view

Under the investigate view, use the radio buttons to choose to flip a fair coin or a biased coin. The probability of tossing heads is displayed. Using the buttons to flip the coin, you can observe the results of the coin tosses under the indicated probability of tossing a head.

Activity:Flip the coin 100 times then consider the following questions:
1. If probability of getting the observed number of heads is large, must the coin be fair?
2. If probability of getting the observed number of heads is very small, is it possible that the coin is fair?

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Test view

In the test view, the probability of heads is initially unknown. You are asked to either "accept" or "reject" the hypothesis that the coin is fair. To guide your decision, gather information about the coin by tossing it. The applet displays the results of the tosses with the probability of getting at most the observed number of heads if the coin is fair. Once you accept or reject the hypothesis, the true probability of tossing a head is revealed.

Activity: Devise a plan to determine whether or not the coin is fair:
• Decide how many times you will flip the coin.
• Determine how small the probability must be for you to reject the stated hypothesis.
Consider the following questions:
1. For you to reject the hypothesis, how small must the given probabilty be?
2. Do you always get the right answer when you make decisions based on this probability?
3. Is it possible to get a very small p-value if the coin is fair?
4. How are your decisions affected by increasing the number of times you flip the coin?
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