Question

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)

Answer 1

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:

H_0: p =0.5

H_a: p > 0.5

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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