perform a chi-square test on the
following probability example:
Heads Tails Total
Observed 108 92 200
Expected 100 100 200
Total 208 192 400
If you flip a coin and observe these results:
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How to perform a chi-square test on a probability example using the results of a coin toss experiment. The observed and expected frequencies, calculates the chi-square value, and consults a table of critical values to estimate the probability of the observed results. The document also discusses the interpretation of the chi-square test results and their implications for the fairness of the coin.
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perform a chi-square test on the
following probability example:
Heads Tails Total Observed 108 92 200 Expected 100 100 200 Total 208 192 400
If you flip a coin and observe these results:
What you need to do is first establish our null hypothesis. In this example, our null hypothesis is that the coin should be equally likely to land head-up or tails-up every time. The null hypothesis allows us to state expected frequencies. For 200 tosses, we would expect 100 heads and 100 tails.
Heads Tails Total
Observed 108 92 200 Expected 100 100 200 Total 208 192 400
consult a table of critical values of the chi-
squared distribution
- two classes (heads and tails), so our degrees of freedom is 1
- Move across the row for 1 df until we find critical numbers that bound our value
- our value of 1.24 to estimate a probability of
- This value means that there is a 73% chance that our coin is biased
- Try this one:
If the offspring were as follows, what would the parents be and what does our chi-square test show? 98 - purple and smooth 108 - purple and wrinkled 96 - yellow and smooth 95 - yellow and wrinkled