Say you perform an experiment in which you flip a coin 20 times. You are looking for statistically significant outcomes (outcomes that have a probability of occurring that is less than your alpha level).

Question

Say you perform an experiment in which you flip a coin 20 times. You are looking for statistically significant outcomes (outcomes that have a probability of occurring that is less than your alpha level).

You choose an alpha level of 0.01.

1.) You decide to do a two-tailed test. What are all the possible outcomes of the experiment that you could interpret as statistically significant?

Answer 1

To determine the possible outcomes that could be interpreted as statistically significant in a two-tailed test, we need to consider the alpha level of 0.01.

In a two-tailed test, the significance is evaluated on both ends of the distribution, so we divide the alpha level by 2 to get the significance level for each tail. In this case, for each tail, the significance level would be 0.01 / 2 = 0.005.

To find the possible outcomes, we need to compare the p-values (or critical values) to the significance level. The p-value is the probability of obtaining a result as extreme as, or more extreme than, the observed data, assuming that the null hypothesis is true.

In this scenario, assuming a fair coin, the null hypothesis would be that the probability of obtaining a head or a tail is 0.5 for each flip. Based on this, we can calculate the p-value or critical value for each outcome.

Here are all the possible outcomes that would be interpreted as statistically significant:

1. If the number of heads is less than or equal to k, where k is the number such that the cumulative probability of getting k or fewer heads is less than or equal to 0.005.

2. If the number of heads is greater than or equal to n - k, where n is the total number of flips (20 in this case) and k is the number such that the cumulative probability of getting k or more heads is less than or equal to 0.005.

You can use a binomial probability distribution or a statistical software to calculate the cumulative probabilities for each outcome and determine the values of k. Using these calculations, you can evaluate each outcome to determine if it is statistically significant based on the alpha level of 0.01.