For all examples, we will assume an alpha of 0.05.

1. You and a friend are planning to use a coin in order to decide who gets to go on a free vacation. The winner of a coin toss will win the trip. However, prior to the coin toss, you want to check to make sure the coin is fair. You therefore wish to use a Chi-Square Goodness of Fit test, along with a randomly flipping the coin 20 times, in order to make sure it does not significantly vary from the expected distribution. For this example, the expected frequency of a heads is 0.5, and the expected frequency of a tails is 0.5. Please calculate the Chi-Square by hand for the following data in the table below, keeping in mind that there are 20 samples, so adjust your expected frequency as necessary (10 points):

Occurrence of heads = 12

Occurrence of Tails = 8

Observed frequency of heads = 12/20 = 0.6

Observed frequency of tails = 8/20 = 0.4