[2] (30 points) During early evening mountain goats come down to water in a Montana location at a mte of 5 per hour. lConsider each goat's arrival independent of the next with arrivals consistent with the rate of 5 per hour. Assume a Poisson model applies. [e] Someone challenged the Poisson model for goat arrival to water. |[lver 9D evenings during the 3-hr early evening block, the recorded number of evenings in which I] to ID goats were observed was only 5; 11 to 15 goats were observed 50 times; 16 to 20 goats were observed 2!} times; and greater than it] goats were observed 15 times. Assume the rate is 51m, as noted above, and observe goats in the 4 intervals. Find the probability for [1-10, 11-15, 16-20, and 20- under the null hypothesis. Then use the Chi-Square goodness of t test to test the Poisson model assumption. Use alpha = [1.05. [i] List the p-value for this test