We discussed in class the scenario of having a friend who flipped a coin 5 times, saw 4 heads and 1 tail, and was convinced he had a weighted coin.
We defined the null hypothesis in this scenario to be that the coin wasn’t weighted, i.e. it was a fair coin. We then showed that, given a a coin that is fair, the sequence of 4 heads and a tail was not a statistically significant event.
What if the scenario was changed, and instead of 4 heads and 1 tail, your friend saw 5 heads. What would your null hypothesis be, and would the event your friend saw be statistically significant? (calculate the answer)
As we are again testing here whether the coin is fair or not, we are testing here whether the probability of getting a heads is greater than 0.5. Therefore the null and the alternative hypothesis here are given as:
For a fair coin, the probability of getting 5 heads in 5 tosses
is computed as:
= 0.5*0.5*.... 5 times
= 0.55 = 0.03125
As the given probability is less than 0.05, therefore the test is significant here for 5% level of significance, and therefore we can conclude here that we have sufficient evidence that the proportion of getting heads is more than 0.5.
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