50f7 4. (28 points) A student in an introductory statistics course investigated whether or not there is evidence that the proportion of milk chocolate M&M's that are green differs from the proportion of dark chocolate M&M's that are green. She purchased a bag of each variety, and her data are summarized in the following table. Green Not Green Total Milk Chocolate 8 33 41 Dark Chocolate 4 3 8 42 Total 12 71 83 (a) Dene the appropriate parameter(s) and state the hypotheses for testing if the proportion of green M&M's differs for milk chocolate and dark chocolate M&M's. (b) Determine the statistic for the test and compute its value for this data. (c) Use the randomization distribution on the right (based on 50 randomization samples) to estimate the p- value here. 10 I0 0.0.0 0.15 0.10 0.05 0. _ . 0.05 0.00 0.05 0.10 ((1) Using a = 0.05, are the results statistically signicant? Why? (6) Make a decision about the null hypothesis and give your conclusion in the context of the problem. (i) Which type of error, Type I or Type 11, could you have made in part (e)? Briey justify your