Activity 3: Developing Intuition about Significance: Fair Coins If we are flipping a coin, how large a proportion of heads do we need to get in order to claim evidence that the coin is biased to give more heads than tails? If the coin is fair, the proportion of heads should be 0.5 , so our null and alternative hypotheses are H0:p=0.5 vs Ha: p>0.5, where p is the proportion of heads. First For each situation below, make a guess about whether or not you think that sample outcome would give convincing evidence for a biased coin (Yes or No) Second Now using Statkey (using at least 5,000 simulated samples) find the p-value in each case above and indicate whether (at a 5% level) there is convincing evidence that the coin is biased. If you are working in a group, consider divide and conquer, before discussing results. Examine the results from the p-values. Consider each of the factors below. Decide whether or not each has an impact on whether or not a sample proportion shows significance. 1. The sample size 2. The sample proportion 3. The number of simulated samples in the randomization distribution.