4. I rolled 36 dice with random.org's dice roller. I'm interested in seeing if the site's dice roller is fair, so I want to see if the data from the 36 dice rolls matches the theoretical distribution. Theoretically, we should get each number 6 times. The data I observed is in the table below. Use this data to run a goodness of fit test to test if the virtual die is fair. Face Observed Frequency Expected Frequency 1 2 3 4 5 6 6 3 5 4 13 5 6 6 6 6 6 6 (a) What are the null and alternative hypotheses? (b) This test uses a chi-square distribution. What are the degrees of freedom? Note: the data we were given was from 1950 - 1975, so we should be hesitant to make predictions about dates outside of that range (c) State the p-value and test statistic (if you use technology, include a screen shot or explain how you used it). (d) At a 5% significance level, do you reject or decline reject the null hypothesis? Briefly write a conclusion.